Metrics for Maksimov and Kolovsky, Equation (3)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze298.0ms (2.7%)

Memory

37.2MiB live, 343.6MiB 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)

sample1.7s (15%)

Memory

-30.3MiB live, 2 249.3MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 949.0ms

ival-mult: 357.0ms (37.6% of total)

ival-cos: 237.0ms (25% of total)

ival-div: 139.0ms (14.6% of total)

ival-pow2: 83.0ms (8.7% of total)

ival-sqrt: 56.0ms (5.9% of total)

ival-add: 55.0ms (5.8% of total)

exact: 12.0ms (1.3% of total)

ival-true: 7.0ms (0.7% of total)

ival-assert: 4.0ms (0.4% of total)

Bogosity

explain220.0ms (2%)

Memory

2.3MiB live, 436.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
42	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))))`
31	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	132	(1.3323943758772344e-160 1.4839255463963041e+113 9.563961151730781e+63)	-	`(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	132	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	42	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	31
↳	`(/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))`	overflow	31
↳	`(+.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	73
↳	`(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))`	overflow	73
`*.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**	31	0

Confusion

	Predicted +	Predicted -
+	73	0
-	93	90

Precision

0.4397590361445783

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	73	0	0
-	93	0	90

Precision?

0.4397590361445783

Recall?

1.0

Freqs

test

number	freq
0	90
1	127
2	39

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

73.0ms

512×

valid

Compiler

Compiled 251 to 55 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 15.0ms (29.5% of total)

ival-cos: 12.0ms (23.6% of total)

ival-pow2: 8.0ms (15.7% of total)

ival-div: 7.0ms (13.8% of total)

ival-sqrt: 6.0ms (11.8% of total)

ival-add: 2.0ms (3.9% of total)

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

exact: 1.0ms (2% of total)

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

preprocess112.0ms (1%)

Memory

32.1MiB live, 71.2MiB 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 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 (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)))) J)

Symmetry

(abs U)

(abs K)

(negabs J)

Compiler

Compiled 27 to 17 computations (37% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.9%	(.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

▶

72.9%

(*.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)

simplify49.0ms (0.4%)

Memory

-17.4MiB live, 29.0MiB 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 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 (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)))) J)
(.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))
#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 (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)))
(+.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 (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))
#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)

localize50.0ms (0.4%)

Memory

21.4MiB live, 90.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.12109375	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
accuracy	0.21941376953688402	(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
accuracy	7.354059344341033	(.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	9.917381397466446	(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

37.0ms

256×

valid

Compiler

Compiled 112 to 19 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 7.0ms (31.5% of total)

ival-cos: 6.0ms (27% of total)

ival-div: 3.0ms (13.5% of total)

ival-sqrt: 2.0ms (9% of total)

ival-pow2: 2.0ms (9% of total)

ival-add: 1.0ms (4.5% of total)

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

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

exact: 0.0ms (0% of total)

series57.0ms (0.5%)

Memory

-31.8MiB live, 60.5MiB 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 (* -2 (* J (cos (* 1/2 K)))) (taylor 0 U) (#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 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))) (taylor 0 U) (#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 (* 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)))))))) (taylor 0 U) (#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 (* 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)))))))) (taylor 0 U) (#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 (taylor 0 U) (#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>) () ())) ())
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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 (.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 (* 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 (.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 (* -2 J) (taylor -inf J) (#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())) ())
#s(alt (* -2 J) (taylor -inf J) (#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())) ())
#s(alt (* -2 J) (taylor -inf J) (#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())) ())
#s(alt (* -2 J) (taylor -inf J) (#s(alt (.f64 #s(literal -2 binary64) J) (patch (.f64 #s(literal -2 binary64) J) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))) (taylor -inf J) (#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 (+ (* -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)))))) (taylor -inf J) (#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 (+ (* -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))))))) (taylor -inf J) (#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>) () ())) ())
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#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>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
18.0ms	J	@	inf	((* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))
6.0ms	J	@	0	((* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))
6.0ms	K	@	0	((* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))
6.0ms	U	@	0	((* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (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)))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))

simplify209.0ms (1.9%)

Memory

33.9MiB live, 259.4MiB 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	4535	3477
0	8519	3319

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 155

Calls

Call 1

Inputs
(* -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
(+ 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)))))))
(* 1/4 (/ (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 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))
(* 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))))))
(* 1/4 (/ (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))))
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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(* -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)))))
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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))))
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(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* -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))))))))))))
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(+ (* -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)
(+ (* -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))))))))
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 (* 1/4 (/ (pow U 2) (pow J 2)))))
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(+ (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)))))))))))))
(* 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))))))))))
(* -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))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(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))))
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(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(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))))))
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(* -1 U)
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(+ (* -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))))
(* -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)
(* 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)
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
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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))))))))
(* -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)
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)))))))
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(* -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 (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)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
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(+ 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)))))))
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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))))

Outputs
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))
(+ (* -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 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 J J) J))) U) U (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U)))
(+ (* -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 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 (fma.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64)) (pow.f64 J #s(literal 5 binary64)))) #s(literal -1/512 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 J J) J)))) (.f64 U U) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (.f64 U U)))
1
#s(literal 1 binary64)
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(fma.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 (.f64 J J) (.f64 J J)))) #s(literal -1/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J)))) (.f64 U U) #s(literal 1 binary64))
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(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (/.f64 #s(literal -1/128 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 (.f64 J J) (.f64 J J))))) (.f64 U U) (/.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J)))) (*.f64 U U) #s(literal 1 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
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(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
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(.f64 (fma.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64) (fma.f64 (/.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)))) #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (.f64 J J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))) J)
(* 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 (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 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64) (fma.f64 (/.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)))) #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (.f64 J J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))))) J)
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 (.f64 J J) (.f64 J J)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64)))
(+ 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)))))))
(fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (fma.f64 (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 (.f64 J J) (.f64 J J)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) #s(literal -1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) 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)))))))
(.f64 (neg.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 (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) #s(literal 1/4 binary64) (.f64 #s(literal 2 binary64) (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)))) (+ (* 1/512 (/ (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))))))))
(.f64 (neg.f64 J) (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 -1/64 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 (/.f64 (.f64 U U) (.f64 (.f64 J J) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) #s(literal 1/4 binary64) (.f64 #s(literal 2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
(* -2 J)
(*.f64 J #s(literal -2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 (.f64 J J) (.f64 J J)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64)))
(+ 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)))))))
(fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (fma.f64 (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (.f64 (.f64 J J) (.f64 J J)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))) #s(literal 1/4 binary64))

rewrite296.0ms (2.7%)

Memory

-27.9MiB live, 235.9MiB 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
(.f64 (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) (pow.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal -1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) (neg.f64 (cos.f64 (.f64 K #s(literal -1/2 binary64))))) (*.f64 #s(literal 2 binary64) J))
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) #s(literal -1 binary64)) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) (.f64 #s(literal 2 binary64) J)) (neg.f64 (cos.f64 (*.f64 K #s(literal -1/2 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) #s(literal 2 binary64)) (.f64 (neg.f64 J) (cos.f64 (*.f64 K #s(literal -1/2 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) J) (.f64 (cos.f64 (*.f64 K #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) #s(literal -2 binary64)) J) (cos.f64 (*.f64 K #s(literal -1/2 binary64))))
(.f64 (.f64 (cos.f64 (.f64 K #s(literal -1/2 binary64))) #s(literal -2 binary64)) (.f64 J (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal -1/2 binary64))) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)))) J)
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal -1/2 binary64))) J) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) #s(literal -2 binary64)) (.f64 (cos.f64 (*.f64 K #s(literal -1/2 binary64))) J))
(.f64 (pow.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal -1/2 binary64))))))
(.f64 (.f64 J #s(literal -2 binary64)) (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) (cos.f64 (*.f64 K #s(literal -1/2 binary64)))))
(.f64 (neg.f64 (cos.f64 (.f64 K #s(literal -1/2 binary64)))) (.f64 (.f64 #s(literal 2 binary64) J) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64)))))
(.f64 (.f64 (cos.f64 (.f64 K #s(literal -1/2 binary64))) J) (.f64 (sqrt.f64 (fma.f64 U (/.f64 U (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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 binary64))) #s(literal -2 binary64)))
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(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) J) U) (cos.f64 (*.f64 K #s(literal -1/2 binary64)))))) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (*.f64 K #s(literal -1/2 binary64)))))) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))))) #s(literal 2 binary64)))

eval97.0ms (0.9%)

Memory: -19.9MiB live, 137.8MiB allocated
Compiler: Compiled 16 532 to 1 737 computations (89.5% saved)

prune104.0ms (0.9%)

Memory

16.9MiB live, 95.8MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	464	15	479
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	465	15	480

Accuracy

99.9%

Counts

480 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.1%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))) (.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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)))))
	38.4%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))))) (+.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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)))))
▶	62.3%	(.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) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
▶	69.5%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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))))))))))
	68.2%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 U (.f64 (.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 #s(literal 2 binary64) J) U)) (.f64 #s(literal 2 binary64) J))))))
	13.6%	(.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 #s(literal -1/2 binary64) U) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J))))
	52.4%	(.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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	36.8%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #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)))))
	39.1%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.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)))))
▶	48.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
▶	26.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
	11.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
	33.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	51.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
▶	39.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Compiler

Compiled 890 to 568 computations (36.2% saved)

simplify228.0ms (2%)

Memory

5.7MiB live, 154.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
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) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
cost-diff	128	(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))
cost-diff	5504	(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64))
cost-diff	0	(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))
cost-diff	0	(fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
cost-diff	0	(fma.f64 #s(literal -1/8 binary64) (*.f64 K K) #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (*.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))))))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 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	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	384	(/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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	512	(.f64 #s(literal 2 binary64) (.f64 K #s(literal -1/2 binary64)))
cost-diff	704	(.f64 (.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J))

Rules

17 972×	`lower-fma.f32`
17 964×	`lower-fma.f64`
3 608×	`lower-*.f32`
3 560×	`lower-*.f64`
2 762×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	766
0	130	766
1	224	750
2	507	732
3	1481	717
4	3584	717
5	3810	717
6	4404	717
7	5787	717
8	6229	717
9	6337	717
10	7438	717
11	7488	717
12	7524	717
0	8296	709

Stop Event

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

localize339.0ms (3%)

Memory

18.4MiB live, 420.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.21941376953688402	(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64))
accuracy	7.354059344341033	(.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) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
accuracy	9.917381397466446	(sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64))))
accuracy	29.98389789280136	#s(approx (cos (/ K 2)) #s(literal 1 binary64))
accuracy	0.0546875	(fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))
accuracy	0.12109375	(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)
accuracy	8.254161355347907	(/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))
accuracy	30.543932015839736	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
accuracy	9.90256804546739	(sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))
accuracy	13.650854093763256	(.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64)))
accuracy	21.80226020938218	(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (*.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))))))
accuracy	26.001628790741336	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
accuracy	0	(neg.f64 U)
accuracy	39.000759874190194	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
accuracy	0.43341862432905487	(+.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	4.216624146446692	(.f64 (.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J))
accuracy	7.354059344341033	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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	9.917381397466446	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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)))))))))

Samples

164.0ms	69×	1	valid
93.0ms	187×	0	valid

Compiler

Compiled 698 to 67 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 215.0ms

ival-cos: 65.0ms (30.2% of total)

ival-mult: 47.0ms (21.8% of total)

ival-add: 38.0ms (17.7% of total)

ival-sqrt: 37.0ms (17.2% of total)

ival-div: 18.0ms (8.4% of total)

adjust: 5.0ms (2.3% of total)

ival-pow2: 3.0ms (1.4% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

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

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

series194.0ms (1.7%)

