Metrics for Maksimov and Kolovsky, Equation (3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze356.0ms (3.4%)

Memory

-15.5MiB live, 423.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	6
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	7
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	8
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	9
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	10
46.9%	46.8%	53%	0.1%	0%	0%	0%	11
46.9%	46.8%	53%	0.1%	0%	0%	0%	12

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.6s (15.4%)

Memory

65.4MiB live, 2 425.7MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 895.0ms

ival-mult: 328.0ms (36.7% of total)

ival-cos: 196.0ms (21.9% of total)

ival-div: 153.0ms (17.1% of total)

ival-pow2: 94.0ms (10.5% of total)

ival-sqrt: 62.0ms (6.9% of total)

ival-add: 41.0ms (4.6% of total)

exact: 12.0ms (1.3% of total)

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

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

Bogosity

explain296.0ms (2.8%)

Memory

-1.5MiB live, 515.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
44	0	-	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))`
28	0	-	-	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))`
0	0	-	-	`K`
0	0	-	-	`(/.f64 K #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	115	(1.9769279153936617e-275 1.9454366718256406e+135 3.904145278203592e+169)	-	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
0	0	-	-	`(*.f64 #s(literal 2 binary64) J)`
0	0	-	-	`U`
0	0	-	-	`(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))`
0	0	-	-	`(/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))`
0	0	-	-	`(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))`
0	0	-	-	`J`
0	0	-	-	`(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`#s(literal -2 binary64)`
0	0	-	-	`(*.f64 #s(literal -2 binary64) J)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`	sensitivity	115	0
`sqrt.f64`	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))`	oflow-rescue	44	0
↳	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))`	overflow	28
↳	`(/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))`	overflow	28
↳	`(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))`	overflow	72
↳	`(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))`	overflow	72
`*.f64`	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`	*no**	28	0

Confusion

	Predicted +	Predicted -
+	72	0
-	85	99

Precision

0.4585987261146497

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	72	0	0
-	85	0	99

Precision?

0.4585987261146497

Recall?

1.0

Freqs

test

number	freq
0	99
1	127
2	30

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

99.0ms

512×

valid

Compiler

Compiled 251 to 55 computations (78.1% saved)

Precisions

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

ival-mult: 15.0ms (30.9% of total)

ival-div: 11.0ms (22.7% of total)

ival-cos: 11.0ms (22.7% of total)

ival-pow2: 5.0ms (10.3% of total)

ival-sqrt: 3.0ms (6.2% of total)

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

exact: 1.0ms (2.1% of total)

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

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

preprocess104.0ms (1%)

Memory

17.2MiB live, 121.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 014×	`neg-mul-1`
984×	`distribute-lft-neg-in`
852×	`lower-*.f32`
842×	`lower-*.f64`
842×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	228
1	182	216
2	603	216
3	2240	216
4	4090	216
5	6770	216
0	17	24
0	28	24
1	44	24
2	87	24
3	211	24
4	609	24
5	1121	24
6	1532	24
7	1595	24
8	1612	24
9	1623	24
10	1625	24
11	1625	24
12	1625	24
0	1625	24

Stop Event

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

Calls

Call 1

Inputs

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Outputs

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))))

Symmetry

(abs U)

(abs K)

(negabs J)

Compiler

Compiled 27 to 17 computations (37% saved)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.4%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Status

Accuracy

Program

▶

73.4%

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Compiler

Compiled 27 to 17 computations (37% saved)

simplify46.0ms (0.4%)

Memory

14.8MiB live, 51.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(cos.f64 (/.f64 K #s(literal 2 binary64)))
cost-diff	0	(*.f64 #s(literal -2 binary64) J)
cost-diff	0	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Rules

852×	`lower-*.f32`
842×	`lower-*.f64`
786×	`associate-*r/`
758×	`lower-/.f32`
754×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	110
0	28	110
1	44	110
2	87	110
3	211	110
4	609	110
5	1121	110
6	1532	110
7	1595	110
8	1612	110
9	1623	110
10	1625	110
11	1625	110
12	1625	110
0	1625	110

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/.f64 K #s(literal 2 binary64))
K
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))
(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))
#s(literal 1 binary64)
(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
U
(.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) J)

Outputs
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/.f64 K #s(literal 2 binary64))
K
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))
(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))
(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))
#s(literal 1 binary64)
(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))
(/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64))))
U
(.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) J)
(*.f64 J #s(literal 2 binary64))

localize76.0ms (0.7%)

Memory

5.4MiB live, 154.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.109375	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
accuracy	0.22722626953688405	(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
accuracy	6.626495792559561	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
accuracy	10.227344923497052	(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))

Samples

44.0ms

256×

valid

Compiler

Compiled 112 to 19 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 11.0ms (44.8% of total)

ival-cos: 5.0ms (20.4% of total)

ival-div: 3.0ms (12.2% of total)

ival-sqrt: 2.0ms (8.2% of total)

ival-pow2: 2.0ms (8.2% of total)

ival-add: 1.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.5%)

Memory

2.5MiB live, 117.0MiB allocated

Counts

6 → 156

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (patch (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 K #s(literal 2 binary64))) (patch (cos.f64 (/.f64 K #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* -1 U) (taylor 0 J) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U)) (taylor 0 J) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3)))))) (taylor 0 J) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3)))))))) (taylor 0 J) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))) (taylor -inf K) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf U) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor 0 J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf J) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (pow J 2))) (taylor 0 K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2)))) (taylor 0 K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2)))))) (taylor 0 K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))) (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))))) (taylor 0 K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (taylor -inf K) (#s(alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

39 calls:

Time	Variable		Point	Expression
9.0ms	J	@	inf	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
5.0ms	J	@	inf	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
4.0ms	K	@	0	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
4.0ms	K	@	inf	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
3.0ms	J	@	0	(* -2 J)

simplify357.0ms (3.4%)

Memory

-61.9MiB live, 614.6MiB allocated

Algorithm

1×	egg-herbie

Rules

19 354×	`lower-fma.f64`
19 354×	`lower-fma.f32`
6 716×	`lower-*.f64`
6 716×	`lower-*.f32`
4 982×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	3717
1	1153	3609
2	4514	3477
0	8499	3319

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 155

Calls

Call 1

Inputs
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* J (cos (* 1/2 K))))
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(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/128 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 4)))))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1/2 (/ U (* J (cos (* 1/2 K)))))
(* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -1 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 3)) (pow U 3))) (/ (cos (* 1/2 K)) U)))) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (pow K 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
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(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
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(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))) (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))

Outputs
(* -1 U)
(neg.f64 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(-.f64 (.f64 (.f64 J J) (fma.f64 #s(literal -2 binary64) (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal 2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (/.f64 (.f64 J J) (.f64 U (*.f64 U U))))))) U)
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(-.f64 (.f64 (.f64 J J) (fma.f64 (.f64 J J) (fma.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (.f64 U (.f64 U U))) (.f64 #s(literal -4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 6 binary64)) (/.f64 (.f64 J J) (pow.f64 U #s(literal 5 binary64)))))) (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U))) U)
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(.f64 J (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 #s(literal 1/2 binary64) K)))) (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(.f64 J (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 #s(literal 1/2 binary64) K)))) (fma.f64 #s(literal -1/512 binary64) (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 J #s(literal 6 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)))) (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)))) (.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
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(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))
(+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))
(.f64 (/.f64 (.f64 U U) (.f64 J J)) (fma.f64 #s(literal 1/16 binary64) (.f64 K K) #s(literal 1/4 binary64)))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))
(fma.f64 (.f64 K K) (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64))) (.f64 (/.f64 (.f64 U U) (.f64 J J)) (fma.f64 #s(literal 1/16 binary64) (.f64 K K) #s(literal 1/4 binary64))))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))) (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))))
(fma.f64 (/.f64 (.f64 U U) (.f64 J J)) (fma.f64 #s(literal 1/16 binary64) (.f64 K K) #s(literal 1/4 binary64)) (.f64 (.f64 K K) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 K K)) (fma.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal -17/2880 binary64)) (/.f64 (.f64 (.f64 U U) #s(literal -1/24 binary64)) (*.f64 J J))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 (.f64 U U) #s(literal 1/4 binary64)) (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))

rewrite262.0ms (2.5%)

Memory

19.4MiB live, 348.0MiB allocated

Rules

3 552×	`lower-*.f32`
3 542×	`lower-*.f64`
3 418×	`lower-fma.f64`
3 418×	`lower-fma.f32`
2 050×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
0	28	66
1	79	66
2	432	66
3	4364	66
0	8129	66

Stop Event

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

Counts

6 → 306

Calls

Call 1

Inputs
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))
(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))

Outputs
(neg.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))))
(neg.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 J #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 J #s(literal 2 binary64)) U)) #s(literal -4 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 6 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 J #s(literal 2 binary64)) U)) #s(literal -4 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))))))
(.f64 #s(literal -2 binary64) (.f64 J (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64))))))
(.f64 J (.f64 #s(literal -2 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64))))))
(.f64 #s(literal 2 binary64) (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (neg.f64 J)) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) (.f64 J (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64))))))
(.f64 (.f64 J #s(literal 2 binary64)) (.f64 (neg.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64))))
(.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))) (*.f64 #s(literal -2 binary64) J))
(.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))))
(.f64 (neg.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 (.f64 J #s(literal 2 binary64)) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))))
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(.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))) (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))))
(.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))) (/.f64 (/.f64 #s(literal -1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) U)))
(.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) U) U)
(.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal -1/2 binary64) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 (.f64 U (/.f64 U (.f64 J #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 (.f64 U #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 J U))))
(.f64 (.f64 U #s(literal 1/2 binary64)) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 U (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (*.f64 J #s(literal 2 binary64)) U)))
(.f64 (/.f64 U (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 J #s(literal 2 binary64))))
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(.f64 (pow.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 J #s(literal 2 binary64))))))
(.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))
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(.f64 (/.f64 (neg.f64 U) #s(literal 2 binary64)) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (neg.f64 J))))
(.f64 (/.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal -1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (*.f64 J #s(literal 2 binary64)) U)))
(.f64 (/.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) J)))
(.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (/.f64 U (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 J U))))
(.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 U (/.f64 U (.f64 J #s(literal 2 binary64)))))
(.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (.f64 J #s(literal 2 binary64))) (/.f64 U (/.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(.f64 (/.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 J U))))
(.f64 (/.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(.f64 (/.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) U)))
(.f64 (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 J U))))
(.f64 (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (/.f64 (*.f64 J #s(literal 2 binary64)) U)))
(.f64 (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (.f64 J #s(literal 2 binary64))) (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (/.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(.f64 (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (/.f64 (sqrt.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) U)))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) J) (/.f64 U (.f64 #s(literal 2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) J) (/.f64 (neg.f64 U) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 U (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 J U))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 (neg.f64 U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (neg.f64 J))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (/.f64 U (.f64 J #s(literal 2 binary64))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 J #s(literal 2 binary64))) (/.f64 U (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (*.f64 U #s(literal 1/2 binary64)))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 U J))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal -2 binary64)) (/.f64 (neg.f64 U) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 (neg.f64 U) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal -2 binary64)))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (neg.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 U (.f64 #s(literal -2 binary64) J)))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) J)) (/.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(.f64 (/.f64 (neg.f64 U) J) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 U (.f64 #s(literal 2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) J))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (neg.f64 U) J))
(.f64 (/.f64 (neg.f64 U) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64))))) U))
(.f64 (/.f64 (neg.f64 U) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) J))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 J #s(literal 2 binary64)))))
(.f64 (.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(.f64 (/.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))) (neg.f64 U))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 U)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (neg.f64 U))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (/.f64 U (.f64 J #s(literal 2 binary64))))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64)))))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 U)))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 U (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 J #s(literal 2 binary64))))))))

eval68.0ms (0.6%)

Memory: 5.7MiB live, 129.3MiB allocated
Compiler: Compiled 16 532 to 1 763 computations (89.3% saved)

prune68.0ms (0.6%)

Memory

-32.8MiB live, 127.8MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	470	9	479
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	471	9	480

Accuracy

100.0%

Counts

480 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
▶	8.5%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
	50.4%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
	52.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 #s(literal -2 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
	32.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
▶	8.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
▶	53.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
▶	27.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
▶	42.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Compiler

Compiled 466 to 286 computations (38.6% saved)

simplify179.0ms (1.7%)