Memory

4.0MiB live, 341.7MiB allocated

Counts

26 → 720

Calls

Call 1

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

Outputs
#s(alt (* 1/4 (/ (pow U 2) (pow J 2))) (taylor 0 U) (#s(alt (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (patch (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (pow J 2))) (taylor 0 U) (#s(alt (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (patch (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (pow J 2))) (taylor 0 U) (#s(alt (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (patch (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (pow J 2))) (taylor 0 U) (#s(alt (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (patch (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (taylor 0 U) (#s(alt (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (taylor 0 U) (#s(alt (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (taylor 0 U) (#s(alt (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (taylor 0 U) (#s(alt (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (* -2 (* J (cos (* 1/2 K)))) (taylor 0 U) (#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 (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))) (taylor 0 U) (#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 (+ (* -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)))))))) (taylor 0 U) (#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 (+ (* -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)))))))) (taylor 0 U) (#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 (* -1 U) (taylor 0 U) (#s(alt (neg.f64 U) (patch (neg.f64 U) #<representation binary64>) () ())) ())
#s(alt (* -1 U) (taylor 0 U) (#s(alt (neg.f64 U) (patch (neg.f64 U) #<representation binary64>) () ())) ())
#s(alt (* -1 U) (taylor 0 U) (#s(alt (neg.f64 U) (patch (neg.f64 U) #<representation binary64>) () ())) ())
#s(alt (* -1 U) (taylor 0 U) (#s(alt (neg.f64 U) (patch (neg.f64 U) #<representation binary64>) () ())) ())
#s(alt (* -2 (* J (cos (* 1/2 K)))) (taylor 0 U) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 1/32 (/ (* (pow K 2) (pow U 2)) J)) (taylor -inf J) (#s(alt (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (patch (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/32 (/ (* (pow K 2) (pow U 2)) J)) (taylor -inf J) (#s(alt (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (patch (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf J) (#s(alt (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2)))) (taylor -inf J) (#s(alt (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2))))) (taylor -inf J) (#s(alt (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2)))))) (taylor -inf J) (#s(alt (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))) (taylor -inf J) (#s(alt (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) (patch (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))) (taylor -inf J) (#s(alt (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) (patch (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))) (taylor -inf J) (#s(alt (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) (patch (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) #<representation binary64>) () ())) ())
#s(alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))) (taylor -inf J) (#s(alt (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) (patch (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) (patch (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) (patch (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) (patch (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt (* J (cos (* 1/2 K))) (taylor -inf J) (#s(alt (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) (patch (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf J) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))) (taylor -inf J) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 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)))))) (taylor -inf J) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 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))))))) (taylor -inf J) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
18.0ms	J	@	-inf	((* (* (/ U (* 2 J)) U) (/ 1/2 J)) (* 2 (* K -1/2)) (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg U) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (+ (* -1/8 (* K K)) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (cos (* K 1/2)) -2) (cos (* K 1/2)) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J)) (* (cos (* K 1/2)) J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
15.0ms	U	@	-inf	((* (* (/ U (* 2 J)) U) (/ 1/2 J)) (* 2 (* K -1/2)) (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg U) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (+ (* -1/8 (* K K)) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (cos (* K 1/2)) -2) (cos (* K 1/2)) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J)) (* (cos (* K 1/2)) J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
15.0ms	K	@	inf	((* (* (/ U (* 2 J)) U) (/ 1/2 J)) (* 2 (* K -1/2)) (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg U) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (+ (* -1/8 (* K K)) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (cos (* K 1/2)) -2) (cos (* K 1/2)) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J)) (* (cos (* K 1/2)) J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
13.0ms	U	@	inf	((* (* (/ U (* 2 J)) U) (/ 1/2 J)) (* 2 (* K -1/2)) (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg U) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (+ (* -1/8 (* K K)) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (cos (* K 1/2)) -2) (cos (* K 1/2)) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J)) (* (cos (* K 1/2)) J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
12.0ms	J	@	0	((* (* (/ U (* 2 J)) U) (/ 1/2 J)) (* 2 (* K -1/2)) (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg U) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (+ (* -1/8 (* K K)) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (cos (* K 1/2)) -2) (cos (* K 1/2)) (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2) (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2)))))))) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J)) (* (cos (* K 1/2)) J) (cos (/ K 2)) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify251.0ms (2.2%)

Memory

-5.4MiB live, 508.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 388×	`lower-fma.f64`
8 388×	`lower-fma.f32`
7 084×	`lower-+.f64`
7 084×	`lower-+.f32`
7 064×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1051	20269
1	3571	19746
0	8208	18533

Stop Event

1×	iter limit
1×	node limit

Counts

720 → 715

Calls

Call 1

Inputs
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* -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)
(* -1 U)
(* -1 U)
(* -1 U)
(* -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))))))))
(* -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))))))))))
(* J (+ 1 (* -1/8 (pow K 2))))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)))))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (+ (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)) (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (* -1/256 (/ (pow K 2) (pow J 3)))))))))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (+ (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)) (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (+ (* -1/256 (/ (pow K 2) (pow J 3))) (* (pow U 2) (+ (* 3/4096 (/ (pow K 2) (pow J 5))) (* 1/1024 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 5))))))))))))
(* -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))))))))
(* -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)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
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(* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3))))))))
(* -1 (* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))))))))
(* 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))
(* -1/2 (/ U J))
(* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -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 K)
(* -1 K)
(* -1 K)
(* -1 K)
(* 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
(+ 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)))
(* -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 (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 (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))))))))))))
(* J (sqrt (+ 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)))))))))))
(+ (* 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)))))))))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* -1/8 (pow K 2)))
(* -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) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 J)))))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (+ (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))) (* (pow K 2) (+ (* 1/23040 J) (* 1/4 (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))))))))
-2
(- (* 1/4 (pow K 2)) 2)
(- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)
(- (* (pow K 2) (+ 1/4 (* (pow K 2) (- (* 1/23040 (pow K 2)) 1/192)))) 2)
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)))
(* 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 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* 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 (+ (* 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)))))))))))
(* -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)
(+ (* -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))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
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(+ 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)))))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* -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 (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 (+ 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)))))))))
(* J (+ 1 (* -1/8 (pow K 2))))
(* -1 (* J (+ (* -1 (+ 1 (* -1/8 (pow K 2)))) (+ (* -1/8 (/ (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))) (pow J 2))) (* -1/32 (/ (* (pow K 2) (pow U 2)) (pow J 2)))))))
(* -1 (* J (+ (* -1 (+ 1 (* -1/8 (pow K 2)))) (+ (* -1/8 (/ (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))) (pow J 2))) (+ (* -1/32 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (+ (* 1/256 (/ (* (pow K 2) (pow U 4)) (pow J 4))) (* 1/128 (/ (* (pow U 4) (+ 1 (* -1/8 (pow K 2)))) (pow J 4)))))))))
(* -1 (* J (+ (* -1 (+ 1 (* -1/8 (pow K 2)))) (+ (* -1/8 (/ (* (pow U 2) (+ 1 (* -1/8 (pow K 2)))) (pow J 2))) (+ (* -1/32 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (+ (* -1/1024 (/ (* (pow U 6) (+ 1 (* -1/8 (pow K 2)))) (pow J 6))) (+ (* 1/256 (/ (* (pow K 2) (pow U 4)) (pow J 4))) (+ (* 1/128 (/ (* (pow U 4) (+ 1 (* -1/8 (pow K 2)))) (pow J 4))) (* 1/64 (/ (* (pow K 2) (* (pow U 2) (+ (* -1/16 (pow U 4)) (* 1/64 (pow U 4))))) (pow J 6)))))))))))
(* -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 (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 (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* 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
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(* -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 (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 U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))))
(* 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
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 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)))
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)))))))

Outputs
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (*.f64 J J))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (*.f64 J J))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (*.f64 J J))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (*.f64 J J))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(fma.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))
(+ (* -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 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 J J) J))) #s(literal 1/64 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (.f64 U U) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(+ (* -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 (fma.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64)) (pow.f64 J #s(literal 5 binary64)))) #s(literal -1/512 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 J J) J)))) (.f64 U U) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (.f64 U U) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(* -1 U)
(neg.f64 U)
(* -1 U)
(neg.f64 U)
(* -1 U)
(neg.f64 U)
(* -1 U)
(neg.f64 U)
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(fma.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))
(+ (* -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 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 J J) J))) #s(literal 1/64 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (.f64 U U) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(+ (* -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 (fma.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64)) (pow.f64 J #s(literal 5 binary64)))) #s(literal -1/512 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 J J) J)))) (.f64 U U) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (.f64 U U) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(.f64 (.f64 (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal -2 binary64))
(+ (* -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))))))
(.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (/.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 K K) J) #s(literal 1/32 binary64))) (.f64 U U) (.f64 (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) 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)))))))
(fma.f64 (.f64 #s(literal -2 binary64) J) (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (/.f64 (.f64 K K) (.f64 (.f64 J J) J)) #s(literal -1/256 binary64) (/.f64 (.f64 #s(literal -1/128 binary64) (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))) (.f64 (.f64 J J) J))) (.f64 U U) (fma.f64 (/.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 K K) J) #s(literal 1/32 binary64))))) (.f64 U U)))
(+ (* -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))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) (fma.f64 (fma.f64 (/.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) (pow.f64 J #s(literal 5 binary64))) #s(literal 1/1024 binary64) (/.f64 (.f64 #s(literal 3/4096 binary64) (.f64 K K)) (pow.f64 J #s(literal 5 binary64)))) (.f64 U U) (fma.f64 (/.f64 (.f64 K K) (.f64 (.f64 J J) J)) #s(literal -1/256 binary64) (/.f64 (.f64 #s(literal -1/128 binary64) (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))) (.f64 (.f64 J J) J))))) (.f64 U U) (.f64 (fma.f64 (/.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 K K) J) #s(literal 1/32 binary64))) #s(literal -2 binary64))) (.f64 U U) (.f64 (.f64 (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal -2 binary64)))
(* J (+ 1 (* -1/8 (pow K 2))))
(.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 K K) J) #s(literal 1/32 binary64))) (.f64 U U) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (+ (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)) (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (* -1/256 (/ (pow K 2) (pow J 3)))))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 K K) (.f64 (.f64 J J) J)) #s(literal -1/256 binary64) (/.f64 (.f64 #s(literal -1/128 binary64) (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))) (.f64 (.f64 J J) J))) (.f64 U U) (fma.f64 (/.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J) #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 K K) J) #s(literal 1/32 binary64)))) (.f64 U U) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (+ (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)) (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (+ (* -1/256 (/ (pow K 2) (pow J 3))) (* (pow U 2) (+ (* 3/4096 (/ (pow K 2) (pow J 5))) (* 1/1024 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 5))))))))))))
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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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(* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2))))))
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(* U (+ (* -1/8 (/ (* (pow J 2) (pow K 2)) (pow U 2))) (+ (* 1/16 (pow K 2)) (+ (* 1/2 (+ 1 (* -1/8 (pow K 2)))) (/ (* (pow J 2) (+ 1 (* -1/8 (pow K 2)))) (pow U 2))))))
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(* U (+ (* -1 (/ (* (pow J 4) (+ 1 (* -1/8 (pow K 2)))) (pow U 4))) (+ (* -1/8 (/ (* (pow J 2) (pow K 2)) (pow U 2))) (+ (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (* (pow J 2) (pow U 4)))) (+ (* 1/16 (pow K 2)) (+ (* 1/2 (+ 1 (* -1/8 (pow K 2)))) (/ (* (pow J 2) (+ 1 (* -1/8 (pow K 2)))) (pow U 2))))))))
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(* U (+ (* -1 (/ (* (pow J 4) (+ 1 (* -1/8 (pow K 2)))) (pow U 4))) (+ (* -1/8 (/ (* (pow J 2) (pow K 2)) (pow U 2))) (+ (* -1/128 (/ (* (pow K 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6)))) (* (pow J 2) (pow U 4)))) (+ (* -1/128 (/ (* (pow K 2) (+ (* 2 (* (pow J 2) (+ (* -64 (pow J 6)) (* 16 (pow J 6))))) (* 256 (pow J 8)))) (* (pow J 2) (pow U 6)))) (+ (* 1/16 (pow K 2)) (+ (* 1/2 (+ 1 (* -1/8 (pow K 2)))) (+ (* 2 (/ (* (pow J 6) (+ 1 (* -1/8 (pow K 2)))) (pow U 6))) (/ (* (pow J 2) (+ 1 (* -1/8 (pow K 2)))) (pow U 2))))))))))
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(* -1 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 (- (+ (* -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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(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
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(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
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(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
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(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
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(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
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(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
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(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
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(* 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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(* 1/2 (* (/ U J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))
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(* U (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))))
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(* U (+ (* -1 (* (/ (pow J 3) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K)))))))))
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(* U (+ (* -1 (* (/ (pow J 3) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (+ (* 2 (* (/ (pow J 5) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 5)))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))))))
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(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))
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(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))))
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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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(* 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)))))))
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(* J (+ 1 (* -1/8 (pow K 2))))
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(* J (+ 1 (+ (* -1/8 (pow K 2)) (+ (* -1/128 (/ (* (pow U 4) (+ 1 (* -1/8 (pow K 2)))) (pow J 4))) (+ (* -1/256 (/ (* (pow K 2) (pow U 4)) (pow J 4))) (+ (* 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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(* J (+ 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))) (+ (* -1/128 (/ (* (pow U 4) (+ 1 (* -1/8 (pow K 2)))) (pow J 4))) (+ (* -1/256 (/ (* (pow K 2) (pow U 4)) (pow J 4))) (+ (* 1/1024 (/ (* (pow U 6) (+ 1 (* -1/8 (pow K 2)))) (pow J 6))) (+ (* 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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(* 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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(* 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)))))))
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(* 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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(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))))))
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(.f64 (neg.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 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/64 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 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))))))))
(.f64 (neg.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 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/64 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 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 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 (neg.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 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/64 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 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))))))))
(.f64 (neg.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 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/64 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 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 J J))) #s(literal 1 binary64))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K)))))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (*.f64 J J)))) #s(literal 1 binary64))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J))))) #s(literal 1 binary64))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K)))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 (pow.f64 U #s(literal 4 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/64 binary64) (fma.f64 (/.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))))
(.f64 (neg.f64 J) (fma.f64 (/.f64 (.f64 (pow.f64 U #s(literal 4 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/64 binary64) (fma.f64 #s(literal 1/512 binary64) (/.f64 (.f64 (pow.f64 U #s(literal 6 binary64)) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 J #s(literal 6 binary64)))) (fma.f64 (/.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(.f64 (.f64 (.f64 K K) (/.f64 (.f64 U U) J)) #s(literal 1/32 binary64))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(.f64 (.f64 (.f64 K K) (/.f64 (.f64 U U) J)) #s(literal 1/32 binary64))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(.f64 (.f64 (.f64 K K) (/.f64 (.f64 U U) J)) #s(literal 1/32 binary64))
(* 1/32 (/ (* (pow K 2) (pow U 2)) J))
(.f64 (.f64 (.f64 K K) (/.f64 (.f64 U U) J)) #s(literal 1/32 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64))) #s(literal -1/128 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (*.f64 J J))) #s(literal 1 binary64))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64))) #s(literal 1/1024 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (*.f64 J J)))) #s(literal 1 binary64))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))
(* J (cos (* 1/2 K)))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)
(* J (cos (* 1/2 K)))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)
(* J (cos (* 1/2 K)))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)
(* J (cos (* 1/2 K)))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 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))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))) #s(literal 1 binary64))
(+ 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)))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))))) #s(literal 1 binary64))

rewrite272.0ms (2.4%)

Memory

2.0MiB live, 372.0MiB allocated

Rules

5 782×	`lower-*.f32`
5 734×	`lower-*.f64`
3 624×	`lower-fma.f32`
3 616×	`lower-fma.f64`
2 874×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	508
0	130	508
1	418	483
2	2826	445
0	8570	441

Stop Event

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

Counts

26 → 491

Calls

Call 1

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

Outputs
(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 U (*.f64 J #s(literal 2 binary64)))) U)
(.f64 (/.f64 (neg.f64 U) (.f64 J #s(literal 2 binary64))) (/.f64 (neg.f64 U) (*.f64 J #s(literal 2 binary64))))
(.f64 (/.f64 U (.f64 #s(literal -2 binary64) J)) (/.f64 U (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (/.f64 #s(literal 1 binary64) J))
(.f64 (/.f64 #s(literal 1/2 binary64) J) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U))
(.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) J) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)))
(.f64 (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) (/.f64 #s(literal 1/2 binary64) J))
(.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (/.f64 U (*.f64 J #s(literal 2 binary64))))
(.f64 U (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)))
(.f64 U (.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 U (*.f64 J #s(literal 2 binary64)))))
(pow.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) U) (/.f64 (*.f64 J #s(literal 2 binary64)) U)) #s(literal -1 binary64))
(pow.f64 (/.f64 J (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) U) #s(literal -2 binary64))
(pow.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U)) (neg.f64 J))
(/.f64 (.f64 (.f64 U #s(literal 1/2 binary64)) (/.f64 U (*.f64 J #s(literal 2 binary64)))) J)
(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) J) (.f64 U U)) (*.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) (.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal -1/2 binary64)) (neg.f64 J))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (.f64 J #s(literal 2 binary64)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U))) (neg.f64 J))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 U U)) (.f64 (.f64 #s(literal -2 binary64) J) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 U U)) (.f64 (neg.f64 J) (.f64 J #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 U U) #s(literal 1 binary64)) (.f64 (.f64 #s(literal -2 binary64) J) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (.f64 (.f64 U U) #s(literal -1/2 binary64)) (.f64 (.f64 J #s(literal 2 binary64)) (neg.f64 J)))
(/.f64 (.f64 (.f64 U U) #s(literal 1/2 binary64)) (.f64 (.f64 J #s(literal 2 binary64)) J))
(/.f64 (.f64 (neg.f64 U) (/.f64 U (.f64 J #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U)) J)
(/.f64 #s(literal 1 binary64) (/.f64 J (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U))))
(/.f64 (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) (*.f64 J #s(literal 2 binary64)))
(/.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (/.f64 (.f64 J #s(literal 2 binary64)) U))
(.f64 (.f64 K #s(literal 2 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal -1 binary64) K)
(.f64 (.f64 #s(literal -1/2 binary64) K) #s(literal 2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 K #s(literal 2 binary64)))
(*.f64 K #s(literal -1 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) K))
(neg.f64 K)
(-.f64 #s(literal 0 binary64) K)
(.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) J))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal 1/2 binary64))))
(.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64)))) (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (fma.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64)))))
(.f64 (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) #s(literal 1 binary64))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1/2 binary64) J) (.f64 (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)))
(.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (.f64 U (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))))
(.f64 U (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))))
(pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) J)
(/.f64 (.f64 (.f64 U U) (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))) (.f64 J #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) #s(literal 1 binary64)) (*.f64 J (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64)))))) (neg.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64))))) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))
(/.f64 (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))) (neg.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64)))) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) (.f64 (.f64 J #s(literal 2 binary64)) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64))))) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (.f64 J #s(literal 2 binary64)))) (neg.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 J (*.f64 J #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(*.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal 1/2 binary64)))))
(.f64 (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) K)) (cos.f64 (*.f64 #s(literal -1/2 binary64) K)))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 K) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) K)) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 K) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 K) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 K)))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 K) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 K) #s(literal 1/2 binary64)))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 K))))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) K))) #s(literal 2 binary64)))
(+.f64 (*.f64 (cos.f64 K) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 (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)))) (neg.f64 U))
(*.f64 #s(literal -1 binary64) U)
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(/.f64 (sqrt.f64 (+.f64 (pow.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (/.f64 (.f64 J #s(literal 2 binary64)) U)) #s(literal -6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (/.f64 (.f64 J #s(literal 2 binary64)) U)) #s(literal -6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (-.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (-.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (/.f64 (.f64 J #s(literal 2 binary64)) U)) #s(literal -6 binary64)) #s(literal 1 binary64)))))
(sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log1p.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))) #s(literal 1/2 binary64)))

eval184.0ms (1.7%)

Memory: 26.7MiB live, 292.8MiB allocated
Compiler: Compiled 50 451 to 2 974 computations (94.1% saved)

prune175.0ms (1.6%)

Memory

-19.3MiB live, 322.0MiB allocated

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	1 233	23	1 256
Fresh	4	6	10
Picked	4	1	5
Done	0	0	0
Total	1 241	30	1 271

Accuracy

99.9%

Counts

1 271 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.1%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))) (.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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)))))
	62.3%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
	60.5%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
	60.5%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #s(literal 2 binary64)) J)))))
	58.0%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
	13.6%	(.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 #s(literal -1/2 binary64) U) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J))))
	52.4%	(.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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
▶	69.5%	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
▶	47.9%	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	43.8%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
	47.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
	47.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))) J))))
	47.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
	52.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
	11.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
	21.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
	12.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
	11.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
	33.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	51.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
	22.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
▶	27.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
✓	39.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
	28.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
▶	25.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
	26.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
	30.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) J)))
	5.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
	21.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
▶	51.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))

Compiler

Compiled 1 642 to 992 computations (39.6% saved)

simplify193.0ms (1.7%)

Memory

7.7MiB live, 199.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
cost-diff	192	(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
cost-diff	0	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
cost-diff	128	(+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))
cost-diff	320	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
cost-diff	320	(fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal -1/192 binary64) J))
cost-diff	1024	(fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64))))
cost-diff	0	(.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)
cost-diff	0	#s(approx (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
cost-diff	0	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
cost-diff	320	(/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))
cost-diff	704	(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))

Rules

9 542×	`lower-fma.f32`
9 526×	`lower-fma.f64`
4 800×	`lower-+.f32`
4 798×	`lower-+.f64`
4 650×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	1026
0	166	1016
1	341	1002
2	866	989
3	2927	972
4	5195	972
5	6687	972
6	7290	972
7	7744	972
8	7845	972
0	9183	929

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))
#s(literal 1/2 binary64)
(*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 K)
K
J
(.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)
(/.f64 U (*.f64 J #s(literal 2 binary64)))
U
(*.f64 J #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
(.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64))
#s(approx (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
(.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)
(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)
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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))))
(fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))
#s(literal -2 binary64)
J
(fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))
(fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64))))
#s(literal -1/32 binary64)
(/.f64 (*.f64 U U) J)
(*.f64 U U)
U
(fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal -1/192 binary64) J))
(.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64))
#s(literal -5/384 binary64)
#s(literal 1/4 binary64)
(*.f64 #s(literal -1/192 binary64) J)
#s(literal -1/192 binary64)
(*.f64 K K)
K
(*.f64 J #s(literal 1/4 binary64))
(.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))
(/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))
(*.f64 U U)
U
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))
(.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (cos (/ K 2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
K
#s(literal 1/2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 K)
K
#s(literal 1/2 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
U