Memory

16.1MiB live, 254.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 (/.f64 K #s(literal 2 binary64)))
cost-diff	0	(*.f64 #s(literal -2 binary64) J)
cost-diff	0	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
cost-diff	0	(fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))
cost-diff	0	(neg.f64 U)
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
cost-diff	768	(.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))))
cost-diff	0	(.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
cost-diff	0	(neg.f64 U)
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) K)
cost-diff	0	(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
cost-diff	0	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))

Rules

6 710×	`lower-*.f32`
6 676×	`lower-*.f64`
4 598×	`lower-fma.f32`
4 590×	`lower-fma.f64`
2 532×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	629
0	98	629
1	191	629
2	492	629
3	1763	629
4	5079	621
0	8888	619

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 #s(literal 1/2 binary64) K)
#s(literal 1/2 binary64)
K
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(neg.f64 U)
U
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
(.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))
#s(literal -2 binary64)
(fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))))
(fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))
(*.f64 K K)
K
#s(literal -1/8 binary64)
#s(literal 1 binary64)
(.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))
J
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))
#s(literal 1/4 binary64)
(/.f64 (.f64 U U) (.f64 J J))
(*.f64 U U)
U
(*.f64 J J)
(.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64)))))
(.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J)))
(.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))
#s(literal 1/32 binary64)
(/.f64 (*.f64 U U) J)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
(.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
(neg.f64 U)
U
(fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))
#s(literal -2 binary64)
(.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U)))
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 #s(literal 1/2 binary64) K)
#s(literal 1/2 binary64)
K
#s(literal 2 binary64)
(/.f64 (.f64 J J) (.f64 U U))
(*.f64 J J)
J
(*.f64 U U)
#s(literal -1 binary64)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/.f64 K #s(literal 2 binary64))
K
#s(literal 2 binary64)
#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(*.f64 U #s(literal -1/2 binary64))
U
#s(literal -1/2 binary64)
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 #s(literal 1/2 binary64) K)
#s(literal 1/2 binary64)

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) K)
(*.f64 K #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
K
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(neg.f64 U)
U
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (.f64 K K) (.f64 (/.f64 (.f64 U (.f64 U #s(literal 1/32 binary64))) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))))) (.f64 (sqrt.f64 (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))) (fma.f64 J (.f64 (.f64 K K) #s(literal -1/8 binary64)) J)))))
(.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))
(.f64 #s(literal -2 binary64) (fma.f64 (.f64 K K) (.f64 (/.f64 (.f64 U (.f64 U #s(literal 1/32 binary64))) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))))) (.f64 (sqrt.f64 (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))) (fma.f64 J (.f64 (.f64 K K) #s(literal -1/8 binary64)) J))))
#s(literal -2 binary64)
(fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))))
(fma.f64 (.f64 K K) (.f64 (/.f64 (.f64 U (.f64 U #s(literal 1/32 binary64))) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))))) (.f64 (sqrt.f64 (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))) (fma.f64 J (.f64 (*.f64 K K) #s(literal -1/8 binary64)) J)))
(fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))
(fma.f64 K (*.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64))
(*.f64 K K)
K
#s(literal -1/8 binary64)
#s(literal 1 binary64)
(.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))
(.f64 J (sqrt.f64 (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) #s(literal 1 binary64))))
J
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))
(fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))
#s(literal 1/4 binary64)
(/.f64 (.f64 U U) (.f64 J J))
(.f64 U (/.f64 U (.f64 J J)))
(*.f64 U U)
U
(*.f64 J J)
(.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64)))))
(.f64 (.f64 K K) (.f64 (/.f64 (.f64 U (.f64 U #s(literal 1/32 binary64))) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) #s(literal 1 binary64))))))
(.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J)))
(.f64 (.f64 K K) (/.f64 (.f64 U (.f64 U #s(literal 1/32 binary64))) J))
(.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))
(/.f64 (.f64 U (.f64 U #s(literal 1/32 binary64))) J)
#s(literal 1/32 binary64)
(/.f64 (*.f64 U U) J)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U U) (/.f64 #s(literal 1/4 binary64) (.f64 J J)) #s(literal 1 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 #s(literal 2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U)) U))
(.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U)) U)
(neg.f64 U)
U
(fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))
(fma.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (.f64 U U)) #s(literal -1 binary64))
#s(literal -2 binary64)
(.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U)))
(.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U)))
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
(pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) K)
(*.f64 K #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
K
#s(literal 2 binary64)
(/.f64 (.f64 J J) (.f64 U U))
(*.f64 J J)
J
(*.f64 U U)
#s(literal -1 binary64)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/.f64 K #s(literal 2 binary64))
K
#s(literal 2 binary64)
#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(*.f64 U #s(literal -1/2 binary64))
U
#s(literal -1/2 binary64)
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) K)
(*.f64 K #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

localize243.0ms (2.3%)

Memory

9.0MiB live, 248.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.109375	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
accuracy	0.109375	(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
accuracy	6.626495792559561	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
accuracy	57.12312269027569	#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
accuracy	0.22265625	(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
accuracy	3.9820436945371056	(.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
accuracy	18.55544729113708	(/.f64 (.f64 J J) (.f64 U U))
accuracy	57.292934617318856	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
accuracy	14.708935416362618	(fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))))
accuracy	16.037276015337827	(.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J)))
accuracy	18.627708270647492	(/.f64 (.f64 U U) (.f64 J J))
accuracy	24.55955300208531	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
accuracy	0	(neg.f64 U)
accuracy	37.08023080568944	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
accuracy	0	(*.f64 #s(literal -2 binary64) J)
accuracy	0	(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
accuracy	0.109375	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
accuracy	29.776795627025457	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))

Samples

98.0ms	204×	0	valid
41.0ms	52×	1	valid

Compiler

Compiled 545 to 57 computations (89.5% saved)

Precisions

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

ival-mult: 46.0ms (48.5% of total)

ival-div: 13.0ms (13.7% of total)

ival-cos: 13.0ms (13.7% of total)

ival-sqrt: 6.0ms (6.3% of total)

ival-add: 6.0ms (6.3% of total)

ival-pow2: 5.0ms (5.3% of total)

adjust: 3.0ms (3.2% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

series120.0ms (1.1%)

Memory

-6.9MiB live, 68.4MiB allocated

Counts

23 → 600

Calls

Call 1

Inputs
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J)) (patch (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (patch (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) K) (patch (.f64 #s(literal 1/2 binary64) K) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) #<representation binary64>) () ())
#s(alt (neg.f64 U) (patch (neg.f64 U) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))) (patch (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))) (patch (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))) (patch (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64)))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64)) (patch (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (patch (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 K #s(literal 2 binary64))) (patch (cos.f64 (/.f64 K #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 U U) (.f64 J J)) (patch (/.f64 (.f64 U U) (.f64 J J)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (patch (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 J J) (.f64 U U)) (patch (/.f64 (.f64 J J) (.f64 U U)) #<representation binary64>) () ())
#s(alt (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (patch (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))) (patch #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))) #<representation binary64>) () ())
#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())

Outputs
#s(alt (* -1 U) (taylor 0 J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U)) (taylor 0 J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3)))))) (taylor 0 J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3)))))))) (taylor 0 J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* J (cos (* 1/2 K)))) (taylor inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))))) (taylor inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))) (taylor inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
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#s(alt (* J (cos (* 1/2 K))) (taylor 0 J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor 0 J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt J (taylor 0 K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (+ J (* -1/8 (* J (pow K 2)))) (taylor 0 K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (+ J (* (pow K 2) (+ (* -1/8 J) (* 1/384 (* J (pow K 2)))))) (taylor 0 K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (+ J (* (pow K 2) (+ (* -1/8 J) (* (pow K 2) (+ (* -1/46080 (* J (pow K 2))) (* 1/384 J)))))) (taylor 0 K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf K) (#s(alt (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (patch (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #<representation binary64>) () ())) ())

Calls

150 calls:

Time	Variable		Point	Expression
23.0ms	U	@	0	(* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1))))))
8.0ms	U	@	inf	(* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1))))))
2.0ms	J	@	inf	(* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1))))))
2.0ms	K	@	0	(* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1))))))
2.0ms	J	@	0	(* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1))))))

simplify473.0ms (4.5%)

Memory

25.3MiB live, 617.0MiB allocated

Algorithm

1×	egg-herbie

Rules

15 380×	`lower-fma.f64`
15 380×	`lower-fma.f32`
9 384×	`lower-*.f64`
9 384×	`lower-*.f32`
6 186×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	750	16214
1	2523	15795
0	9142	14826

Stop Event

1×	iter limit
1×	node limit

Counts

600 → 591

Calls

Call 1

Inputs
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* 2 (* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))))
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(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))))
(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (+ (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))) (* -2 (/ (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (pow J 2))) (* 2 (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))))) (pow U 6))))))))
(* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))
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(+ (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(+ (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))
(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
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(- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)
-1
(- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)
(- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)
(- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(/ (pow U 2) (pow J 2))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
(/ (pow J 2) (pow U 2))
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
(pow (cos (* 1/2 K)) 2)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/128 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 4)))))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1/2 (/ U (* J (cos (* 1/2 K)))))
(* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -1 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 3)) (pow U 3))) (/ (cos (* 1/2 K)) U)))) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (pow K 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
J
(+ J (* -1/8 (* J (pow K 2))))
(+ J (* (pow K 2) (+ (* -1/8 J) (* 1/384 (* J (pow K 2))))))
(+ J (* (pow K 2) (+ (* -1/8 J) (* (pow K 2) (+ (* -1/46080 (* J (pow K 2))) (* 1/384 J))))))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))

Outputs
(* -1 U)
(neg.f64 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) (neg.f64 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(fma.f64 (.f64 J J) (fma.f64 #s(literal -2 binary64) (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (/.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 J J)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))) (.f64 U (.f64 U U)))) (neg.f64 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
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U
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(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))
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(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))))))
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(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (+ (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))) (* -2 (/ (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (pow J 2))) (* 2 (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))))) (pow U 6)))))))
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(* 2 (* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))))
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(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))))))
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(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))))
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(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (+ (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))) (* -2 (/ (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (pow J 2))) (* 2 (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))))) (pow U 6))))))))
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(* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))
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(+ (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
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(+ (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
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(+ (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
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(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))
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(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
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(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
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(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(.f64 (.f64 K K) (fma.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (/.f64 J (.f64 K K)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64)) (.f64 J (.f64 #s(literal -1/8 binary64) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))))))
(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))
(.f64 (.f64 K K) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64)) (.f64 J (.f64 #s(literal -1/8 binary64) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))
(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
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(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
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(* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
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(+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))
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(+ (* 1/16 (* (pow K 2) U)) (+ (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))) (* (pow J 2) (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U)))))
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(+ (* 1/16 (* (pow K 2) U)) (+ (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))) (* (pow J 2) (+ (* -1/4 (/ (pow K 2) U)) (+ (* (pow J 2) (+ (* -1 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 3))) (* 3/8 (/ (pow K 2) (pow U 3))))) (/ 1 U))))))
(fma.f64 U (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 J J) (fma.f64 (.f64 J J) (fma.f64 #s(literal 3/8 binary64) (/.f64 (.f64 K K) (.f64 U (.f64 U U))) (/.f64 (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)) (.f64 U (.f64 U U)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 K K) U) (/.f64 #s(literal 1 binary64) U)))))
(+ (* 1/16 (* (pow K 2) U)) (+ (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))) (* (pow J 2) (+ (* -1/4 (/ (pow K 2) U)) (+ (* (pow J 2) (+ (* -1 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 3))) (+ (* 3/8 (/ (pow K 2) (pow U 3))) (* (pow J 2) (+ (* -5/4 (/ (pow K 2) (pow U 5))) (* 2 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 5)))))))) (/ 1 U))))))
(fma.f64 (.f64 J J) (fma.f64 (.f64 J J) (fma.f64 (.f64 J J) (fma.f64 #s(literal -5/4 binary64) (/.f64 (.f64 K K) (pow.f64 U #s(literal 5 binary64))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 K K) #s(literal 2 binary64)) (pow.f64 U #s(literal 5 binary64)))) (fma.f64 #s(literal 3/8 binary64) (/.f64 (.f64 K K) (.f64 U (.f64 U U))) (/.f64 (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)) (.f64 U (.f64 U U))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 K K) U) (/.f64 #s(literal 1 binary64) U))) (.f64 U (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (*.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64)))))
(* J (+ 1 (* -1/8 (pow K 2))))
(fma.f64 J (.f64 (.f64 K K) #s(literal -1/8 binary64)) J)
(* J (+ 1 (+ (* -1/8 (pow K 2)) (+ (* 1/32 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/8 (/ (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))) (pow J 2)))))))
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(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
J
(+ J (* -1/8 (* J (pow K 2))))
(fma.f64 J (.f64 (.f64 K K) #s(literal -1/8 binary64)) J)
(+ J (* (pow K 2) (+ (* -1/8 J) (* 1/384 (* J (pow K 2))))))
(fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/384 binary64)) (.f64 J #s(literal -1/8 binary64)))) J)
(+ J (* (pow K 2) (+ (* -1/8 J) (* (pow K 2) (+ (* -1/46080 (* J (pow K 2))) (* 1/384 J))))))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J (.f64 (.f64 K K) #s(literal -1/46080 binary64)) (.f64 J #s(literal 1/384 binary64))) (.f64 J #s(literal -1/8 binary64))) J)
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))

rewrite426.0ms (4%)