Outputs
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 U (.f64 (fma.f64 J (cos.f64 K) J) (.f64 #s(literal 2 binary64) J))) U #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (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)))) (sqrt.f64 (fma.f64 (/.f64 U (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 #s(literal 2 binary64) J))) U #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 (/.f64 U (.f64 (fma.f64 J (cos.f64 K) J) (.f64 #s(literal 2 binary64) J))) U #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))
(fma.f64 (/.f64 U (.f64 (fma.f64 J (cos.f64 K) J) (.f64 #s(literal 2 binary64) J))) U #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))
(/.f64 #s(literal 1 binary64) (fma.f64 J (cos.f64 K) J))
#s(literal 1/2 binary64)
(*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)
(*.f64 J (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 K)
K
J
(.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U)
(.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U)
(/.f64 U (*.f64 J #s(literal 2 binary64)))
(/.f64 U (*.f64 #s(literal 2 binary64) J))
U
(*.f64 J #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) J)
#s(literal 2 binary64)
#s(literal 1 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (.f64 J (.f64 #s(literal -1/8 binary64) K)) K J)) #s(literal -2 binary64)))
(.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64))
(.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (.f64 J (.f64 #s(literal -1/8 binary64) K)) K J)) #s(literal -2 binary64))
#s(approx (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
#s(approx (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (.f64 J (.f64 #s(literal -1/8 binary64) K)) K J))
(.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)
(fma.f64 (.f64 J (.f64 #s(literal -1/8 binary64) K)) K J)
(fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/8 binary64) K) K #s(literal 1 binary64))
(*.f64 K K)
K
#s(literal -1/8 binary64)
#s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (fma.f64 (/.f64 (.f64 U U) J) (fma.f64 (.f64 K K) #s(literal -5/1536 binary64) #s(literal -1/32 binary64)) (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 K K) (fma.f64 (.f64 (/.f64 U J) #s(literal -1/4 binary64)) U (*.f64 #s(literal -2 binary64) J)))))
#s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))))
#s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (fma.f64 (/.f64 (.f64 U U) J) (fma.f64 (.f64 K K) #s(literal -5/1536 binary64) #s(literal -1/32 binary64)) (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 K K) (fma.f64 (.f64 (/.f64 U J) #s(literal -1/4 binary64)) U (*.f64 #s(literal -2 binary64) J))))
(fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))
(fma.f64 (fma.f64 (/.f64 (.f64 U U) J) (fma.f64 (.f64 K K) #s(literal -5/1536 binary64) #s(literal -1/32 binary64)) (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 K K) (fma.f64 (.f64 (/.f64 U J) #s(literal -1/4 binary64)) U (*.f64 #s(literal -2 binary64) J)))
#s(literal -2 binary64)
J
(fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))
(fma.f64 (fma.f64 (/.f64 (.f64 U U) J) (fma.f64 (.f64 K K) #s(literal -5/1536 binary64) #s(literal -1/32 binary64)) (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))
(fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64))))
(fma.f64 (/.f64 (.f64 U U) J) (fma.f64 (.f64 K K) #s(literal -5/1536 binary64) #s(literal -1/32 binary64)) (.f64 J (fma.f64 (.f64 K K) #s(literal -1/192 binary64) #s(literal 1/4 binary64))))
#s(literal -1/32 binary64)
(/.f64 (*.f64 U U) J)
(*.f64 U U)
U
(fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (*.f64 J #s(literal 1/4 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal -5/1536 binary64) (/.f64 (.f64 U U) J) (.f64 #s(literal -1/192 binary64) J)) K) K (.f64 #s(literal 1/4 binary64) J))
(fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal -1/192 binary64) J))
(fma.f64 #s(literal -5/1536 binary64) (/.f64 (.f64 U U) J) (.f64 #s(literal -1/192 binary64) J))
(.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64))
(.f64 #s(literal -5/384 binary64) (/.f64 (.f64 U U) J))
#s(literal -5/384 binary64)
#s(literal 1/4 binary64)
(*.f64 #s(literal -1/192 binary64) J)
#s(literal -1/192 binary64)
(*.f64 K K)
K
(*.f64 J #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) J)
(.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64))
#s(literal -1/4 binary64)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (sqrt.f64 (fma.f64 (/.f64 U (.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) U #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (/.f64 U (.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) U #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 (/.f64 U (.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) U #s(literal 1 binary64)))
(+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))
(fma.f64 (/.f64 U (.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) U #s(literal 1 binary64))
(/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))
(/.f64 (.f64 U U) (.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)))
(*.f64 U U)
U
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))
(.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))
(.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))
(.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #s(literal -2 binary64)) J)
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
J
#s(approx (cos (/ K 2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
K
#s(literal 1/2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (neg.f64 U) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K))))))
(.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
(.f64 (.f64 (neg.f64 U) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K))))
(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
#s(literal 1 binary64)
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 K)
K
#s(literal 1/2 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
U

localize476.0ms (4.3%)

Memory

16.6MiB live, 596.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.11328125	(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
accuracy	0.16015625	(.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
accuracy	0.43341862432905487	(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	30.594059510904927	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
accuracy	7.357965594341033	(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
accuracy	9.917381397466446	(sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)))
accuracy	18.025590009198016	(/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))
accuracy	29.98389789280136	#s(approx (cos (/ K 2)) #s(literal 1 binary64))
accuracy	7.090360290212399	(fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (*.f64 J #s(literal 1/4 binary64)))
accuracy	8.247982525942996	(/.f64 (*.f64 U U) J)
accuracy	27.548327134174304	#s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))))
accuracy	30.543932015839736	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
accuracy	0	(*.f64 K K)
accuracy	3.092628920449146	(.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)
accuracy	26.001628790741336	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
accuracy	28.34963811367549	#s(approx (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
accuracy	0.43341862432905487	(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	2.1579278506291963	(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))
accuracy	7.357965594341033	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
accuracy	9.917381397466446	(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)))

Samples

233.0ms	187×	0	valid
152.0ms	69×	1	valid

Compiler

Compiled 833 to 109 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 315.0ms

ival-mult: 136.0ms (43.1% of total)

ival-div: 56.0ms (17.8% of total)

const: 40.0ms (12.7% of total)

ival-cos: 30.0ms (9.5% of total)

ival-add: 23.0ms (7.3% of total)

ival-sqrt: 15.0ms (4.8% of total)

adjust: 9.0ms (2.9% of total)

ival-pow2: 3.0ms (1% 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)

series443.0ms (4%)

Memory

-188.5MiB live, 356.8MiB allocated

Counts

28 → 816

Calls

Call 1

Inputs
#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) (patch (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)) (patch (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)) #<representation binary64>) () ())
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#s(alt (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (patch (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) #<representation binary64>) () ())
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#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64)))))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64))))) (patch #s(approx (+ ( (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))) #<representation binary64>) () ())
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#s(alt (.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) (patch (.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) (patch (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())
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#s(alt (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 K K) (patch (.f64 K K) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 U U) J) (patch (/.f64 (.f64 U U) J) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64))) (patch (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (patch #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #<representation binary64>) () ())
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#s(alt (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 U) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))) (taylor 0 U) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))) (taylor 0 U) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))) (taylor 0 U) (#s(alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* J (cos (* 1/2 K)))) (taylor 0 U) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (+ 1/2 (* 1/2 (cos K))))))) (taylor 0 U) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos K)))))) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos K))) 2))))))) (taylor 0 U) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos K)))))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 5) (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (* 1/64 (/ (cos (* 1/2 K)) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos K))) 2))))))))) (taylor 0 U) (#s(alt (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) (patch (.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J) #<representation binary64>) () ())) ())
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#s(alt (+ 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))))))) (taylor -inf J) (#s(alt (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
274.0ms	U	@	0	((+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1) (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (* (+ (* (* K K) -1/8) 1) J) (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2)))) (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ 1 (+ (* (cos K) 1/2) 1/2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (+ (* (cos K) 1/2) 1/2) (* K K) (/ (* U U) J) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4)) (cos (/ K 2)) (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)))
23.0ms	U	@	-inf	((+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1) (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (* (+ (* (* K K) -1/8) 1) J) (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2)))) (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ 1 (+ (* (cos K) 1/2) 1/2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (+ (* (cos K) 1/2) 1/2) (* K K) (/ (* U U) J) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4)) (cos (/ K 2)) (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)))
13.0ms	K	@	-inf	((+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1) (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (* (+ (* (* K K) -1/8) 1) J) (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2)))) (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ 1 (+ (* (cos K) 1/2) 1/2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (+ (* (cos K) 1/2) 1/2) (* K K) (/ (* U U) J) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4)) (cos (/ K 2)) (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)))
11.0ms	K	@	inf	((+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1) (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (* (+ (* (* K K) -1/8) 1) J) (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2)))) (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ 1 (+ (* (cos K) 1/2) 1/2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (+ (* (cos K) 1/2) 1/2) (* K K) (/ (* U U) J) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4)) (cos (/ K 2)) (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)))
10.0ms	J	@	inf	((+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1) (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (* (cos (* K 1/2)) -2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (* (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) -2) (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (* (+ (* (* K K) -1/8) 1) J) (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2)))) (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ 1 (+ (* (cos K) 1/2) 1/2)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (sqrt (+ (* (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (* (/ U (* J 2)) U)) 1)) (+ (* (cos K) 1/2) 1/2) (* K K) (/ (* U U) J) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4)) (cos (/ K 2)) (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)))

simplify253.0ms (2.3%)

Memory

-17.9MiB live, 419.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 598×	`lower-fma.f64`
9 598×	`lower-fma.f32`
6 982×	`lower-+.f64`
6 982×	`lower-+.f32`
5 594×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1368	25484
1	4652	24999
0	8647	23271

Stop Event

1×	iter limit
1×	node limit

Counts

816 → 812

Calls

Call 1

Inputs
1
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (+ 1/2 (* 1/2 (cos K)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos K)))))) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos K))) 2)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos K)))))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 5) (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (* 1/64 (/ (cos (* 1/2 K)) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos K))) 2)))))))))
(* -2 (cos (* 1/2 K)))
(+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))))
(+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos K))) 2)))))))
(+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (* 1/64 (/ (cos (* 1/2 K)) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos 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))))))))
(* -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))))))))))
(* J (+ 1 (* -1/8 (pow K 2))))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)))))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (+ (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)) (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (* -1/256 (/ (pow K 2) (pow J 3)))))))))
(+ (* J (+ 1 (* -1/8 (pow K 2)))) (* (pow U 2) (+ (* 1/32 (/ (pow K 2) J)) (+ (* 1/8 (/ (+ 1 (* -1/8 (pow K 2))) J)) (* (pow U 2) (+ (* -1/128 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 3))) (+ (* -1/256 (/ (pow K 2) (pow J 3))) (* (pow U 2) (+ (* 3/4096 (/ (pow K 2) (pow J 5))) (* 1/1024 (/ (+ 1 (* -1/8 (pow K 2))) (pow J 5))))))))))))
(+ (* -1/192 (* J (pow K 2))) (* 1/4 J))
(+ (* -1/192 (* J (pow K 2))) (+ (* 1/4 J) (* (pow U 2) (- (* -5/1536 (/ (pow K 2) J)) (* 1/32 (/ 1 J))))))
(+ (* -1/192 (* J (pow K 2))) (+ (* 1/4 J) (* (pow U 2) (- (* -5/1536 (/ (pow K 2) J)) (* 1/32 (/ 1 J))))))
(+ (* -1/192 (* J (pow K 2))) (+ (* 1/4 J) (* (pow U 2) (- (* -5/1536 (/ (pow K 2) J)) (* 1/32 (/ 1 J))))))
(* -1/192 J)
(+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J)))
(+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J)))
(+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J)))
(* -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))))))))
(* -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)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
1
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 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))))))))
(* -2 (cos (* 1/2 K)))
(+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))))
(+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* (pow J 2) (cos (* 1/2 K))))))))
(+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* (pow J 2) (cos (* 1/2 K))))))))
(* -2 (* J (cos (* 1/2 K))))
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(* (pow U 2) (- (+ (* -1/192 (/ (* J (pow K 2)) (pow U 2))) (+ (* -5/1536 (/ (pow K 2) J)) (* 1/4 (/ J (pow U 2))))) (* 1/32 (/ 1 J))))
(* -5/1536 (/ (pow U 2) J))
(* (pow U 2) (- (* -1/192 (/ J (pow U 2))) (* 5/1536 (/ 1 J))))
(* (pow U 2) (- (* -1/192 (/ J (pow U 2))) (* 5/1536 (/ 1 J))))
(* (pow U 2) (- (* -1/192 (/ J (pow U 2))) (* 5/1536 (/ 1 J))))
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)))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
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)))
(/ U J)
(* -1 (* U (- (* -2 (/ (* J (pow (cos (* 1/2 K)) 2)) (pow U 2))) (/ 1 J))))
(* -1 (* U (- (+ (* -2 (/ (* J (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) (/ 1 J))))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* J (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) (/ 1 J))))
(* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))
(* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))))))
(* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3))))))))
(* -1 (* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1/2 (* (/ U J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* U (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K))))))))
(* -1 (* U (+ (* -1 (* (/ (pow J 3) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))))))
(* -1 (* U (+ (* -1 (* (/ (pow J 3) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (+ (* 2 (* (/ (pow J 5) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 5)))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K))))))))))
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(* -5/1536 (/ (* (pow K 2) (pow U 2)) J))
(* (pow U 2) (+ (* -1/192 (/ (* J (pow K 2)) (pow U 2))) (+ (* -5/1536 (/ (pow K 2) J)) (* 1/4 (/ J (pow U 2))))))
(* (pow U 2) (+ (* -1/192 (/ (* J (pow K 2)) (pow U 2))) (+ (* -5/1536 (/ (pow K 2) J)) (* 1/4 (/ J (pow U 2))))))
(* (pow U 2) (+ (* -1/192 (/ (* J (pow K 2)) (pow U 2))) (+ (* -5/1536 (/ (pow K 2) J)) (* 1/4 (/ J (pow U 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))))
(* -1/2 (/ 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 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* 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 (+ (* 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)))))))))))
(/ 1/2 J)
(+ (* 1/8 (/ (pow K 2) J)) (* 1/2 (/ 1 J)))
(+ (* (pow K 2) (+ (* 1/48 (/ (pow K 2) J)) (* 1/8 (/ 1 J)))) (* 1/2 (/ 1 J)))
(+ (* (pow K 2) (+ (* (pow K 2) (+ (* 17/5760 (/ (pow K 2) J)) (* 1/48 (/ 1 J)))) (* 1/8 (/ 1 J)))) (* 1/2 (/ 1 J)))
(* -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 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))
(+ (* -2 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* -2 (* (pow K 2) (+ (* -1/8 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 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)))))))))))))) (* -2 (+ (* -1/8 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (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)))))))))) (+ (* -1/46080 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (+ (* 1/12288 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 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))))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 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))))))))))))))))))
(* -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 (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))))))))))))
(* J (sqrt (+ 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)))))))))))
(+ (* 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)))))))))))
J
(+ J (* -1/8 (* J (pow K 2))))
(+ J (* -1/8 (* J (pow K 2))))
(+ J (* -1/8 (* J (pow K 2))))
(+ (* -1/32 (/ (pow U 2) J)) (* 1/4 J))
(+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J))))))
(+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J))))))
(+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J))))))
(* -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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(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 J)))))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))
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(* 4 (pow J 2))
(+ (* -1 (* (pow J 2) (pow K 2))) (* 4 (pow J 2)))
(+ (* 4 (pow J 2)) (* (pow K 2) (+ (* -1 (pow J 2)) (* 1/12 (* (pow J 2) (pow K 2))))))
(+ (* 4 (pow J 2)) (* (pow K 2) (+ (* -1 (pow J 2)) (* (pow K 2) (+ (* -1/360 (* (pow J 2) (pow K 2))) (* 1/12 (pow J 2)))))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* 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 (+ (* 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)))))))))))
(* -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))))))))))))
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(* -2 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))
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1
(+ 1 (* 1/4 (pow K 2)))
(+ 1 (* (pow K 2) (+ 1/4 (* 1/24 (pow K 2)))))
(+ 1 (* (pow K 2) (+ 1/4 (* (pow K 2) (+ 1/24 (* 17/2880 (pow K 2)))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
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(+ (* -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))))))))))))))))
(* -1 U)
(+ (* -1 U) (* -1 (* (pow K 2) (+ (* -1/8 U) (* 1/8 U)))))
(+ (* -1 U) (* (pow K 2) (+ (* -1 (* (pow K 2) (+ (* -1/64 U) (+ (* 1/384 U) (* 5/384 U))))) (* -1 (+ (* -1/8 U) (* 1/8 U))))))
(+ (* -1 U) (* (pow K 2) (+ (* -1 (+ (* -1/8 U) (* 1/8 U))) (* (pow K 2) (+ (* -1 (* (pow K 2) (+ (* -5/3072 U) (+ (* -1/46080 U) (+ (* 1/3072 U) (* 61/46080 U)))))) (* -1 (+ (* -1/64 U) (+ (* 1/384 U) (* 5/384 U)))))))))
-1
(- (* -1/8 (pow K 2)) 1)
(- (* (pow K 2) (- (* -5/384 (pow K 2)) 1/8)) 1)
(- (* (pow K 2) (- (* (pow K 2) (- (* -61/46080 (pow K 2)) 5/384)) 1/8)) 1)
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
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(+ (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)))))))))))
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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 K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(* 1/4 J)
(+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J)))))
(+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J)))))
(+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* -5/1536 (/ (pow U 2) J)))))
1
(+ 1 (* -1/8 (pow K 2)))
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(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(* 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))))))))))
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(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))))
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(/ 1/2 (* J (+ 1/2 (* 1/2 (cos K)))))
(/ 1/2 (* J (+ 1/2 (* 1/2 (cos K)))))
(/ 1/2 (* J (+ 1/2 (* 1/2 (cos K)))))
(/ 1/2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
(* -2 (* (cos (* 1/2 K)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
(* -2 (* (cos (* 1/2 K)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
(* -2 (* (cos (* 1/2 K)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))
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1
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(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
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1
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Outputs
1
#s(literal 1 binary64)
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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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(* U (+ (* 1/16 (pow K 2)) (* 1/2 (+ 1 (* -1/8 (pow K 2))))))
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(* U (+ (* -1/8 (/ (* (pow J 2) (pow K 2)) (pow U 2))) (+ (* 1/16 (pow K 2)) (+ (* 1/2 (+ 1 (* -1/8 (pow K 2)))) (/ (* (pow J 2) (+ 1 (* -1/8 (pow K 2)))) (pow U 2))))))
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(* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3))))))))
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(* U (+ (* -1 (* (/ (pow J 3) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (+ (* 1/2 (* (/ 1 J) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* (/ J (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K))))))))
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(.f64 (neg.f64 J) (fma.f64 (.f64 (.f64 K K) (/.f64 (.f64 U U) (.f64 J J))) #s(literal 5/1536 binary64) (fma.f64 #s(literal 1/192 binary64) (.f64 K K) #s(literal -1/4 binary64))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/8 binary64) #s(literal 1 binary64)))
(+ 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)))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 U U)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J))))) #s(literal 1 binary64))

rewrite226.0ms (2%)

Memory

-14.0MiB live, 276.3MiB allocated

Rules

5 522×	`lower-*.f32`
5 478×	`lower-*.f64`
4 124×	`lower-fma.f32`
4 108×	`lower-fma.f64`
2 450×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	792
0	166	730
1	644	707
2	4785	671
0	8729	655

Stop Event

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

Counts

28 → 446

Calls

Call 1

Inputs
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
(.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64))
#s(approx (+ (* (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J))
(.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)
(fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64))))
(fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal -1/192 binary64) J))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (*.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))
(+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64)))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(*.f64 K K)
(/.f64 (*.f64 U U) J)
(fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (*.f64 J #s(literal 1/4 binary64)))
#s(approx (cos (/ K 2)) #s(literal 1 binary64))
(/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))
(sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)))

Outputs
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))))))
(.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))))))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J)))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64)) (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J)))) (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (.f64 #s(literal 2 binary64) J))) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) U) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) (*.f64 #s(literal 2 binary64) J))) U #s(literal -1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (.f64 #s(literal 4 binary64) (.f64 J J))) (/.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (*.f64 U U))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (.f64 #s(literal 4 binary64) (.f64 J J))) (/.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (*.f64 U U))))
(neg.f64 (/.f64 (.f64 (neg.f64 U) U) (.f64 (.f64 (.f64 #s(literal 4 binary64) (*.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (.f64 U U) (.f64 (neg.f64 (.f64 #s(literal 4 binary64) (.f64 J J))) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))))
(exp.f64 (-.f64 (.f64 (log.f64 U) #s(literal 2 binary64)) (.f64 (log.f64 (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #s(literal -2 binary64)) J)) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (.f64 #s(literal 4 binary64) (.f64 J J))) (/.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (.f64 U U)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 U (.f64 (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #s(literal -2 binary64)) J))) #s(literal 2 binary64)))
(.f64 (pow.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (*.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log1p.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal 4 binary64) (*.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64)) (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (*.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 (.f64 (.f64 U U) U) (.f64 (.f64 U U) U)) (.f64 (.f64 (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (/.f64 (.f64 (.f64 U U) (.f64 U U)) (.f64 (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))))))
(sqrt.f64 (fma.f64 (/.f64 U (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) U #s(literal 1 binary64)))
(exp.f64 (.f64 (log1p.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 J J)) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1/2 binary64)))

eval207.0ms (1.9%)

Memory: 47.1MiB live, 346.9MiB allocated
Compiler: Compiled 56 795 to 3 841 computations (93.2% saved)

prune186.0ms (1.7%)

Memory

-12.1MiB live, 326.4MiB allocated

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	1 429	15	1 444
Fresh	14	10	24
Picked	3	2	5
Done	0	1	1
Total	1 446	28	1 474

Accuracy

99.9%

Counts

1 474 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.1%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))) (.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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)))))
▶	62.3%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
✓	69.5%	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	58.0%	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	60.5%	(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	43.8%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
	28.8%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
▶	13.6%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
	51.0%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	52.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
	21.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
	11.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
	33.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	26.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
	27.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
	3.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
✓	39.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
	28.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
	26.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #s(literal -1/4 binary64))))))
	26.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64))))))
	26.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
	30.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) J)))
	21.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
▶	51.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
	51.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) U))
✓	51.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
▶	30.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
▶	24.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))