Memory

-16.7MiB live, 582.5MiB allocated

Rules

4 548×	`lower-/.f32`
4 536×	`lower-/.f64`
4 464×	`lower-*.f32`
4 430×	`lower-*.f64`
4 292×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	442
0	98	442
1	317	414
2	1922	408
0	8530	408

Stop Event

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

Counts

23 → 523

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 #s(literal 1/2 binary64) K)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(neg.f64 U)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
(.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))))
(fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (*.f64 J J)) #s(literal 1 binary64))))))
(fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))
(.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
(fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/.f64 (.f64 U U) (.f64 J J))
(.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J)))
(/.f64 (.f64 J J) (.f64 U U))
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(neg.f64 (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64))))))))
(.f64 #s(literal -2 binary64) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 J (.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (neg.f64 J)))
(.f64 (.f64 J #s(literal 2 binary64)) (neg.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (neg.f64 (*.f64 J #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(.f64 (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)
(.f64 (neg.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (*.f64 J #s(literal 2 binary64)))
(.f64 (neg.f64 (.f64 J #s(literal 2 binary64))) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos.f64 (/.f64 K #s(literal -2 binary64)))
(pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (sqrt.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (sqrt.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) K)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 K #s(literal -2 binary64)))
(neg.f64 (/.f64 K #s(literal -2 binary64)))
(/.f64 K #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) K))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) K))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) K)))
(/.f64 (neg.f64 K) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 K)) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 K))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) K) #s(literal -1 binary64))
(*.f64 K #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 K #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) K)
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) K) #s(literal -1 binary64)))
(*.f64 (neg.f64 K) #s(literal -1/2 binary64))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(+.f64 #s(literal 0 binary64) (neg.f64 U))
(-.f64 #s(literal 0 binary64) U)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) U)) (/.f64 (*.f64 U U) (+.f64 #s(literal 0 binary64) U)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) (/.f64 (.f64 U (.f64 U U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))))
(neg.f64 U)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) U) (*.f64 U (neg.f64 U))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U))) (-.f64 #s(literal 0 binary64) (.f64 U (*.f64 U U)))))
(/.f64 (*.f64 U (neg.f64 U)) (+.f64 #s(literal 0 binary64) U))
(/.f64 (neg.f64 (*.f64 U (neg.f64 U))) (neg.f64 (+.f64 #s(literal 0 binary64) U)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 U) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 U U) (.f64 #s(literal 0 binary64) (neg.f64 U)))))
(*.f64 U #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) U)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (.f64 K K) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))))) (.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))) (.f64 J (fma.f64 K (*.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))))))
(+.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (*.f64 J J)) #s(literal 1 binary64)))))))
(+.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))) (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (*.f64 J J)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))))) (-.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))))) (/.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))) (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))))))) (-.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))))))
(fma.f64 #s(literal -2 binary64) (.f64 K (.f64 K (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))))))) (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))
(fma.f64 #s(literal -2 binary64) (.f64 (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))))
(fma.f64 (.f64 K K) (.f64 (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64))))) #s(literal -2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))
(fma.f64 (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64)) (.f64 (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))) #s(literal -2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 K K)) (/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) U) (/.f64 U (.f64 J J)) #s(literal 1 binary64)))))))
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(/.f64 #s(literal 1 binary64) (/.f64 J (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (.f64 U U))))
(/.f64 #s(literal 1 binary64) (/.f64 J (.f64 (.f64 K K) (.f64 (.f64 U U) #s(literal 1/32 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 J (.f64 U U)) (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 J) (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (.f64 U (neg.f64 U)))))
(/.f64 #s(literal 1 binary64) (/.f64 J (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) (.f64 K K))))
(/.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (/.f64 J (*.f64 U U)))
(/.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (.f64 U U)) J)
(/.f64 (.f64 (.f64 K K) (.f64 (.f64 U U) #s(literal 1/32 binary64))) J)
(/.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (/.f64 J (.f64 U U)))
(/.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (.f64 U (neg.f64 U))) (neg.f64 J))
(/.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) (.f64 K K)) J)
(/.f64 (neg.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64))) (neg.f64 (/.f64 J (*.f64 U U))))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (.f64 U U))) (neg.f64 J))
(/.f64 (neg.f64 (.f64 (.f64 K K) (.f64 (.f64 U U) #s(literal 1/32 binary64)))) (neg.f64 J))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 J (.f64 U U))))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (.f64 U (neg.f64 U)))) (neg.f64 (neg.f64 J)))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) (.f64 K K))) (neg.f64 J))
(.f64 K (.f64 K (/.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) J)))
(.f64 (.f64 K K) (/.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) J))
(.f64 #s(literal 1/32 binary64) (.f64 (/.f64 (.f64 U U) J) (.f64 K K)))
(.f64 (/.f64 (.f64 U U) J) (.f64 (.f64 K K) #s(literal 1/32 binary64)))
(.f64 (/.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) J) (.f64 K K))
(.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (/.f64 (.f64 U U) J))
(.f64 (.f64 K (/.f64 (.f64 (.f64 U U) #s(literal 1/32 binary64)) J)) K)
(.f64 (.f64 (.f64 K K) (/.f64 (.f64 U U) J)) #s(literal 1/32 binary64))
(.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) U) (/.f64 U J))
(.f64 (.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) (*.f64 U U)) (/.f64 #s(literal 1 binary64) J))
(.f64 (/.f64 K J) (/.f64 (.f64 K #s(literal 1/32 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 U U))))
(.f64 (/.f64 (.f64 K K) J) (/.f64 #s(literal 1/32 binary64) (/.f64 #s(literal 1 binary64) (*.f64 U U))))
(.f64 (/.f64 #s(literal 1/32 binary64) J) (/.f64 (.f64 K K) (/.f64 #s(literal 1 binary64) (*.f64 U U))))
(.f64 (/.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) J) (/.f64 (.f64 U U) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (.f64 K K) #s(literal 1/32 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 U (neg.f64 U)) J))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 U U) (*.f64 J J))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal 2 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 J) #s(literal 2 binary64)) (.f64 (log.f64 U) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 U (neg.f64 U))) (/.f64 (.f64 J J) (*.f64 U (neg.f64 U))))
(neg.f64 (/.f64 (.f64 J J) (.f64 U (neg.f64 U))))
(neg.f64 (/.f64 (neg.f64 (.f64 J J)) (.f64 U U)))
(/.f64 J (/.f64 (*.f64 U U) J))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 J J)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (.f64 U U) (.f64 J J)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J J)) (/.f64 #s(literal 1 binary64) U)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (*.f64 J J) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (/.f64 J U) J)))
(/.f64 (.f64 J J) (.f64 U U))
(/.f64 (/.f64 (.f64 J J) (.f64 U U)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 U U) (.f64 J J))))
(/.f64 (neg.f64 (.f64 J J)) (.f64 U (neg.f64 U)))
(/.f64 (neg.f64 J) (neg.f64 (/.f64 (*.f64 U U) J)))
(/.f64 (/.f64 J U) (/.f64 U J))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 U U)) (/.f64 #s(literal 1 binary64) (.f64 J J)))
(/.f64 (/.f64 (*.f64 J J) U) U)
(/.f64 (neg.f64 (neg.f64 (.f64 J J))) (neg.f64 (.f64 U (neg.f64 U))))
(/.f64 (neg.f64 (/.f64 (*.f64 J J) U)) (neg.f64 U))
(/.f64 (neg.f64 (/.f64 (.f64 J J) (.f64 U U))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 U (*.f64 J J)))
(/.f64 (.f64 (.f64 J J) #s(literal 1 binary64)) (*.f64 U U))
(/.f64 (*.f64 (/.f64 J U) J) U)
(/.f64 (neg.f64 (/.f64 J U)) (neg.f64 (/.f64 U J)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 U U))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 J J))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (.f64 J J)))) (neg.f64 (neg.f64 (.f64 U (neg.f64 U)))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) U)) (neg.f64 (/.f64 U (*.f64 J J))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (*.f64 J J) U))) (neg.f64 (neg.f64 U)))
(/.f64 (neg.f64 (.f64 (.f64 J J) #s(literal 1 binary64))) (*.f64 U (neg.f64 U)))
(/.f64 (neg.f64 (*.f64 (/.f64 J U) J)) (neg.f64 U))
(pow.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 J J) (.f64 U U)) #s(literal 1 binary64))
(pow.f64 (/.f64 U J) #s(literal -2 binary64))
(pow.f64 (/.f64 J U) #s(literal 2 binary64))
(.f64 J (/.f64 J (.f64 U U)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 J J) (*.f64 U U)))
(.f64 (.f64 J J) (/.f64 #s(literal 1 binary64) (*.f64 U U)))
(.f64 (.f64 J J) (pow.f64 (/.f64 #s(literal 1 binary64) U) #s(literal 2 binary64)))
(.f64 (neg.f64 (.f64 J J)) (/.f64 #s(literal 1 binary64) (*.f64 U (neg.f64 U))))
(*.f64 (/.f64 J U) (/.f64 J U))
(*.f64 (/.f64 J U) (/.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 #s(literal 1 binary64) J)))
(.f64 (/.f64 J (.f64 U U)) J)
(.f64 (/.f64 J (.f64 U U)) (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 U U)) (*.f64 J J))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 U U)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 J J)) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 J J) U) (/.f64 #s(literal 1 binary64) U))
(.f64 (/.f64 J #s(literal 1 binary64)) (/.f64 J (.f64 U U)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 U (neg.f64 U))) (neg.f64 (*.f64 J J)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 U (neg.f64 U))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 J J))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (.f64 J J) U))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 J J)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 U U)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 J J))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 U (neg.f64 U))))
(*.f64 (/.f64 J (neg.f64 U)) (/.f64 (neg.f64 J) U))
(.f64 (/.f64 J #s(literal -1 binary64)) (/.f64 (neg.f64 J) (.f64 U U)))
(.f64 (/.f64 #s(literal -1 binary64) U) (/.f64 (.f64 J J) (neg.f64 U)))
(*.f64 (/.f64 (neg.f64 J) U) (/.f64 J (neg.f64 U)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64))))))
(exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))))))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))) (cos.f64 (-.f64 (.f64 K #s(literal 1/2 binary64)) (.f64 K #s(literal 1/2 binary64)))))))
(/.f64 (+.f64 (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))) (cos.f64 (-.f64 (.f64 K #s(literal 1/2 binary64)) (.f64 K #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))) (cos.f64 (-.f64 (.f64 K #s(literal 1/2 binary64)) (.f64 K #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))))) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))))))
(pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64))))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)

eval432.0ms (4.1%)

Memory: 15.1MiB live, 451.4MiB allocated
Compiler: Compiled 54 251 to 3 130 computations (94.2% saved)

prune335.0ms (3.2%)

Memory

16.0MiB live, 292.4MiB allocated

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	1 319	12	1 331
Fresh	2	2	4
Picked	3	2	5
Done	0	0	0
Total	1 324	16	1 340

Accuracy

100.0%

Counts

1 340 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
▶	42.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
	42.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (sqrt.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) J)))
	32.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
	42.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (exp.f64 (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
✓	53.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
✓	42.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
▶	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
▶	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
	29.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))))
▶	31.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
	2.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 U #s(literal 2 binary64)))))
▶	30.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))

Compiler

Compiled 582 to 369 computations (36.6% saved)

simplify374.0ms (3.5%)

Memory

-7.1MiB live, 317.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
cost-diff	320	(fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64)))
cost-diff	320	(fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (*.f64 J #s(literal 1/4 binary64)))
cost-diff	320	(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
cost-diff	320	(fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (*.f64 J #s(literal 1/4 binary64)))
cost-diff	320	(fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))
cost-diff	0	#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
cost-diff	192	(.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))
cost-diff	1408	(fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))
cost-diff	0	(*.f64 #s(literal -2 binary64) J)
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
cost-diff	128	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64))))))
cost-diff	640	(.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))
cost-diff	5824	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))

Rules

17 114×	`lower-fma.f32`
17 102×	`lower-fma.f64`
5 008×	`lower-*.f32`
4 984×	`lower-*.f64`
3 062×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	663
0	109	686
1	233	634
2	639	579
3	1728	572
4	3096	569
5	6041	569
6	7471	569
0	8247	537

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64))))))
#s(literal 1/2 binary64)
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))
(cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))
#s(literal 2 binary64)
(*.f64 K #s(literal 1/2 binary64))
K
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))
(.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))
U
(fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))
K
(*.f64 K #s(literal -1/8 binary64))
#s(literal -1/8 binary64)
(fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))
(*.f64 K K)
#s(literal 1/8 binary64)
#s(literal -1 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))
K
(.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64))))
(fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (*.f64 J #s(literal 1/4 binary64)))
(.f64 J (.f64 K K))
J
(*.f64 K K)
#s(literal -1/192 binary64)
(*.f64 J #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J)))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))
(*.f64 K K)
K
(fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64)))
J
#s(literal -1/192 binary64)
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(.f64 J (.f64 K K))
#s(literal 1/23040 binary64)
(*.f64 J #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (cos.f64 K))
(cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))))
(cos.f64 K)
(.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))
K
#s(literal 2 binary64)
(*.f64 K #s(literal 1/2 binary64))
K
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (neg.f64 U)))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (neg.f64 U))
(.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))
(neg.f64 U)
U
(fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))
#s(literal -1 binary64)
K
(*.f64 K #s(literal -1/8 binary64))
#s(literal -1/8 binary64)
(fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))
(fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal -1 binary64))
(*.f64 K K)
#s(literal 1/8 binary64)
#s(literal -1 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))
(fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))
(.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
K
(.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64))))
(.f64 (.f64 J K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (*.f64 J #s(literal 1/4 binary64)))
(.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))
(.f64 J (.f64 K K))
J
(*.f64 K K)
#s(literal -1/192 binary64)
(*.f64 J #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))
(.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
(*.f64 K K)
K
(fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (*.f64 J #s(literal 1/4 binary64)))
(.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))
(fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64)))
(.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)))
J
#s(literal -1/192 binary64)
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(.f64 J (.f64 K K))
#s(literal 1/23040 binary64)
(*.f64 J #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)

localize403.0ms (3.8%)

Memory

-29.6MiB live, 324.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.171875	(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
accuracy	6.9613821056934535	(.f64 J (.f64 K K))
accuracy	28.273100477537174	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J)))
accuracy	29.776795627025457	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
accuracy	0.11328125	(fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (*.f64 J #s(literal 1/4 binary64)))
accuracy	6.9613821056934535	(.f64 J (.f64 K K))
accuracy	28.13838218558543	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J)))
accuracy	29.776795627025457	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
accuracy	0.00390625	(fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))
accuracy	24.55955300208531	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
accuracy	27.740601133667884	(fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))
accuracy	37.85262947177798	#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))
accuracy	0	(*.f64 #s(literal -2 binary64) J)
accuracy	25.469960700265293	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))
accuracy	29.776795627025457	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
accuracy	0.0703125	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))
accuracy	0.109375	(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
accuracy	0.45387436983699375	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64))))))
accuracy	36.82741060073028	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))

Samples

125.0ms	113×	1	valid
109.0ms	143×	0	valid

Compiler

Compiled 462 to 76 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 201.0ms

ival-mult: 105.0ms (52.3% of total)

ival-cos: 27.0ms (13.4% of total)

ival-add: 18.0ms (9% of total)

ival-div: 16.0ms (8% of total)

adjust: 11.0ms (5.5% of total)

ival-sqrt: 9.0ms (4.5% of total)

const: 9.0ms (4.5% of total)

ival-pow2: 3.0ms (1.5% of total)

exact: 1.0ms (0.5% of total)

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

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

series119.0ms (1.1%)

Memory

26.2MiB live, 101.0MiB allocated

Counts

24 → 576

Calls

Call 1

Inputs
#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (patch (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J)) (patch #s(approx ( (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())
#s(alt (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (patch (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))) (patch (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))) (patch #s(approx ( -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)) (patch (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64))) (patch (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J)))) #<representation binary64>) () ())
#s(alt #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J)) (patch (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (patch (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (patch (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J)))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J)))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (.f64 #s(literal -2 binary64) J)) (patch (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)) (patch (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 J (.f64 K K)) (patch (.f64 J (.f64 K K)) #<representation binary64>) () ())
#s(alt #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/8 (pow K 2))) (taylor 0 K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8))) (taylor 0 K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8))) (taylor 0 K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor -inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor -inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor -inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* 1/2 (cos K)))) (taylor -inf K) (#s(alt (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt K (taylor 0 K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor 0 K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor 0 K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor 0 K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor inf K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor inf K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor inf K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor inf K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor -inf K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt K (taylor -inf K) (#s(alt (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) (patch (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 1/23040 (* J (pow K 2))) (taylor inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor -inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor -inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor -inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/23040 (* J (pow K 2))) (taylor -inf K) (#s(alt (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) (patch (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64)) #<representation binary64>) () ())) ())

Calls

144 calls:

Time	Variable		Point	Expression
30.0ms	J	@	inf	(* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J))
3.0ms	J	@	-inf	(+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J))
2.0ms	J	@	0	(* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J))
1.0ms	J	@	inf	(+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J))
1.0ms	J	@	inf	(+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J))

simplify406.0ms (3.8%)

Memory

1.8MiB live, 505.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 464×	`lower-fma.f64`
11 464×	`lower-fma.f32`
7 910×	`lower-*.f64`
7 910×	`lower-*.f32`
3 884×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	539	13140
1	1813	12755
2	7100	12744
0	8119	11893

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 559

Calls

Call 1

Inputs
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
K
K
K
K
K
K
K
K
K
K
K
K
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/8 (pow K 2))) 1))
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
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(* -2 (* J (cos (* 1/2 K))))
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(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
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(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
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U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
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(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2)))))))
(+ (* -2 (* (pow J 2) (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U)))) (* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))))
(+ (* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))) (* (pow J 2) (+ (* -2 (* (pow J 2) (+ (* -1 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 3))) (* 3/8 (/ (pow K 2) (pow U 3)))))) (* -2 (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U))))))
(+ (* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))) (* (pow J 2) (+ (* -2 (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U))) (* (pow J 2) (+ (* -2 (* (pow J 2) (+ (* -5/4 (/ (pow K 2) (pow U 5))) (* 2 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 5)))))) (* -2 (+ (* -1 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 3))) (* 3/8 (/ (pow K 2) (pow U 3))))))))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* J (+ (* -2 (+ 1 (* -1/8 (pow K 2)))) (* -2 (/ (+ (* 1/32 (* (pow K 2) (pow U 2))) (* 1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))))) (pow J 2)))))
(* J (+ (* -2 (+ 1 (* -1/8 (pow K 2)))) (+ (* -2 (/ (+ (* -1/128 (* (pow U 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/256 (* (pow K 2) (pow U 4)))) (pow J 4))) (* -2 (/ (+ (* 1/32 (* (pow K 2) (pow U 2))) (* 1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))))) (pow J 2))))))
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(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))
(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))))))
(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (+ (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))) (* -2 (/ (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (pow J 2))) (* 2 (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))))) (pow U 6)))))))
(* 2 (* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))))
(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))))))
(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))))
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(* -2 J)
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(* -1/192 (* J (pow K 4)))
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(* (pow K 4) (+ (* -2 (/ J (pow K 4))) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))))
(* (pow K 4) (+ (* -2 (/ J (pow K 4))) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))))
(* -1/192 (* J (pow K 4)))
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(* (pow K 4) (+ (* -2 (/ J (pow K 4))) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))))
(* (pow K 4) (+ (* -2 (/ J (pow K 4))) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
(* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2))
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(* -1 (* J (+ 2 (* (pow K 2) (- (* 1/192 (pow K 2)) 1/4)))))
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(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
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U
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U
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-1
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(* (pow K 2) (- 1/8 (/ 1 (pow K 2))))
(* (pow K 2) (- 1/8 (/ 1 (pow K 2))))
(* (pow K 2) (- 1/8 (/ 1 (pow K 2))))
(* 1/8 (pow K 2))
(* (pow K 2) (- 1/8 (/ 1 (pow K 2))))
(* (pow K 2) (- 1/8 (/ 1 (pow K 2))))
(* (pow K 2) (- 1/8 (/ 1 (pow K 2))))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* J (pow K 2))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 K K) #s(literal 1 binary64))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (*.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
K
K
K
K
K
K
K
K
K
K
K
K
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow K 2)))
(fma.f64 K (*.f64 K #s(literal -1/4 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (*.f64 K K) #s(literal -1/1440 binary64) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos K)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(* -1 U)
(neg.f64 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))) U) (neg.f64 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(-.f64 (.f64 (.f64 J J) (fma.f64 #s(literal 2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (/.f64 (.f64 J J) (.f64 U (.f64 U U)))) (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))) U))) U)
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(fma.f64 (.f64 J J) (fma.f64 (.f64 J J) (fma.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 U (.f64 U U))) (.f64 #s(literal -4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (/.f64 (.f64 J J) (pow.f64 U #s(literal 5 binary64)))))) (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))) U)) (neg.f64 U))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(.f64 J (fma.f64 #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/512 binary64) (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 J #s(literal 6 binary64)) (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64))))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(.f64 J (neg.f64 (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64))))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(neg.f64 (.f64 J (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 J #s(literal 6 binary64)) (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64)))) #s(literal 1/512 binary64) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (/.f64 (.f64 #s(literal -1/64 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(fma.f64 (.f64 K K) (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 U U) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (.f64 #s(literal 1/4 binary64) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(fma.f64 (.f64 K K) (fma.f64 (fma.f64 #s(literal 1/384 binary64) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (fma.f64 (.f64 J (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (/.f64 (.f64 U U) J) #s(literal -1/256 binary64))))) (.f64 #s(literal -2 binary64) (.f64 K K)) (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 U U) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (.f64 #s(literal 1/4 binary64) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (.f64 #s(literal -2 binary64) (fma.f64 K (.f64 K (fma.f64 #s(literal -1/46080 binary64) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) J) (fma.f64 #s(literal -1/4 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 13/2880 binary64) (.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal -1/96 binary64))) (.f64 (.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (/.f64 (.f64 U U) (.f64 (.f64 J J) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) #s(literal -1/32 binary64))) (.f64 #s(literal 1/12288 binary64) (/.f64 (.f64 U U) J))) (.f64 (.f64 J (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) #s(literal -1/16 binary64)))))) (fma.f64 #s(literal 1/384 binary64) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (fma.f64 (.f64 J (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (.f64 (.f64 U U) (.f64 U U))) (.f64 (.f64 (.f64 J J) (.f64 J J)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (/.f64 (.f64 U U) J) #s(literal -1/256 binary64))))))) (fma.f64 #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 U U) J) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (.f64 #s(literal 1/4 binary64) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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U
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(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
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U
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(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
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(* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
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(* J (+ (* -2 (+ 1 (* -1/8 (pow K 2)))) (+ (* -2 (/ (+ (* -1/128 (* (pow U 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/256 (* (pow K 2) (pow U 4)))) (pow J 4))) (* -2 (/ (+ (* 1/32 (* (pow K 2) (pow U 2))) (* 1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))))) (pow J 2))))))
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(.f64 (.f64 (*.f64 K K) J) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 (*.f64 K K) J) #s(literal 1/23040 binary64))

rewrite287.0ms (2.7%)