Compiler

Compiled 1 267 to 749 computations (40.9% saved)

simplify98.0ms (0.9%)

Memory

-11.6MiB live, 106.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
cost-diff	192	(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
cost-diff	0	(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
cost-diff	0	#s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64))
cost-diff	0	(.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
cost-diff	640	(.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (*.f64 K K))
cost-diff	640	(.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (*.f64 K K))
cost-diff	704	(fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64)))
cost-diff	704	(fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))
cost-diff	0	(/.f64 U J)
cost-diff	0	#s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J))
cost-diff	0	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
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 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
cost-diff	704	(fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))

Rules

4 502×	`lower-*.f32`
4 478×	`lower-*.f64`
3 246×	`lower-/.f32`
3 238×	`lower-/.f64`
1 852×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	605
0	117	645
1	227	601
2	640	536
3	2394	475
4	6032	475
0	8228	467

Stop Event

1×	iter limit
1×	node limit
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 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 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 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))
(fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))
(/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))
(*.f64 U #s(literal 1/2 binary64))
U
#s(literal 1/2 binary64)
(*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)
#s(approx (cos (/ K 2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
#s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J))
(/.f64 U J)
U
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U)))
(fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))
(.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (*.f64 K K))
(.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (*.f64 K K))
(neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64))))
(fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64)))
#s(literal -5/3072 binary64)
U
(*.f64 U #s(literal 5/3072 binary64))
#s(literal 5/3072 binary64)
(*.f64 K K)
K
(neg.f64 U)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
(.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))
#s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64))
#s(literal -1 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
K
#s(literal 1/2 binary64)
U
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(literal -1 binary64)
(sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 K)
K
#s(literal 1/2 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 K #s(literal 1/2 binary64))
U

Outputs
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) #s(literal 1 binary64))))
(.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))
#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 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) #s(literal 1 binary64)))
(fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))) #s(literal 1 binary64))
(/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J))
(.f64 (/.f64 U (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1/2 binary64))
(*.f64 U #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) U)
U
#s(literal 1/2 binary64)
(*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)
#s(approx (cos (/ K 2)) #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
#s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J))
(/.f64 U J)
U
J
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg.f64 U)))
#s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U)))
#s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg.f64 U))
(fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))
(neg.f64 U)
(.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (*.f64 K K))
#s(literal 0 binary64)
(.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (*.f64 K K))
#s(literal 0 binary64)
(neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64))))
#s(literal 0 binary64)
(fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64)))
#s(literal 0 binary64)
#s(literal -5/3072 binary64)
U
(*.f64 U #s(literal 5/3072 binary64))
(*.f64 #s(literal 5/3072 binary64) U)
#s(literal 5/3072 binary64)
(*.f64 K K)
K
(neg.f64 U)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) U) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))
(.f64 (.f64 #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) U) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
#s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64))
#s(literal -1 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) U)
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 K #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) K)
K
#s(literal 1/2 binary64)
U
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (neg.f64 U)) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
(/.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (neg.f64 U)) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(literal -1 binary64)
(sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 K)
K
#s(literal 1/2 binary64)
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) U)
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 K #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) K)
U

localize418.0ms (3.7%)

Memory

29.8MiB live, 604.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1328125	(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
accuracy	0.140625	(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
accuracy	0.37968859502372876	(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
accuracy	26.53863383210956	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
accuracy	0.09375	(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
accuracy	0.140625	(.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))
accuracy	22.483384466947392	#s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64))
accuracy	26.53863383210956	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
accuracy	14.76554243824885	(.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (*.f64 K K))
accuracy	14.896276425276058	(fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))
accuracy	26.53863383210956	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
accuracy	51.56075143197365	(fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64)))
accuracy	0	(/.f64 U J)
accuracy	6.655973085768339	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
accuracy	47.27208023116962	#s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J))
accuracy	0.10384750976844201	(fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))
accuracy	6.652066835768339	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
accuracy	8.038641307183495	(sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))
accuracy	25.687033338307444	#s(approx (cos (/ K 2)) #s(literal 1 binary64))

Samples

164.0ms	153×	1	valid
94.0ms	61×	2	valid
75.0ms	23×	5	exit
23.0ms	11×	4	exit
3.0ms	2×	3	exit
3.0ms	6×	0	valid

Compiler

Compiled 497 to 70 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 307.0ms

ival-mult: 70.0ms (22.8% of total)

ival-div: 52.0ms (17% of total)

const: 42.0ms (13.7% of total)

ival-sqrt: 38.0ms (12.4% of total)

adjust: 33.0ms (10.8% of total)

ival-cos: 32.0ms (10.4% of total)

ival-add: 21.0ms (6.9% of total)

ival-hypot: 13.0ms (4.2% of total)

ival-neg: 5.0ms (1.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series132.0ms (1.2%)

Memory

-17.0MiB live, 137.9MiB allocated

Counts

23 → 564

Calls

Call 1

Inputs
#s(alt (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 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 (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) (patch (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) #<representation binary64>) () ())
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#s(alt (/.f64 U J) (patch (/.f64 U J) #<representation binary64>) () ())
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#s(alt (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (patch (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (patch (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())
#s(alt #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (patch #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U) (patch (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (patch (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (cos (/ K 2)) #s(literal 1 binary64)) (patch #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U)))) (patch #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U)))) #<representation binary64>) () ())
#s(alt (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 U) (#s(alt (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))) (taylor 0 U) (#s(alt (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))) (taylor 0 U) (#s(alt (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))) (taylor 0 U) (#s(alt (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* J (cos (* 1/2 K)))) (taylor 0 U) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))) (taylor 0 U) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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)))))))) (taylor 0 U) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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)))))))) (taylor 0 U) (#s(alt (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) (patch (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* J (cos (* 1/2 K)))) (taylor 0 U) (#s(alt (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) (patch (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))) (taylor 0 U) (#s(alt (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) (patch (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) #<representation binary64>) () ())) ())
#s(alt (+ (* -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)))))))) (taylor 0 U) (#s(alt (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) (patch (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) #<representation binary64>) () ())) ())
#s(alt (+ (* -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)))))))) (taylor 0 U) (#s(alt (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) (patch (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J) #<representation binary64>) () ())) ())
#s(alt (* -2 (cos (* 1/2 K))) (taylor 0 U) (#s(alt #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) (patch #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))) (taylor 0 U) (#s(alt #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) (patch #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* (pow J 2) (cos (* 1/2 K)))))))) (taylor 0 U) (#s(alt #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) (patch #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* (pow J 2) (cos (* 1/2 K)))))))) (taylor 0 U) (#s(alt #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) (patch #s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) #<representation binary64>) () ())) ())
#s(alt (/ U J) (taylor 0 U) (#s(alt (/.f64 U J) (patch (/.f64 U J) #<representation binary64>) () ())) ())
#s(alt (/ U J) (taylor 0 U) (#s(alt (/.f64 U J) (patch (/.f64 U J) #<representation binary64>) () ())) ())
#s(alt (/ U J) (taylor 0 U) (#s(alt (/.f64 U J) (patch (/.f64 U J) #<representation binary64>) () ())) ())
#s(alt (/ U J) (taylor 0 U) (#s(alt (/.f64 U J) (patch (/.f64 U J) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (taylor inf K) (#s(alt (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (taylor inf K) (#s(alt (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))) (taylor inf K) (#s(alt #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (patch #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))) (taylor inf K) (#s(alt #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (patch #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))) (taylor inf K) (#s(alt #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (patch #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))) (taylor inf K) (#s(alt #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (patch #s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* U (cos (* 1/2 K))) (taylor inf K) (#s(alt (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U) (patch (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (taylor inf K) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (taylor inf K) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (taylor inf K) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (taylor inf K) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) (patch (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))))) (taylor inf K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))))) (taylor inf K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))))))) (taylor inf K) (#s(alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))) (patch #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))) (taylor inf K) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))) (taylor inf K) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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Calls

9 calls:

Time	Variable		Point	Expression
11.0ms	K	@	inf	((+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ U J) (+ (* (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* K K)) (neg U)) (+ (* -5/3072 U) (* U 5/3072)) (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U) (* (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (* (cos (* K 1/2)) U)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (sqrt (+ (* (cos K) 1/2) 1/2)) (cos (/ K 2)) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (+ (* (cos K) 1/2) 1/2))
6.0ms	U	@	0	((+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ U J) (+ (* (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* K K)) (neg U)) (+ (* -5/3072 U) (* U 5/3072)) (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U) (* (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (* (cos (* K 1/2)) U)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (sqrt (+ (* (cos K) 1/2) 1/2)) (cos (/ K 2)) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (+ (* (cos K) 1/2) 1/2))
6.0ms	K	@	-inf	((+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ U J) (+ (* (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* K K)) (neg U)) (+ (* -5/3072 U) (* U 5/3072)) (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U) (* (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (* (cos (* K 1/2)) U)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (sqrt (+ (* (cos K) 1/2) 1/2)) (cos (/ K 2)) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (+ (* (cos K) 1/2) 1/2))
4.0ms	U	@	inf	((+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ U J) (+ (* (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* K K)) (neg U)) (+ (* -5/3072 U) (* U 5/3072)) (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U) (* (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (* (cos (* K 1/2)) U)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (sqrt (+ (* (cos K) 1/2) 1/2)) (cos (/ K 2)) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (+ (* (cos K) 1/2) 1/2))
4.0ms	U	@	-inf	((+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (* (* -2 J) (cos (/ K 2))) (* -2 J) (* (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) J) (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/ U J) (+ (* (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* K K)) (neg U)) (+ (* -5/3072 U) (* U 5/3072)) (* (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* K K)) (* (neg (+ (* -5/3072 U) (* U 5/3072))) (* K K)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U) (* (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (* (cos (* K 1/2)) U)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/ -1 (sqrt (+ (* (cos K) 1/2) 1/2))) (sqrt (+ (* (cos K) 1/2) 1/2)) (cos (/ K 2)) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1)) (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (+ (* (cos K) 1/2) 1/2))

simplify295.0ms (2.6%)

Memory

15.2MiB live, 258.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 040×	`lower-fma.f64`
12 040×	`lower-fma.f32`
8 736×	`lower-*.f64`
8 736×	`lower-*.f32`
3 880×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	676	14847
1	2225	14122
0	8411	13237