Memory

-12.1MiB live, 436.5MiB allocated

Rules

5 204×	`lower-*.f32`
5 180×	`lower-*.f64`
5 036×	`lower-fma.f32`
5 022×	`lower-fma.f64`
2 610×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	579
0	109	576
1	437	521
2	3269	515
0	8136	494

Stop Event

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

Counts

24 → 335

Calls

Call 1

Inputs
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))
(.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1/2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))
(*.f64 #s(literal -2 binary64) J)
(fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))
(.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))))
(fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (*.f64 J #s(literal 1/4 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
(fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))
(.f64 J (.f64 K K))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)))) #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))) #s(literal 1/4 binary64))))
(fabs.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64)))))))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64)))))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (fabs.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) K))))
(/.f64 (sqrt.f64 (+.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64)))))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))) #s(literal 1/4 binary64))) (sqrt.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
(pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)))))
(.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))))))
(.f64 (pow.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (sqrt.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))
(/.f64 (*.f64 #s(literal 2 binary64) K) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 K)) #s(literal -2 binary64))
(/.f64 (*.f64 (neg.f64 K) #s(literal 2 binary64)) #s(literal -2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) K))
(.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) K))
(*.f64 K #s(literal 1 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) K) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) K)
(.f64 (.f64 #s(literal 2 binary64) K) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))
(+.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)))))
(exp.f64 (.f64 (log.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1/2 binary64))
(fma.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64)))))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64)))))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))))
(/.f64 (+.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(/.f64 (exp.f64 (log.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (exp.f64 (log.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64)))))))))) (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) K))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)))
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64))))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) #s(literal -1 binary64))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
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(/.f64 (neg.f64 (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))) (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64)))))) (neg.f64 (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (*.f64 K K) #s(literal 1/23040 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 K (.f64 K J)) (.f64 K (.f64 K J))) #s(literal 1/530841600 binary64)) (.f64 (.f64 J J) #s(literal 1/36864 binary64))) (-.f64 (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))) (.f64 J #s(literal -1/192 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 J J) #s(literal 1/36864 binary64)) (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64)))) (.f64 (.f64 (.f64 K (.f64 K J)) (.f64 K (.f64 K J))) #s(literal 1/530841600 binary64)))) (.f64 (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64)))) (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (*.f64 K K) #s(literal 1/23040 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))) (-.f64 (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))) (.f64 J #s(literal -1/192 binary64))) (.f64 (.f64 J J) #s(literal 1/36864 binary64))) (fma.f64 (.f64 J (.f64 J J)) #s(literal -1/7077888 binary64) (.f64 (.f64 (.f64 K (.f64 K J)) (.f64 (.f64 K (.f64 K J)) (.f64 K (.f64 K J)))) #s(literal 1/12230590464000 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64)))) (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))) (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (*.f64 K K) #s(literal 1/23040 binary64)))))) #s(literal -1 binary64))
(.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)))
(.f64 J (+.f64 #s(literal -1/192 binary64) (.f64 (*.f64 K K) #s(literal 1/23040 binary64))))
(.f64 (fma.f64 (.f64 J (.f64 J J)) #s(literal -1/7077888 binary64) (.f64 (.f64 (.f64 K (.f64 K J)) (.f64 (.f64 K (.f64 K J)) (.f64 K (.f64 K J)))) #s(literal 1/12230590464000 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))) (-.f64 (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))) (.f64 J #s(literal -1/192 binary64))) (.f64 (*.f64 J J) #s(literal 1/36864 binary64)))))
(.f64 (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))) (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 J (-.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) #s(literal 1/23040 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))) (.f64 J #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J))))
(.f64 (fabs.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (*.f64 #s(literal -2 binary64) J))
(.f64 #s(literal -2 binary64) (.f64 J (fabs.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(.f64 J (.f64 (fabs.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) #s(literal -2 binary64)))
(.f64 (.f64 #s(literal -2 binary64) J) (fabs.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 (fabs.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) #s(literal -2 binary64)) J)
(.f64 (.f64 (fabs.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) J) #s(literal -2 binary64))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 K K) #s(literal 1/8 binary64)))
(+.f64 (.f64 (.f64 K K) #s(literal 1/8 binary64)) #s(literal -1 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K))) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))))
(fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1/8 binary64) (*.f64 K K) #s(literal -1 binary64))
(fma.f64 (*.f64 K #s(literal 1/8 binary64)) K #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) (-.f64 #s(literal 1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))) (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/512 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/512 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) (-.f64 #s(literal 1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))
(/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/512 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/512 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) (-.f64 #s(literal 1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64))) (neg.f64 (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)))) (-.f64 #s(literal -1 binary64) (.f64 (.f64 K K) #s(literal 1/8 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K))) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)) (fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) (-.f64 #s(literal 1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))) (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/512 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/512 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) (-.f64 #s(literal 1 binary64) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
(.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))))
(.f64 K (.f64 K J))
(.f64 J (.f64 K K))
(.f64 (.f64 K K) J)
(.f64 (.f64 K J) K)
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (.f64 J (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))) (.f64 J #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J)))
(.f64 J (.f64 (*.f64 K K) #s(literal 1/23040 binary64)))
(.f64 (.f64 K K) (*.f64 J #s(literal 1/23040 binary64)))
(.f64 (.f64 K (*.f64 K J)) #s(literal 1/23040 binary64))
(.f64 #s(literal 1/23040 binary64) (.f64 K (*.f64 K J)))
(.f64 (.f64 K J) (*.f64 K #s(literal 1/23040 binary64)))
(.f64 (.f64 (*.f64 K K) #s(literal 1/23040 binary64)) J)
(.f64 (.f64 #s(literal 1/23040 binary64) J) (*.f64 K K))
(.f64 (.f64 #s(literal 1/23040 binary64) (*.f64 K J)) K)

eval133.0ms (1.2%)

Memory: 13.5MiB live, 281.9MiB allocated
Compiler: Compiled 28 840 to 1 550 computations (94.6% saved)

prune152.0ms (1.4%)

Memory

3.5MiB live, 341.2MiB allocated

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	948	16	964
Fresh	5	4	9
Picked	4	1	5
Done	0	2	2
Total	957	23	980

Accuracy

100.0%

Counts

980 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
	16.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (fabs.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) K)))) (*.f64 #s(literal -2 binary64) J)))
	42.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
	14.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))))) (*.f64 #s(literal -2 binary64) J)))
	41.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)))
	32.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
▶	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
	42.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (exp.f64 (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
✓	53.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
▶	42.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
✓	42.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
▶	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
	29.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K #s(approx (+ ( (* J (* K K)) -1/192) (* J 1/4)) (.f64 #s(literal 1/4 binary64) J))) (.f64 #s(literal -2 binary64) J))))
✓	31.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
▶	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
	30.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
	30.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
▶	29.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
	30.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
	3.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))

Compiler

Compiled 892 to 566 computations (36.5% saved)

simplify285.0ms (2.7%)

Memory

12.0MiB live, 449.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))
cost-diff	0	#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
cost-diff	320	(fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))
cost-diff	0	(.f64 K (.f64 J (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))
cost-diff	0	#s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
cost-diff	320	(fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))
cost-diff	0	(.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))
cost-diff	0	#s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
cost-diff	0	#s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))
cost-diff	0	(neg.f64 U)
cost-diff	0	(.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))

Rules

14 916×	`lower-fma.f32`
14 902×	`lower-fma.f64`
5 152×	`lower-*.f32`
5 126×	`lower-*.f64`
4 172×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	815
0	135	805
1	298	763
2	739	733
3	1975	733
4	3411	733
5	6212	733
6	7336	733
0	8021	718

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))
#s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(cos.f64 K)
K
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))
(neg.f64 U)
U
#s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))
#s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))
(.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))
J
(fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))
K
(.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
(*.f64 K K)
#s(literal -1/192 binary64)
#s(literal 1/4 binary64)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))
(fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))
K
(.f64 K (.f64 J (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))
(.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))
J
(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
(*.f64 K K)
#s(literal -1/192 binary64)
#s(literal 1/4 binary64)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))
(.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))
U
(fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))
(fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (*.f64 K K)) #s(literal -1 binary64))
#s(literal 1/64 binary64)
(.f64 (.f64 K K) (*.f64 K K))
(*.f64 K K)
K
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))
(*.f64 K #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(.f64 K (.f64 K #s(literal -1/8 binary64)))
(*.f64 K #s(literal -1/8 binary64))
#s(literal -1/8 binary64)

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))))
(.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))
(.f64 (.f64 #s(literal -2 binary64) J) #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))))
#s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(cos.f64 K)
K
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))
(neg.f64 U)
U
#s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64)))))
#s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))
#s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64))))
(.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))
(.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
J
(fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))
(fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64))
K
(.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))
(.f64 K (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
(fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64))
(*.f64 K K)
#s(literal -1/192 binary64)
#s(literal 1/4 binary64)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64)))))
#s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64))))
(fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))
(.f64 J (fma.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
K
(.f64 K (.f64 J (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))
(.f64 K (.f64 J (fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64))))
(.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))
(.f64 J (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)))
J
(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
(fma.f64 #s(literal -1/192 binary64) (*.f64 K K) #s(literal 1/4 binary64))
(*.f64 K K)
#s(literal -1/192 binary64)
#s(literal 1/4 binary64)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 K #s(literal 1/64 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 K #s(literal 1/64 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))))))
(.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))
(.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 K #s(literal 1/64 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))))
U
(fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))
(fma.f64 K (.f64 K #s(literal -1/8 binary64)) (/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 K #s(literal 1/64 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (*.f64 K K)) #s(literal -1 binary64))
(fma.f64 (.f64 K (.f64 K K)) (*.f64 K #s(literal 1/64 binary64)) #s(literal -1 binary64))
#s(literal 1/64 binary64)
(.f64 (.f64 K K) (*.f64 K K))
(.f64 K (.f64 K (*.f64 K K)))
(*.f64 K K)
K
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))
(*.f64 K #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(.f64 K (.f64 K #s(literal -1/8 binary64)))
(.f64 (.f64 K K) #s(literal -1/8 binary64))
(*.f64 K #s(literal -1/8 binary64))
#s(literal -1/8 binary64)

localize480.0ms (4.5%)

Memory

16.9MiB live, 565.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.29158108505431535	(/.f64 #s(literal 1 binary64) (fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)))
accuracy	24.55955300208531	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
accuracy	27.853704422649738	(fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))
accuracy	37.85262947177798	#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))
accuracy	0.08984375	(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
accuracy	2.907245528670645	(.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))
accuracy	27.71150721647649	#s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))
accuracy	36.82741060073028	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
accuracy	0.08984375	(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
accuracy	2.621367330470072	(.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))
accuracy	28.13838218558543	#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))
accuracy	29.776795627025457	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
accuracy	0	(neg.f64 U)
accuracy	3.9820436945371056	(.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))
accuracy	31.472132417957383	#s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))
accuracy	57.292934617318856	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
accuracy	0.0703125	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
accuracy	0.109375	(.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))
accuracy	0.45387436983699375	(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
accuracy	36.82741060073028	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))

Samples

241.0ms	113×	1	valid
140.0ms	143×	0	valid

Compiler

Compiled 527 to 96 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 306.0ms

ival-mult: 87.0ms (28.4% of total)

ival-sqrt: 58.0ms (18.9% of total)

ival-cos: 54.0ms (17.6% of total)

ival-add: 37.0ms (12.1% of total)

const: 32.0ms (10.4% of total)

ival-div: 15.0ms (4.9% of total)

adjust: 14.0ms (4.6% of total)

ival-pow2: 7.0ms (2.3% of total)

exact: 1.0ms (0.3% of total)

ival-neg: 1.0ms (0.3% of total)

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

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

series98.0ms (0.9%)

Memory

-16.7MiB live, 143.4MiB allocated

Counts

24 → 588

Calls

Call 1

Inputs
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J)) (patch (.f64 #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (patch #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))) (patch (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (neg.f64 U) (patch (neg.f64 U) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)) (patch #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))) (patch #s(approx ( (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) (patch #s(approx (+ ( K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)) (patch (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))) #<representation binary64>) () ())
#s(alt #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())
#s(alt (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (patch (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))) (patch (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))) #<representation binary64>) () ())
#s(alt #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))))) (patch #s(approx ( -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))) (patch (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))) #<representation binary64>) () ())
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Outputs
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#s(alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))) (taylor inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))) (taylor -inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))) (taylor -inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))) (taylor -inf J) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (taylor 0 K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (taylor 0 K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (taylor 0 K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))))) (taylor 0 K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))) #<representation binary64>) () ())) ())
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#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor 0 J) (#s(alt #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) (patch #s(approx (+ ( K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) (patch #s(approx (+ ( K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) (patch #s(approx (+ ( K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) (patch #s(approx (+ ( K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) (patch #s(approx (+ ( K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor 0 J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor 0 J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor 0 J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor -inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor -inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor -inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* J (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)) (taylor -inf J) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -2 J) (taylor 0 K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 J) (* 1/4 (* J (pow K 2)))) (taylor 0 K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J)))) (taylor 0 K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J)))) (taylor 0 K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/192 (* J (pow K 4))) (taylor inf K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow K 4) (+ (* -2 (/ J (pow K 4))) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))) (taylor inf K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow K 4) (+ (* -2 (/ J (pow K 4))) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))) (taylor inf K) (#s(alt (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) (patch (.f64 J (fma.f64 K (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))) (taylor inf K) (#s(alt (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) (patch (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))) (taylor inf K) (#s(alt (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) (patch (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/192 (* J (pow K 2))) (taylor -inf K) (#s(alt (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) (patch (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))) (taylor -inf K) (#s(alt (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) (patch (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))) (taylor -inf K) (#s(alt (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) (patch (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2))))) (taylor -inf K) (#s(alt (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) (patch (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/8 (pow K 2))) (taylor 0 K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow K 2) (- (* 1/64 (pow K 2)) 1/8))) (taylor 0 K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/64 (* -1/512 (pow K 2)))) 1/8))) (taylor 0 K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 8 (pow K 2)) (taylor inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 8 (* 64 (/ 1 (pow K 2)))) (pow K 2)) (taylor inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 8 (/ 512 (pow K 4))) (* 64 (/ 1 (pow K 2)))) (pow K 2)) (taylor inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 8 (/ 512 (pow K 4))) (+ (* 64 (/ 1 (pow K 2))) (* 4096 (/ 1 (pow K 6))))) (pow K 2)) (taylor inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 8 (pow K 2)) (taylor -inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 8 (* 64 (/ 1 (pow K 2)))) (pow K 2)) (taylor -inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 8 (/ 512 (pow K 4))) (* 64 (/ 1 (pow K 2)))) (pow K 2)) (taylor -inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 8 (/ 512 (pow K 4))) (+ (* 64 (/ 1 (pow K 2))) (* 4096 (/ 1 (pow K 6))))) (pow K 2)) (taylor -inf K) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

147 calls:

Time	Variable		Point	Expression
13.0ms	K	@	-inf	(* K (* J (+ (* (* K K) -1/192) 1/4)))
10.0ms	J	@	0	(* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1))))))
2.0ms	U	@	0	(* U (+ (* (+ (* 1/64 (* (* K K) (* K K))) -1) (/ 1 (+ (* K (* K 1/8)) 1))) (* K (* K -1/8))))
1.0ms	K	@	inf	(+ (* (+ (* 1/64 (* (* K K) (* K K))) -1) (/ 1 (+ (* K (* K 1/8)) 1))) (* K (* K -1/8)))
1.0ms	K	@	0	(+ (* (+ (* 1/64 (* (* K K) (* K K))) -1) (/ 1 (+ (* K (* K 1/8)) 1))) (* K (* K -1/8)))

simplify728.0ms (6.8%)

Memory

-178.0MiB live, 560.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 640×	`lower-fma.f64`
10 640×	`lower-fma.f32`
8 274×	`lower-*.f64`
8 274×	`lower-*.f32`
3 966×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	610	14570
1	2011	14201
2	7829	14194
0	8048	13213

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 580

Calls

Call 1

Inputs
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
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(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* (pow K 2) (+ (* -2 (* (/ J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2)))))))
(+ (* -2 (* (pow J 2) (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U)))) (* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))))
(+ (* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))) (* (pow J 2) (+ (* -2 (* (pow J 2) (+ (* -1 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 3))) (* 3/8 (/ (pow K 2) (pow U 3)))))) (* -2 (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U))))))
(+ (* -2 (+ (* 1/16 (* (pow K 2) U)) (* 1/2 (* U (+ 1 (* -1/8 (pow K 2))))))) (* (pow J 2) (+ (* -2 (+ (* -1/4 (/ (pow K 2) U)) (/ 1 U))) (* (pow J 2) (+ (* -2 (* (pow J 2) (+ (* -5/4 (/ (pow K 2) (pow U 5))) (* 2 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 5)))))) (* -2 (+ (* -1 (/ (+ 1 (* -1/8 (pow K 2))) (pow U 3))) (* 3/8 (/ (pow K 2) (pow U 3))))))))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* J (+ (* -2 (+ 1 (* -1/8 (pow K 2)))) (* -2 (/ (+ (* 1/32 (* (pow K 2) (pow U 2))) (* 1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))))) (pow J 2)))))
(* J (+ (* -2 (+ 1 (* -1/8 (pow K 2)))) (+ (* -2 (/ (+ (* -1/128 (* (pow U 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/256 (* (pow K 2) (pow U 4)))) (pow J 4))) (* -2 (/ (+ (* 1/32 (* (pow K 2) (pow U 2))) (* 1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))))) (pow J 2))))))
(* J (+ (* -2 (+ 1 (* -1/8 (pow K 2)))) (+ (* -2 (/ (+ (* -1/64 (* (pow K 2) (* (pow U 2) (+ (* -1/16 (pow U 4)) (* 1/64 (pow U 4)))))) (* 1/1024 (* (pow U 6) (+ 1 (* -1/8 (pow K 2)))))) (pow J 6))) (+ (* -2 (/ (+ (* -1/128 (* (pow U 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/256 (* (pow K 2) (pow U 4)))) (pow J 4))) (* -2 (/ (+ (* 1/32 (* (pow K 2) (pow U 2))) (* 1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))))) (pow J 2)))))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -1 (* J (+ (* -2 (/ (+ (* -1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2))))) (* -1/32 (* (pow K 2) (pow U 2)))) (pow J 2))) (* 2 (+ 1 (* -1/8 (pow K 2)))))))
(* -1 (* J (+ (* -2 (/ (+ (* -1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2))))) (* -1/32 (* (pow K 2) (pow U 2)))) (pow J 2))) (+ (* -2 (/ (+ (* 1/256 (* (pow K 2) (pow U 4))) (* 1/128 (* (pow U 4) (+ 1 (* -1/8 (pow K 2)))))) (pow J 4))) (* 2 (+ 1 (* -1/8 (pow K 2))))))))
(* -1 (* J (+ (* -2 (/ (+ (* -1/8 (* (pow U 2) (+ 1 (* -1/8 (pow K 2))))) (* -1/32 (* (pow K 2) (pow U 2)))) (pow J 2))) (+ (* -2 (/ (+ (* -1/1024 (* (pow U 6) (+ 1 (* -1/8 (pow K 2))))) (* 1/64 (* (pow K 2) (* (pow U 2) (+ (* -1/16 (pow U 4)) (* 1/64 (pow U 4))))))) (pow J 6))) (+ (* -2 (/ (+ (* 1/256 (* (pow K 2) (pow U 4))) (* 1/128 (* (pow U 4) (+ 1 (* -1/8 (pow K 2)))))) (pow J 4))) (* 2 (+ 1 (* -1/8 (pow K 2)))))))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(+ (* -2 (* J (+ 1 (* -1/8 (pow K 2))))) (* -2 (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J))))))
(+ (* -2 (* J (+ 1 (* -1/8 (pow K 2))))) (* (pow U 2) (+ (* -2 (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (* -1/256 (/ (pow K 2) (pow J 3)))))) (* -2 (+ (* 1/32 (/ (pow K 2) J)) (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)))))))
(+ (* -2 (* J (+ 1 (* -1/8 (pow K 2))))) (* (pow U 2) (+ (* -2 (+ (* 1/32 (/ (pow K 2) J)) (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)))) (* (pow U 2) (+ (* -2 (* (pow U 2) (+ (* 3/4096 (/ (pow K 2) (pow J 5))) (* 1/1024 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 5)))))) (* -2 (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (* -1/256 (/ (pow K 2) (pow J 3))))))))))
(* -2 (* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))))
(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))
(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))))))
(* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (+ (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))) (* -2 (/ (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (pow J 2))) (* 2 (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))))) (pow U 6)))))))
(* 2 (* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))))
(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))))))
(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2)))))))
(* -1 (* U (+ (* -2 (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2)))))) (+ (* -2 (/ (+ (* -1 (* (pow J 4) (+ 1 (* -1/8 (pow K 2))))) (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (pow J 2)))) (pow U 4))) (+ (* -2 (/ (+ (* -1/8 (* (pow J 2) (pow K 2))) (* (pow J 2) (+ 1 (* -1/8 (pow K 2))))) (pow U 2))) (* -2 (/ (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (pow J 2))) (* 2 (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))))) (pow U 6))))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* U (- (+ (* -1/8 (pow K 2)) (* 1/64 (/ (pow K 4) (+ 1 (* 1/8 (pow K 2)))))) (/ 1 (+ 1 (* 1/8 (pow K 2))))))
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
1/4
(+ 1/4 (* -1/192 (pow K 2)))
(+ 1/4 (* -1/192 (pow K 2)))
(+ 1/4 (* -1/192 (pow K 2)))
(* -1/192 (pow K 2))
(* (pow K 2) (- (* 1/4 (/ 1 (pow K 2))) 1/192))
(* (pow K 2) (- (* 1/4 (/ 1 (pow K 2))) 1/192))
(* (pow K 2) (- (* 1/4 (/ 1 (pow K 2))) 1/192))
(* -1/192 (pow K 2))
(* (pow K 2) (- (* 1/4 (/ 1 (pow K 2))) 1/192))
(* (pow K 2) (- (* 1/4 (/ 1 (pow K 2))) 1/192))
(* (pow K 2) (- (* 1/4 (/ 1 (pow K 2))) 1/192))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* J (+ 1/4 (* -1/192 (pow K 2))))
(* 1/4 J)
(+ (* -1/192 (* J (pow K 2))) (* 1/4 J))
(+ (* -1/192 (* J (pow K 2))) (* 1/4 J))
(+ (* -1/192 (* J (pow K 2))) (* 1/4 J))
(* -1/192 (* J (pow K 2)))
(* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))
(* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))
(* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))
(* -1/192 (* J (pow K 2)))
(* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))
(* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))
(* (pow K 2) (+ (* -1/192 J) (* 1/4 (/ J (pow K 2)))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/64 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/64 (* -1/512 (pow K 2)))) 1/8)))
(/ 8 (pow K 2))
(/ (- 8 (* 64 (/ 1 (pow K 2)))) (pow K 2))
(/ (- (+ 8 (/ 512 (pow K 4))) (* 64 (/ 1 (pow K 2)))) (pow K 2))
(/ (- (+ 8 (/ 512 (pow K 4))) (+ (* 64 (/ 1 (pow K 2))) (* 4096 (/ 1 (pow K 6))))) (pow K 2))
(/ 8 (pow K 2))
(/ (- 8 (* 64 (/ 1 (pow K 2)))) (pow K 2))
(/ (- (+ 8 (/ 512 (pow K 4))) (* 64 (/ 1 (pow K 2)))) (pow K 2))
(/ (- (+ 8 (/ 512 (pow K 4))) (+ (* 64 (/ 1 (pow K 2))) (* 4096 (/ 1 (pow K 6))))) (pow K 2))