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 561

Calls

Call 1

Inputs
1
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 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))))))))
(* -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))))))))
(* -2 (cos (* 1/2 K)))
(+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))))
(+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* (pow J 2) (cos (* 1/2 K))))))))
(+ (* -2 (cos (* 1/2 K))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* (pow J 2) (cos (* 1/2 K))))))))
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
0
0
0
0
0
0
0
0
0
0
0
0
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 5) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (* 1/64 (/ (cos (* 1/2 K)) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* U (cos (* 1/2 K)))
(* U (cos (* 1/2 K)))
(* U (cos (* 1/2 K)))
(* U (cos (* 1/2 K)))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 5) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (* 1/64 (/ (cos (* 1/2 K)) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos (* -1 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)))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) (* J (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 5) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (* 1/64 (/ (cos (* 1/2 K)) (* (pow J 3) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))) (/ 1 (pow U 2))))
(* -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))
(* -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))
(* -1 (/ U J))
(* U (- (* -2 (/ (* J (pow (cos (* 1/2 K)) 2)) (pow U 2))) (/ 1 J)))
(* U (- (+ (* -2 (/ (* J (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) (/ 1 J)))
(* U (- (+ (* -4 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* J (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) (/ 1 J)))
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
0
0
0
0
0
0
0
0
0
0
0
0
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))))
(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))))))
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(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* U (cos (* 1/2 K)))
(* U (cos (* 1/2 K)))
(* U (cos (* 1/2 K)))
(* U (cos (* 1/2 K)))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))
(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))))
(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))))))
(* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos (* -1 K))))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K)))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3))))))))
(* 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 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos (* -1 K))))))))
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U
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U
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(/ U J)
(/ U J)
(/ U J)
(/ U J)
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(* -1 U)
(* -1 U)
(* -1 U)
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(+ (* -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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(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
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(* -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 (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))
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(* -1 U)
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(* -1 (* (pow K 2) (+ (* -5/3072 U) (* 5/3072 U))))
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(* -1 (* (pow K 2) (+ (* -5/3072 U) (* 5/3072 U))))
(* -1 (* (pow K 2) (+ (* -5/3072 U) (* 5/3072 U))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
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U
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1
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(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))
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(/ U J)
(/.f64 U J)
(/ U J)
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(/ U J)
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(/ U J)
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0
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
(* -2 (* J (cos (* 1/2 K))))
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1
#s(literal 1 binary64)
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(fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64)))))
(+ (* -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))))))
(fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal 1/64 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))))))
(+ (* -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)))))))
(fma.f64 #s(literal -2 binary64) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (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 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 J #s(literal 4 binary64)) (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal 1/64 binary64) (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J J))))))
(/ U J)
(/.f64 U J)
(/ U J)
(/.f64 U J)
(/ U J)
(/.f64 U J)
(/ U J)
(/.f64 U J)
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K)))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal 1/512 binary64) (pow.f64 U #s(literal 6 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 J #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K)))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal 1/512 binary64) (pow.f64 U #s(literal 6 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 J #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1 binary64))
(+ 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))))))
(fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 J J))) #s(literal 1 binary64)))
(+ 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)))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 U #s(literal 6 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (pow.f64 J #s(literal 6 binary64)))) #s(literal 1/1024 binary64) (fma.f64 (/.f64 (pow.f64 U #s(literal 4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (pow.f64 J #s(literal 4 binary64)))) #s(literal -1/128 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 U U) (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 J J)))))) #s(literal 1 binary64))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K)))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos (* -1 K)))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos (* -1 K))))))) (* 2 (cos (* 1/2 K))))))))
(.f64 (neg.f64 J) (fma.f64 (.f64 #s(literal 1/512 binary64) (pow.f64 U #s(literal 6 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 J #s(literal 6 binary64)))) (fma.f64 (.f64 #s(literal -1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (pow.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 J #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J) J)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))))))

rewrite249.0ms (2.2%)

Memory

5.3MiB live, 194.9MiB allocated

Rules

4 242×	`lower-fma.f32`
4 234×	`lower-fma.f64`
4 116×	`lower-*.f32`
4 088×	`lower-*.f64`
3 792×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	479
0	117	431
1	390	381
2	2719	358
0	9081	355

Stop Event

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

Counts

23 → 409

Calls

Call 1

Inputs
(fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
#s(approx (* (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J))
(/.f64 U J)
(fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))
(fma.f64 #s(literal -5/3072 binary64) U (*.f64 U #s(literal 5/3072 binary64)))
(.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (*.f64 K K))
(.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (*.f64 K K))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
(.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U))
#s(approx (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) #s(literal -1 binary64))
(.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (cos (/ K 2)) #s(literal 1 binary64))
(sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))

Outputs
(.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 #s(literal 1/4 binary64) (.f64 U U))) (.f64 (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 1 binary64))))
(.f64 (+.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 U U) U) (.f64 (.f64 U U) U))) (.f64 (.f64 (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (.f64 #s(literal 1/4 binary64) (.f64 U U))) (.f64 (.f64 (.f64 (.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 (*.f64 J #s(approx (cos (/ K 2)) #s(literal 1 binary64))) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))))))
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eval259.0ms (2.3%)

Memory: 13.7MiB live, 243.6MiB allocated
Compiler: Compiled 32 032 to 2 166 computations (93.2% saved)

prune261.0ms (2.3%)

Memory

4.9MiB live, 245.1MiB allocated

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	999	9	1 008
Fresh	4	16	20
Picked	2	3	5
Done	0	3	3
Total	1 005	31	1 036

Accuracy

99.9%

Counts

1 036 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.1%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))) (.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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)))))
	62.3%	(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
✓	69.5%	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	58.0%	(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	60.5%	(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	36.5%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
	43.8%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
	28.8%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
✓	13.6%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
	13.5%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
	13.5%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
	51.0%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
	12.6%	(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 binary64)))) J)
	11.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (/.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
	52.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
	21.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
	33.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	26.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
	27.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
	3.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
✓	39.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
	28.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
	26.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64))))))
	26.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
	30.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 binary64))))) J)))
	21.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
	51.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
✓	51.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
✓	30.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
	25.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
✓	24.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))

Compiler

Compiled 2 168 to 718 computations (66.9% saved)

regimes211.0ms (1.9%)

Memory

-35.4MiB live, 177.6MiB allocated

Counts

63 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 binary64)))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (/.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 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))) (/.f64 (.f64 #s(literal -1/2 binary64) U) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.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)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 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) #s(approx (cos (/ K 2)) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #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 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #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) (/.f64 U (.f64 (.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 #s(literal 2 binary64) J) U)) (.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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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 (.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 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))))) (+.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 (.f64 J #s(literal -2 binary64)) (.f64 J #s(literal -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)))))) (.f64 #s(literal 0 binary64) (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (.f64 K #s(literal -1/2 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 (fma.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))

Calls

6 calls:

63.0ms	(.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)))))
39.0ms	(/.f64 K #s(literal 2 binary64))
31.0ms	U
21.0ms	K
17.0ms	J

Results

Accuracy	Segments	Branch
86.9%	2	`J`
72.9%	1	`K`
84.4%	2	`U`
99.8%	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)))))`
72.9%	1	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
72.9%	1	`(/.f64 K #s(literal 2 binary64))`

Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes20.0ms (0.2%)

Memory

29.2MiB live, 29.2MiB allocated

Counts

60 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
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(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #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) (/.f64 U (.f64 (.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 #s(literal 2 binary64) J) U)) (.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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) (+.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))))))))))

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

Calls

1 calls:

15.0ms

(*.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
98.6%	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)

regimes55.0ms (0.5%)

Memory

-26.5MiB live, 20.5MiB allocated

Counts

59 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 binary64)))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (/.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 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))) (/.f64 (.f64 #s(literal -1/2 binary64) U) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.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)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 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) #s(approx (cos (/ K 2)) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #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 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #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) (/.f64 U (.f64 (.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 #s(literal 2 binary64) J) U)) (.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)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 U (.f64 (.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 #s(literal 2 binary64) J) U)) (.f64 #s(literal 2 binary64) J))))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))

Calls

1 calls:

51.0ms

(*.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
98.6%	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)

regimes19.0ms (0.2%)

Memory

20.1MiB live, 20.1MiB allocated

Counts

58 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 binary64)))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (/.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 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))) (/.f64 (.f64 #s(literal -1/2 binary64) U) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.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)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 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) #s(approx (cos (/ K 2)) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #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 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #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 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) J)) (*.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)

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

Calls

1 calls:

15.0ms

(*.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
96.8%	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)

regimes28.0ms (0.3%)

Memory

-13.2MiB live, 25.4MiB allocated

Counts

57 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 binary64)))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* (/ (* U 1/2) (* (cos (/ K 2)) J)) (/ (* U 1/2) (* (cos (/ K 2)) J))) 1))) (.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (/.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (.f64 U (/.f64 (.f64 #s(literal -1/4 binary64) U) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 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))) (/.f64 (.f64 #s(literal -1/2 binary64) U) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.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)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (fma.f64 (.f64 #s(literal -2 binary64) (.f64 J J)) (cos.f64 (.f64 K #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (cos.f64 (.f64 K #s(literal 1/2 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) #s(approx (cos (/ K 2)) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (.f64 (fma.f64 (.f64 J (/.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 U U))) #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))) (*.f64 U U))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J (fma.f64 (.f64 K K) #s(literal 1/4 binary64) #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 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (*.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))

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

Calls

1 calls:

24.0ms

(*.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
89.2%	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)

regimes16.0ms (0.1%)

Memory

23.7MiB live, 23.7MiB 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 binary64)))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (/.f64 (.f64 (neg.f64 U) (cos.f64 (.f64 K #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) U)))

Outputs

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

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

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

Calls

1 calls:

12.0ms

(*.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
89.2%	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)

regimes66.0ms (0.6%)

Memory

-23.8MiB live, 49.6MiB allocated

Counts

43 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 binary64))) J))))
(.f64 (.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 #s(approx (+ ( (cos K) 1/2) 1/2) (fma.f64 (.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64))) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (/.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) #s(approx (* (cos (* K 1/2)) J) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/46080 binary64) (.f64 #s(literal 1/384 binary64) J)) (.f64 K K) (.f64 #s(literal -1/8 binary64) J)) (.f64 K K) J)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) U) (.f64 (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) #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) (/.f64 (.f64 (.f64 (/.f64 U (.f64 #s(literal 2 binary64) J)) U) (/.f64 #s(literal 1/2 binary64) J)) #s(approx (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))) (fma.f64 (*.f64 K K) #s(literal -1/4 binary64) #s(literal 1 binary64)))))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (exp.f64 (*.f64 (log.f64 (/.f64 J U)) #s(literal -1 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 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) J) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (*.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))

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

Calls

2 calls:

32.0ms

11.0ms

(*.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
74.3%	2	`J`
88.1%	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 31 to 20 computations (35.5% saved)

regimes13.0ms (0.1%)

Memory

23.0MiB live, 23.0MiB 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (/.f64 U (.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
(.f64 (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 U U) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64))))) #s(literal 1 binary64))) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (.f64 K K) #s(literal 1/384 binary64)) (.f64 K K) #s(literal -1/8 binary64)) (*.f64 K K) #s(literal 1 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 (sqrt.f64 (fma.f64 #s(approx (/ 1/2 (* (+ (* (cos K) 1/2) 1/2) J)) (/.f64 #s(literal 1/2 binary64) J)) (*.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) U) #s(literal 1 binary64))) (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)

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

Calls

1 calls:

10.0ms

(*.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
86.7%	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)

regimes51.0ms (0.5%)

Memory

-11.0MiB live, 36.0MiB allocated

Counts

32 → 5

Calls

Call 1

Inputs
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #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))
(.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 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)

Calls

2 calls:

38.0ms

(*.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)))))

10.0ms

Results

Accuracy	Segments	Branch
66.6%	2	`U`
85.7%	5	`(.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)

regimes31.0ms (0.3%)

Memory

-13.2MiB live, 25.5MiB allocated

Counts

31 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (* U (/ U (* J J))) 1/4) 1)) (.f64 (/.f64 U J) #s(literal 1/2 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 U U)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) J))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) #s(approx (cos (/ K 2)) #s(literal 1 binary64)))) #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64))) J) (.f64 (.f64 (.f64 K K) (.f64 (/.f64 (.f64 U U) J) #s(literal 1/32 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) J (/.f64 (.f64 (.f64 U U) #s(literal -1/4 binary64)) (.f64 #s(approx (cos ( K 1/2)) (fma.f64 (*.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64))) J))))

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

Calls

1 calls:

29.0ms

(*.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
82.7%	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)

regimes9.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB allocated

Counts

24 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 #s(literal -2 binary64) J)) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 K K) K)) (.f64 (.f64 K K) K) #s(literal 1 binary64)) J) (fma.f64 (.f64 (.f64 K K) (.f64 K K)) #s(literal 1/64 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 K K) #s(literal -1/8 binary64)))))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (fma.f64 (fma.f64 (/.f64 (.f64 K K) U) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) U)) (.f64 J J) (fma.f64 (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) U) #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 K K) U) #s(literal 1/16 binary64))))) #s(literal -2 binary64)))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (fma.f64 (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 (.f64 K K) J) (.f64 J #s(literal 1/4 binary64))) K) K (.f64 #s(literal -2 binary64) J))) (sqrt.f64 (fma.f64 (/.f64 (.f64 U #s(literal 1/2 binary64)) (.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) (/.f64 (.f64 U #s(literal 1/2 binary64)) (*.f64 #s(approx (cos (/ K 2)) #s(literal 1 binary64)) J)) #s(literal 1 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (*.f64 (/.f64 U J) U) #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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 U U) J) #s(literal -5/384 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal -1/192 binary64) J)) (.f64 K K) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) U)))

Outputs

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

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

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

Calls

1 calls:

7.0ms

(*.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
77.0%	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)

regimes50.0ms (0.5%)

Memory

9.4MiB live, 46.9MiB allocated

Counts

17 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 K K) #s(literal 1/4 binary64)) J)) (.f64 K K) (.f64 (/.f64 (*.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 #s(approx (+ (* -1/32 (/ (* U U) J)) (+ (* (+ (* (* (/ (* U U) J) -5/384) 1/4) (* -1/192 J)) (* K K)) (* J 1/4))) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/192 binary64) (.f64 J #s(literal 1/4 binary64)))) (.f64 K K) (.f64 (/.f64 (.f64 U U) 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 (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 #s(literal -2 binary64) J (fma.f64 (fma.f64 #s(literal -1/32 binary64) (/.f64 (.f64 U U) J) (.f64 J #s(literal 1/4 binary64))) (.f64 K K) (.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 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)))) (.f64 (.f64 J #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (.f64 U (/.f64 U (.f64 J J))) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)

Calls

5 calls:

27.0ms	(cos.f64 (/.f64 K #s(literal 2 binary64)))
5.0ms	(.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)))))
5.0ms	(/.f64 K #s(literal 2 binary64))
5.0ms	J
5.0ms	K

Results

Accuracy	Segments	Branch
54.6%	2	`J`
50.0%	5	`K`
50.0%	5	`(/.f64 K #s(literal 2 binary64))`
55.7%	3	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
71.1%	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 48 to 34 computations (29.2% saved)

regimes29.0ms (0.3%)

Memory

-19.0MiB live, 18.6MiB allocated

Counts

13 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) J) #s(literal -1/4 binary64) (.f64 #s(literal -2 binary64) J))))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 #s(literal 1 binary64) (/.f64 J U))) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 U U) U)) (+.f64 #s(literal 0 binary64) (fma.f64 U U (*.f64 #s(literal 0 binary64) U)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) #s(approx (* (neg (sqrt (/ 1 (+ (* (cos K) 1/2) 1/2)))) (* (cos (* K 1/2)) U)) (fma.f64 (.f64 (.f64 (neg.f64 (fma.f64 #s(literal -5/3072 binary64) U (.f64 U #s(literal 5/3072 binary64)))) (.f64 K K)) (.f64 K K)) (.f64 K K) (neg.f64 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)))) #s(approx (+ (* (* (cos (* K 1/2)) -2) J) (/ (* (* U U) -1/4) (* (cos (* K 1/2)) J))) (fma.f64 (/.f64 (.f64 U U) 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)))) (neg.f64 U))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)

Calls

2 calls:

24.0ms

(*.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)))))

5.0ms

Results

Accuracy	Segments	Branch
49.9%	2	`U`
64.0%	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)

regimes4.0ms (0%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

9 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) (.f64 (fma.f64 (.f64 K K) #s(literal -1/8 binary64) #s(literal 1 binary64)) J)) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 (neg.f64 U) U) (+.f64 #s(literal 0 binary64) U)))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (*.f64 (/.f64 #s(literal 1 binary64) J) U)) 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 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (fma.f64 (.f64 (.f64 K K) J) #s(literal -1/8 binary64) J))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)

Calls

1 calls:

3.0ms

(*.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
63.5%	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)

regimes8.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

5 → 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))
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J)
(.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 (neg.f64 U) J)) J)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (+ ( (+ (* -1/8 (* K K)) 1) (* (sqrt (+ (* (* U (/ U (* J J))) 1/4) 1)) J)) (* (* (* K K) (* (/ (* U U) J) 1/32)) (sqrt (/ 1 (+ (* (* U (/ U (* J J))) 1/4) 1))))) #s(approx (* (+ (* (* K K) -1/8) 1) J) (.f64 (.f64 (*.f64 K K) J) #s(literal -1/8 binary64)))) #s(literal -2 binary64)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* (* (/ U (* 2 J)) U) (/ 1/2 J)) (+ 1/2 (* 1/2 (cos (* 2 (* K -1/2))))))))) (.f64 #s(approx (neg (sqrt (/ 1 (+ ( (cos K) 1/2) 1/2)))) #s(literal -1 binary64)) #s(approx (* (cos (* K 1/2)) U) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 K K) #s(literal 1 binary64)) U))))

Outputs

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

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

Calls

3 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

(cos.f64 (/.f64 K #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
51.1%	2	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
39.1%	1	`J`
51.1%	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 38 to 26 computations (31.6% saved)

regimes33.0ms (0.3%)

Memory

-21.8MiB live, 18.4MiB 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:

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	(cos.f64 (/.f64 K #s(literal 2 binary64)))
1.0ms	(/.f64 K #s(literal 2 binary64))
1.0ms	U
1.0ms	K

Results

Accuracy	Segments	Branch
39.1%	1	`J`
39.1%	1	`K`
39.1%	1	`(/.f64 K #s(literal 2 binary64))`
39.1%	1	`U`
39.1%	1	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
39.1%	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)))))`

Compiler

Compiled 52 to 37 computations (28.8% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-1.3887110186042642e+247	-6.539456755085403e+243
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-2.6588698724994425e+63	-1.4197058871593294e+57
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-2.4143205093269893e+306	-3.464467129431955e+302

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-2.4143205093269893e+306	-3.464467129431955e+302

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272
0.0ms	-1.6777514295853514e-8	-1.7170741577571875e-15
0.0ms	-2.4143205093269893e+306	-3.464467129431955e+302

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	1.6187078203300715e+308	+inf
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272
0.0ms	-inf	-2.4143205093269893e+306

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272
0.0ms	-5.3997668517152946e-74	-1.0959201845060315e-77
0.0ms	-2.4143205093269893e+306	-3.464467129431955e+302

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272
0.0ms	-5.3997668517152946e-74	-1.0959201845060315e-77
0.0ms	-2.4143205093269893e+306	-3.464467129431955e+302

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272
0.0ms	-2.1923968335258803e-69	-5.3997668517152946e-74
0.0ms	-4.1476258192171e+298	-4.829308717847324e+294

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0828074960721213e-272	2.2621782986992618e-272

Compiler

Compiled 30 to 23 computations (23.3% saved)

simplify46.0ms (0.4%)

Memory

8.9MiB live, 46.5MiB allocated

Algorithm

1×	egg-herbie

Rules

94×	`*-commutative_binary64`
22×	`+-commutative_binary64`
14×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	2856
1	281	2856
2	297	2856
3	313	2856
4	323	2856
5	328	2856
6	329	2856

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 +inf.0 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 (fma.f64 (.f64 (pow.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -2 binary64) #s(literal -1 binary64)) (neg.f64 U)))))
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#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Outputs
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(if (<=.f64 (.f64 (sqrt.f64 (+.f64 (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))) (.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (.f64 J #s(literal -2 binary64)))) #s(literal -6090821257124999/304541062856249971261043199621099634714882089299843985214622076787904646586450815702050470808812820600790778632231520880733099058287596688955562103009770419360352428123639782183462176734064176511024987296225574339802674935168589842054573862983405175400866837597008673346307143437247315968 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U)) (.f64 #s(approx ( (sqrt (+ (/ (* U U) (* (* (* -2 J) (cos (/ K 2))) (* (* -2 J) (cos (/ K 2))))) 1)) (* (cos (* K 1/2)) -2)) (/.f64 U J)) J))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

soundness1.8s (16.1%)

Memory

-33.1MiB live, 1 573.7MiB allocated

Rules

19 354×	`lower-fma.f64`
19 354×	`lower-fma.f32`
12 040×	`lower-fma.f64`
12 040×	`lower-fma.f32`
9 598×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	676	14847
1	2225	14122
0	8411	13237
0	82	479
0	117	431
1	390	381
2	2719	358
0	9081	355
0	76	508
0	130	508
1	418	483
2	2826	445
0	8570	441
0	360	3717
1	1153	3609
2	4535	3477
0	8519	3319
0	114	792
0	166	730
1	644	707
2	4785	671
0	8729	655
0	1368	25484
1	4652	24999
0	8647	23271
0	17	66
0	28	66
1	79	66
2	432	66
3	4364	66
0	8129	66
0	1051	20269
1	3571	19746
0	8208	18533

Stop Event

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

Compiler

Compiled 3 434 to 1 148 computations (66.6% saved)

preprocess175.0ms (1.6%)

Memory: 35.2MiB live, 415.7MiB allocated
Remove: (abs K)
Compiler: Compiled 4 452 to 672 computations (84.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze298.0ms (2.7%)

sample1.7s (15%)

explain220.0ms (2%)

preprocess112.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify49.0ms (0.4%)

localize50.0ms (0.4%)

series57.0ms (0.5%)

simplify209.0ms (1.9%)

rewrite296.0ms (2.7%)

eval97.0ms (0.9%)

prune104.0ms (0.9%)

simplify228.0ms (2%)

localize339.0ms (3%)

series194.0ms (1.7%)

simplify251.0ms (2.2%)

rewrite272.0ms (2.4%)

eval184.0ms (1.7%)

prune175.0ms (1.6%)

simplify193.0ms (1.7%)

localize476.0ms (4.3%)

series443.0ms (4%)

simplify253.0ms (2.3%)

rewrite226.0ms (2%)

eval207.0ms (1.9%)

prune186.0ms (1.7%)

simplify98.0ms (0.9%)

localize418.0ms (3.7%)

series132.0ms (1.2%)

simplify295.0ms (2.6%)

rewrite249.0ms (2.2%)

eval259.0ms (2.3%)

prune261.0ms (2.3%)

regimes211.0ms (1.9%)

regimes20.0ms (0.2%)

regimes55.0ms (0.5%)

regimes19.0ms (0.2%)

regimes28.0ms (0.3%)

regimes16.0ms (0.1%)

regimes66.0ms (0.6%)

regimes13.0ms (0.1%)

regimes51.0ms (0.5%)

regimes31.0ms (0.3%)

regimes9.0ms (0.1%)

regimes50.0ms (0.5%)

regimes29.0ms (0.3%)

regimes4.0ms (0%)

regimes8.0ms (0.1%)

regimes33.0ms (0.3%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify46.0ms (0.4%)

soundness1.8s (16.1%)

preprocess175.0ms (1.6%)

end0.0ms (0%)

Profiling