Outputs
(* -1 U)
(neg.f64 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(fma.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) U) (neg.f64 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(-.f64 (.f64 (.f64 J J) (fma.f64 #s(literal 2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (/.f64 (.f64 J J) (.f64 U (.f64 U U)))) (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U))) U)
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(-.f64 (.f64 (.f64 J J) (fma.f64 (.f64 J J) (fma.f64 #s(literal -4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 6 binary64)) (/.f64 (.f64 J J) (pow.f64 U #s(literal 5 binary64)))) (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (.f64 U (.f64 U U))))) (/.f64 (.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U))) U)
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(.f64 J (fma.f64 #s(literal 1/64 binary64) (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)))) (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(.f64 J (fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 #s(literal 1/2 binary64) K)))) (fma.f64 #s(literal 1/64 binary64) (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)))) (/.f64 (.f64 #s(literal -1/512 binary64) (pow.f64 U #s(literal 6 binary64))) (.f64 (pow.f64 J #s(literal 6 binary64)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64))))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))) (neg.f64 J))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(neg.f64 (.f64 J (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (fma.f64 (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 #s(literal 1/2 binary64) K)))) #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64))))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(neg.f64 (.f64 J (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)))) #s(literal -1/64 binary64) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 J #s(literal 6 binary64)) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)))) #s(literal 1/512 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
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(* -1 U)
(neg.f64 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
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(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
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(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
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U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
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(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
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(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
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(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(fma.f64 #s(literal -2 binary64) J (.f64 K (.f64 J (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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U
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(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
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(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
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(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(fma.f64 #s(literal -2 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(fma.f64 (.f64 U U) (fma.f64 U (.f64 U (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)) (.f64 J (.f64 J J))))) (/.f64 #s(literal -1/4 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(fma.f64 (.f64 U U) (fma.f64 (.f64 U U) (fma.f64 #s(literal -1/512 binary64) (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)) (pow.f64 J #s(literal 5 binary64)))) (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)) (.f64 J (.f64 J J))))) (/.f64 #s(literal -1/4 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J)))
(* -1 U)
(neg.f64 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(.f64 U (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
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(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
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U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(.f64 (neg.f64 U) (fma.f64 #s(literal 2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (/.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 U #s(literal 4 binary64)))) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
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(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(fma.f64 #s(literal -2 binary64) J (.f64 K (.f64 J (.f64 K (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(.f64 (.f64 #s(literal -2 binary64) J) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
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(/ (- (+ 8 (/ 512 (pow K 4))) (* 64 (/ 1 (pow K 2)))) (pow K 2))
(/.f64 (+.f64 (/.f64 #s(literal 512 binary64) (pow.f64 K #s(literal 4 binary64))) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -64 binary64) (.f64 K K)))) (.f64 K K))
(/ (- (+ 8 (/ 512 (pow K 4))) (+ (* 64 (/ 1 (pow K 2))) (* 4096 (/ 1 (pow K 6))))) (pow K 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 512 binary64) (pow.f64 K #s(literal 4 binary64))) (+.f64 #s(literal 8 binary64) (/.f64 #s(literal -64 binary64) (.f64 K K)))) (/.f64 #s(literal 4096 binary64) (pow.f64 K #s(literal 6 binary64)))) (.f64 K K))

rewrite273.0ms (2.6%)

Memory

7.0MiB live, 433.9MiB allocated

Rules

5 164×	`lower-*.f32`
5 138×	`lower-*.f64`
4 534×	`lower-fma.f32`
4 520×	`lower-fma.f64`
2 452×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	716
0	135	689
1	557	605
2	3779	584
0	8300	565

Stop Event

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

Counts

24 → 294

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))
#s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))
(neg.f64 U)
#s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))))
#s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))
(.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64)))
(fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J)))
(.f64 K (.f64 J (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))
(fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64))))))
(.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))
(.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 K (*.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64)))

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))))
(.f64 #s(literal -2 binary64) (.f64 J #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))))
(.f64 J (.f64 #s(literal -2 binary64) #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))))
(.f64 (.f64 #s(literal -2 binary64) J) #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))))
(.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J))
(.f64 (.f64 #s(literal -2 binary64) #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))) J)
(.f64 (.f64 #s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) J) #s(literal -2 binary64))
#s(approx (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) #s(literal 1/4 binary64)))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) #s(literal 1/4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64)))))) (.f64 (cos.f64 K) #s(literal 1/4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64))) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) #s(literal 1/4 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64)))))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 K)))))
(pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (.f64 (cos.f64 K) #s(literal 1/4 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64)))))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 (.f64 U #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))
(-.f64 #s(literal 0 binary64) (.f64 U #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(neg.f64 (.f64 U #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(.f64 U (neg.f64 #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 U #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
(.f64 #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)) (neg.f64 U))
(.f64 (.f64 #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)) #s(literal -1 binary64)) U)
(+.f64 #s(literal 0 binary64) (neg.f64 U))
(-.f64 #s(literal 0 binary64) U)
(neg.f64 U)
(/.f64 (*.f64 U (neg.f64 U)) (+.f64 #s(literal 0 binary64) U))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U))))
(*.f64 U #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) U)
#s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))))
#s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))
(+.f64 (.f64 #s(literal -2 binary64) J) (.f64 (.f64 J (.f64 K K)) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))))
(+.f64 (.f64 (.f64 J (.f64 K K)) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))
(-.f64 (/.f64 (.f64 K (.f64 (.f64 J (.f64 K (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 (.f64 J (.f64 K K)) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))))) (fma.f64 J (.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (fma.f64 J (.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (*.f64 J #s(literal 2 binary64)))))
(fma.f64 #s(literal -2 binary64) J (.f64 (.f64 J (.f64 K K)) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))))
(fma.f64 J #s(literal -2 binary64) (.f64 (.f64 J (.f64 K K)) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))))
(fma.f64 J (.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J))
(fma.f64 K (.f64 J (.f64 K (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 J (.f64 K K)) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 K K) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 K (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J K) (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 K K) (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 J (.f64 K (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) K (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) J (.f64 #s(literal -2 binary64) J))
(fma.f64 (.f64 J K) (.f64 K (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal -2 binary64) J))
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(/.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64)) #s(literal 1/64 binary64)) (+.f64 #s(literal 1/16 binary64) (-.f64 (.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64)) (.f64 (*.f64 K K) #s(literal -1/768 binary64)))))
(/.f64 (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) #s(literal -1/16 binary64)) (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64)) #s(literal 1/64 binary64))) (neg.f64 (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 K K) #s(literal -1/768 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) #s(literal -1/16 binary64))) (neg.f64 (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))))
(/.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) (.f64 K K))))
(pow.f64 (/.f64 (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 K K) #s(literal -1/768 binary64)))) (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64)) #s(literal 1/64 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)) (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) #s(literal -1/16 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (*.f64 K K) #s(literal -1/768 binary64))))))
(.f64 (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))))
(+.f64 (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K))) (.f64 J #s(literal 1/4 binary64)))
(+.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K))))
(-.f64 (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K)))) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))) (/.f64 (.f64 (.f64 J J) #s(literal 1/16 binary64)) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 J #s(literal 1/4 binary64) (.f64 J (.f64 #s(literal -1/192 binary64) (*.f64 K K))))
(fma.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 K (.f64 (.f64 K #s(literal -1/192 binary64)) J) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 #s(literal -1/192 binary64) (.f64 J (.f64 K K)) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 #s(literal 1/4 binary64) J (.f64 J (.f64 #s(literal -1/192 binary64) (*.f64 K K))))
(fma.f64 (.f64 K K) (.f64 J #s(literal -1/192 binary64)) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 K K) (.f64 #s(literal -1/192 binary64) J) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 #s(literal -1/192 binary64) (.f64 K K)) J (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 J K) (.f64 K #s(literal -1/192 binary64)) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 J #s(literal -1/192 binary64)) (.f64 K K) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 #s(literal -1/192 binary64) J) (.f64 K K) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 #s(literal -1/192 binary64) (.f64 J K)) K (*.f64 J #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 J #s(literal 1/4 binary64)) (-.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)))) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K))))) (fma.f64 #s(literal 1/64 binary64) (.f64 J (.f64 J J)) (.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64))) (.f64 J (.f64 J J))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))) (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))))))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 J (.f64 J J)) (.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64))) (.f64 J (.f64 J J)))) (fma.f64 (.f64 J #s(literal 1/4 binary64)) (-.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)))) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K))))))
(/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 J (.f64 J J)) (.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64))) (.f64 J (.f64 J J)))) (fma.f64 (.f64 J J) #s(literal 1/16 binary64) (-.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K)))) (.f64 (.f64 (.f64 J (.f64 #s(literal -1/192 binary64) (*.f64 K K))) J) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))) (.f64 J (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 J (.f64 J J)) (.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64))) (.f64 J (.f64 J J))))) (neg.f64 (fma.f64 (.f64 J #s(literal 1/4 binary64)) (-.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)))) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K)))))))
(/.f64 (neg.f64 (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))))) (neg.f64 (.f64 J (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 J J) #s(literal 1/16 binary64)) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K))))) (-.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)))))
(/.f64 (.f64 J (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64)) #s(literal 1/64 binary64))) (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (*.f64 K K) #s(literal -1/768 binary64)))))
(/.f64 (.f64 J (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) #s(literal -1/16 binary64))) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64)) #s(literal 1/64 binary64)) J) (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (*.f64 K K) #s(literal -1/768 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 K (.f64 K (.f64 K K))) #s(literal 1/36864 binary64) #s(literal -1/16 binary64)) J) (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))
(pow.f64 (/.f64 (fma.f64 (.f64 J #s(literal 1/4 binary64)) (-.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)))) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (.f64 K K))))) (fma.f64 #s(literal 1/64 binary64) (.f64 J (.f64 J J)) (.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64))) (.f64 J (.f64 J J))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))) (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J (fma.f64 K (*.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64))))) #s(literal -1 binary64))
(.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))
(.f64 (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) J)
(.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 J (.f64 J J)) (.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal -1/7077888 binary64))) (.f64 J (.f64 J J)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 J #s(literal 1/4 binary64)) (-.f64 (.f64 J #s(literal 1/4 binary64)) (.f64 J (.f64 #s(literal -1/192 binary64) (.f64 K K)))) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 J (.f64 K K)) (.f64 J (*.f64 K K)))))))
(.f64 (.f64 (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 J (fma.f64 K (.f64 K #s(literal -1/192 binary64)) #s(literal -1/4 binary64)))))
(exp.f64 (.f64 (log1p.f64 (.f64 (*.f64 K K) #s(literal 1/8 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(pow.f64 (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (.f64 (.f64 K K) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (pow.f64 (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K (.f64 K K)) (.f64 (.f64 K (.f64 K K)) #s(literal 1/512 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal 1 binary64)) (.f64 (*.f64 K K) #s(literal 1/8 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal -1 binary64))) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64)))

eval140.0ms (1.3%)

Memory: -3.0MiB live, 313.6MiB allocated
Compiler: Compiled 25 330 to 1 396 computations (94.5% saved)

prune252.0ms (2.4%)

Memory

23.4MiB live, 502.8MiB allocated

Pruning

28 alts after pruning (21 fresh and 7 done)

	Pruned	Kept	Total
New	896	9	905
Fresh	3	12	15
Picked	1	4	5
Done	0	3	3
Total	900	28	928

Accuracy

100.0%

Counts

928 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
	4.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
	16.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (fabs.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) K)))) (*.f64 #s(literal -2 binary64) J)))
	42.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
	32.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
✓	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
	42.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (exp.f64 (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
✓	53.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
	41.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (.f64 (sqrt.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J)))
✓	42.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
	14.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
✓	42.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
✓	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(approx (+ (* (* K K) -1/192) 1/4) #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
	29.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
✓	31.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
	29.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
✓	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal -1 binary64)) U) (.f64 K (.f64 (.f64 K #s(literal -1/8 binary64)) U)))))
	30.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
	30.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
	29.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (+.f64 (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 K (.f64 (*.f64 K #s(literal -1/8 binary64)) U)))))
	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (fma.f64 K (.f64 K (fma.f64 #s(literal 1/64 binary64) (.f64 K K) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (/.f64 #s(literal 8 binary64) (.f64 K K))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) #s(literal 1 binary64)) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
	30.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
	3.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))

Compiler

Compiled 1 487 to 591 computations (60.3% saved)

regimes97.0ms (0.9%)

Memory

-0.5MiB live, 205.6MiB allocated

Counts

47 → 3

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K #s(approx (+ ( (* J (* K K)) -1/192) (* J 1/4)) (.f64 #s(literal 1/4 binary64) J))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(approx (+ (* (* K K) -1/192) 1/4) #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 U #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (+.f64 (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 K (.f64 (*.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) #s(literal 1 binary64)) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (/.f64 #s(literal 8 binary64) (.f64 K K))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (fma.f64 K (.f64 K (fma.f64 #s(literal 1/64 binary64) (.f64 K K) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal -1 binary64)) U) (.f64 K (.f64 (.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (.f64 (sqrt.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (sqrt.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 #s(literal -2 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (fabs.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) K)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (exp.f64 (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Outputs

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (*.f64 (neg.f64 U) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))

Calls

6 calls:

19.0ms	(/.f64 K #s(literal 2 binary64))
17.0ms	J
16.0ms	U
16.0ms	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
13.0ms	(cos.f64 (/.f64 K #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
79.0%	2	`J`
73.4%	1	`K`
84.0%	2	`U`
99.9%	3	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`
73.4%	1	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
73.4%	1	`(/.f64 K #s(literal 2 binary64))`

Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes31.0ms (0.3%)

Memory

7.9MiB live, 84.0MiB allocated

Counts

45 → 4

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K #s(approx (+ ( (* J (* K K)) -1/192) (* J 1/4)) (.f64 #s(literal 1/4 binary64) J))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(approx (+ (* (* K K) -1/192) 1/4) #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 U #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (+.f64 (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 K (.f64 (*.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) #s(literal 1 binary64)) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (/.f64 #s(literal 8 binary64) (.f64 K K))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (fma.f64 K (.f64 K (fma.f64 #s(literal 1/64 binary64) (.f64 K K) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal -1 binary64)) U) (.f64 K (.f64 (.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (.f64 (sqrt.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (sqrt.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 #s(literal -2 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 K #s(literal 2 binary64))))) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal -1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (fabs.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) K)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1 binary64))))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 K #s(literal 1 binary64)))))))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (exp.f64 (log.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) J)))

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))

Calls

2 calls:

14.0ms

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

13.0ms

Results

Accuracy	Segments	Branch
75.8%	3	`U`
83.3%	4	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes13.0ms (0.1%)

Memory

-3.2MiB live, 35.2MiB allocated

Counts

35 → 3

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K #s(approx (+ ( (* J (* K K)) -1/192) (* J 1/4)) (.f64 #s(literal 1/4 binary64) J))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(approx (+ (* (* K K) -1/192) 1/4) #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 U #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (+.f64 (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 K (.f64 (*.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) #s(literal 1 binary64)) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (/.f64 #s(literal 8 binary64) (.f64 K K))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (fma.f64 K (.f64 K (fma.f64 #s(literal 1/64 binary64) (.f64 K K) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal -1 binary64)) U) (.f64 K (.f64 (.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (pow (+ 1/2 ( 1/2 (cos (* 2 (* K 1/2))))) 1/2) (.f64 (sqrt.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 J (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/32 binary64) (/.f64 (.f64 U U) J))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (sqrt.f64 (+.f64 (cos.f64 (.f64 K #s(literal 1 binary64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))

Outputs

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (*.f64 (neg.f64 U) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))

Calls

1 calls:

9.0ms

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
80.9%	3	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes109.0ms (1%)

Memory

-2.9MiB live, 159.9MiB allocated

Counts

29 → 4

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K #s(approx (+ ( (* J (* K K)) -1/192) (* J 1/4)) (.f64 #s(literal 1/4 binary64) J))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(approx (+ (* (* K K) -1/192) 1/4) #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 U #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (+.f64 (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 K (.f64 (*.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) #s(literal 1 binary64)) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/192 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/23040 binary64))) (.f64 J #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (/.f64 #s(literal 8 binary64) (.f64 K K))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) (fma.f64 K (.f64 K (fma.f64 #s(literal 1/64 binary64) (.f64 K K) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 K (.f64 K #s(literal 1/8 binary64)) #s(literal 1 binary64))) (.f64 K (*.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal 1 binary64))) (.f64 (fma.f64 K (.f64 #s(literal 1/64 binary64) (.f64 K (.f64 K K))) #s(literal -1 binary64)) U) (.f64 K (.f64 (.f64 K #s(literal -1/8 binary64)) U)))))

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))

Calls

6 calls:

44.0ms	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
27.0ms	J
9.0ms	(cos.f64 (/.f64 K #s(literal 2 binary64)))
9.0ms	K
8.0ms	(/.f64 K #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
56.9%	3	`U`
51.3%	2	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
45.8%	3	`K`
45.8%	3	`(/.f64 K #s(literal 2 binary64))`
54.0%	2	`J`
68.4%	4	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`

Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes11.0ms (0.1%)

Memory

-14.1MiB live, 27.0MiB allocated

Counts

23 → 3

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 J (fma.f64 #s(literal 1/4 binary64) (.f64 K K) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K #s(approx (+ ( (* J (* K K)) -1/192) (* J 1/4)) (.f64 #s(literal 1/4 binary64) J))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(approx (+ (* (* K K) -1/192) 1/4) #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(approx (+ (* (* K K) 1/8) -1) (.f64 (.f64 K K) #s(literal 1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 K (.f64 K #s(literal -1/8 binary64)) (fma.f64 (*.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* K (* K (+ (* (* J (* K K)) -1/192) (* J 1/4)))) (* -2 J)) (.f64 J (fma.f64 K (.f64 K (fma.f64 (*.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (.f64 K #s(literal 1/8 binary64)) K (+.f64 #s(literal -1 binary64) (.f64 K (.f64 K #s(literal -1/8 binary64))))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 (fma.f64 K (.f64 K #s(literal 1/16 binary64)) (fma.f64 (.f64 K K) #s(literal -1/16 binary64) #s(literal 1/2 binary64))) (.f64 U #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U #s(literal -1/8 binary64)) (.f64 K K) (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (fma.f64 (.f64 U (.f64 K #s(literal -1/8 binary64))) K (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (pow (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))) 1/2) (* -2 J)) (fma.f64 K (.f64 K (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (+.f64 (.f64 U (fma.f64 (.f64 K K) #s(literal 1/8 binary64) #s(literal -1 binary64))) (.f64 K (.f64 (*.f64 K #s(literal -1/8 binary64)) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (fma.f64 (.f64 J (.f64 K K)) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (*.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4))) (* -2 J)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* -2 (+ (* (+ (* (* K K) -1/8) 1) (* J (sqrt (+ (* 1/4 (/ (* U U) (* J J))) 1)))) (* (* (* K K) (* 1/32 (/ (* U U) J))) (sqrt (/ 1 (+ (* 1/4 (/ (* U U) (* J J))) 1)))))) (.f64 U (fma.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 K K) (.f64 K K)) #s(literal -1 binary64)) #s(approx (/ 1 (+ (* K (* K 1/8)) 1)) #s(literal 1 binary64)) (.f64 K (.f64 K #s(literal -1/8 binary64)))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) #s(approx (+ ( (* K K) (+ (* J -1/192) (* (* J (* K K)) 1/23040))) (* J 1/4)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))) (.f64 #s(literal -2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64))) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 U (.f64 U U))) (+.f64 #s(literal 0 binary64) (fma.f64 U U (.f64 #s(literal 0 binary64) U)))) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))

Outputs

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (*.f64 (neg.f64 U) #s(approx (+ (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))

Calls

1 calls:

8.0ms

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
63.4%	3	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes4.0ms (0%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))

Outputs

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))

#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Calls

2 calls:

2.0ms

(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))

2.0ms

Results

Accuracy	Segments	Branch
55.0%	2	`U`
54.2%	2	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes9.0ms (0.1%)

Memory

-5.3MiB live, 33.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Outputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Calls

6 calls:

2.0ms	U
1.0ms	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
1.0ms	(/.f64 K #s(literal 2 binary64))
1.0ms	K
1.0ms	J

Results

Accuracy	Segments	Branch
42.1%	1	`K`
42.1%	1	`(/.f64 K #s(literal 2 binary64))`
42.1%	1	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
42.1%	1	`J`
42.1%	1	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`
42.1%	1	`U`

Compiler

Compiled 52 to 37 computations (28.8% saved)

bsearch1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	4.170291515007617e+307	+inf
0.0ms	-inf	-1.1637470530574984e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	4.170291515007617e+307	+inf
0.0ms	-4.23133259364859e-87	-1.1215132545137313e-93
0.0ms	-1.3197865484216505e+286	-4.159632122068558e+285

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	4.170291515007617e+307	+inf
0.0ms	-1.3197865484216505e+286	-4.159632122068558e+285

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	-1.9974814201295742e-260	6.605378826071475e-278
0.0ms	-1.4726171129002215e-79	-3.389626064759649e-82
0.0ms	-1.3197865484216505e+286	-4.159632122068558e+285

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch2.0ms (0%)

Memory

-37.0MiB live, 1.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
1.0ms	-1.9974814201295742e-260	6.605378826071475e-278
0.0ms	-1.3197865484216505e+286	-4.159632122068558e+285

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch3.0ms (0%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.007874006496127	0.008844734675597701

Samples

2.0ms

16×

valid

Compiler

Compiled 46 to 34 computations (26.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-cos: 1.0ms (61.2% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

ival-pow2: 0.0ms (0% of total)

simplify17.0ms (0.2%)

Memory

4.0MiB live, 41.4MiB allocated

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	1024
1	105	1024
2	113	1024
3	120	1024
4	123	1024
5	124	1024

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -inf.0 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -8958978968711217/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -1668739871813211/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -5539569662801113/553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -5539569662801113/553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 U #s(literal 1224979098644775/144115188075855872 binary64)) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Outputs
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -inf.0 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -inf.0 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -8958978968711217/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -8958978968711217/2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal 50000000000000000548953181472022770870246154838655923168405341451578792702455745768581664489247344449530624834860586257805795141871570044164153504599073023015635832251466513592848744849794279521669192233082500589213448813106472588814045597893353729061391985085892207552645901446603936636487442857715111559168 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -1668739871813211/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -5539569662801113/553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -1668739871813211/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 #s(literal -2 binary64) J) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -5539569662801113/553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -5539569662801113/553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -10000000000000000329886110340869674854270880115045078636847583141738025727786089878914788718586324412860117381629402398400588202211517615861824081167237790591132705927077058380451118207922609574937392980048643791654301923722148311225012721166820834263125344653917287293299907083743789056 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -5539569662801113/553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) #s(approx (+ ( -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) (* U U)))) -1) #s(literal -1 binary64))))))
(if (<=.f64 U #s(literal 1224979098644775/144115188075855872 binary64)) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 #s(literal -2 binary64) J))) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

soundness553.0ms (5.2%)

Memory

32.0MiB live, 506.9MiB allocated

Rules

19 354×	`lower-fma.f64`
19 354×	`lower-fma.f32`
15 380×	`lower-fma.f64`
15 380×	`lower-fma.f32`
9 384×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	750	16214
1	2523	15795
0	9142	14826
0	360	3717
1	1153	3609
2	4514	3477
0	8499	3319

Stop Event

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

Compiler

Compiled 755 to 273 computations (63.8% saved)

preprocess124.0ms (1.2%)

Memory

-20.6MiB live, 269.4MiB allocated

Remove

(negabs J)

(abs K)

Compiler

Compiled 1 722 to 358 computations (79.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze356.0ms (3.4%)

sample1.6s (15.4%)

explain296.0ms (2.8%)

preprocess104.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify46.0ms (0.4%)

localize76.0ms (0.7%)

series50.0ms (0.5%)

simplify357.0ms (3.4%)

rewrite262.0ms (2.5%)

eval68.0ms (0.6%)

prune68.0ms (0.6%)

simplify179.0ms (1.7%)

localize243.0ms (2.3%)

series120.0ms (1.1%)

simplify473.0ms (4.5%)

rewrite426.0ms (4%)

eval432.0ms (4.1%)

prune335.0ms (3.2%)

simplify374.0ms (3.5%)

localize403.0ms (3.8%)

series119.0ms (1.1%)

simplify406.0ms (3.8%)

rewrite287.0ms (2.7%)

eval133.0ms (1.2%)

prune152.0ms (1.4%)

simplify285.0ms (2.7%)

localize480.0ms (4.5%)

series98.0ms (0.9%)

simplify728.0ms (6.8%)

rewrite273.0ms (2.6%)

eval140.0ms (1.3%)

prune252.0ms (2.4%)

regimes97.0ms (0.9%)

regimes31.0ms (0.3%)

regimes13.0ms (0.1%)

regimes109.0ms (1%)

regimes11.0ms (0.1%)

regimes4.0ms (0%)

regimes9.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch2.0ms (0%)

bsearch3.0ms (0%)

simplify17.0ms (0.2%)

soundness553.0ms (5.2%)

preprocess124.0ms (1.2%)

end0.0ms (0%)

Profiling