Metrics for Maksimov and Kolovsky, Equation (3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze341.0ms (2.9%)

Memory

-2.8MiB live, 549.3MiB 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)

sample1.9s (16.2%)

Memory

-112.6MiB live, 2 655.7MiB allocated

Samples

1.5s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-mult: 591.0ms (48.9% of total)

ival-cos: 227.0ms (18.8% of total)

ival-div: 149.0ms (12.3% of total)

ival-pow2: 102.0ms (8.4% of total)

ival-sqrt: 71.0ms (5.9% of total)

ival-add: 49.0ms (4.1% of total)

exact: 12.0ms (1% of total)

ival-true: 6.0ms (0.5% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain230.0ms (2%)

Memory

-34.3MiB live, 440.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
33	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))))`
29	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	123	(1.3612630139401349e-261 4.712133039676416e+198 -5.210376540715427e+215)	-	`(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	123	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	33	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	29
↳	`(/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))`	overflow	29
↳	`(+.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	62
↳	`(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))`	overflow	62
`*.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**	29	0

Confusion

	Predicted +	Predicted -
+	62	0
-	89	105

Precision

0.4105960264900662

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	62	0	0
-	89	0	105

Precision?

0.4105960264900662

Recall?

1.0

Freqs

test

number	freq
0	105
1	117
2	34

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

67.0ms

512×

valid

Compiler

Compiled 251 to 55 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 15.0ms (33.1% of total)

ival-cos: 11.0ms (24.3% of total)

ival-div: 6.0ms (13.2% of total)

ival-sqrt: 5.0ms (11% of total)

ival-pow2: 5.0ms (11% of total)

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

exact: 1.0ms (2.2% of total)

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

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

preprocess135.0ms (1.2%)

Memory

-12.4MiB live, 107.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Symmetry

(abs U)

(abs K)

(negabs J)

Compiler

Compiled 27 to 17 computations (37% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.0%	(.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)))))

Status

Accuracy

Program

▶

77.0%

(*.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)))))

Compiler

Compiled 27 to 17 computations (37% saved)

simplify45.0ms (0.4%)

Memory

10.5MiB live, 47.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize61.0ms (0.5%)

Memory

-7.5MiB live, 108.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
accuracy	0.2623825195368841	(pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
accuracy	6.872306861636425	(.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	7.758232521255066	(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: 21.0ms

ival-mult: 7.0ms (33.2% of total)

ival-cos: 5.0ms (23.7% of total)

ival-div: 3.0ms (14.2% of total)

ival-sqrt: 2.0ms (9.5% of total)

ival-pow2: 2.0ms (9.5% of total)

ival-add: 1.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.3%)

Memory

17.6MiB live, 52.5MiB allocated

Counts

6 → 156

Calls

Call 1

Inputs
#<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)))))>
#<alt (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal -2 binary64) J)>
#<alt (cos.f64 (/.f64 K #s(literal 2 binary64)))>
#<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))))>
#<alt (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))>

Outputs
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))>
#<alt (* 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))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))>
#<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)))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))>
#<alt (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
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#<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))))))))>
#<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))))))))>
#<alt (* -1 U)>
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#<alt (* 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))>
#<alt (* 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))>
#<alt U>
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#<alt (* -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)))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
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#<alt (* -2 (* J (cos (* 1/2 K))))>
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#<alt (* -2 J)>
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#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
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#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt 1>
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#<alt (cos (* 1/2 K))>
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#<alt (cos (* 1/2 K))>
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#<alt 1>
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#<alt (+ 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)))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
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#<alt (* 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)))))>
#<alt (* 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))))))>
#<alt (* -1/2 (/ U (* J (cos (* 1/2 K)))))>
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#<alt (* -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))))))>
#<alt (* -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)))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
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#<alt 1>
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#<alt 1>
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#<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)))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))>
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#<alt (+ (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)))))))))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
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#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
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#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
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#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))>
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#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
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#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>

Calls

39 calls:

Time	Variable		Point	Expression
6.0ms	U	@	0	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
4.0ms	K	@	inf	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
4.0ms	K	@	0	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
3.0ms	J	@	0	(* -2 J)
2.0ms	K	@	-inf	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify418.0ms (3.6%)

Memory

6.6MiB live, 475.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 155

Calls

Call 1

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

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

rewrite336.0ms (2.9%)

Memory

14.2MiB live, 368.4MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

6 → 306

Calls

Call 1

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

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

eval128.0ms (1.1%)

Memory: -41.6MiB live, 124.8MiB allocated
Compiler: Compiled 16 532 to 1 763 computations (89.3% saved)

prune151.0ms (1.3%)

Memory

10.7MiB live, 133.7MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	468	11	479
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	11	480

Accuracy

99.9%

Counts

480 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.7%	(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))))) (.f64 (.f64 J #s(literal 2 binary64)) (.f64 J #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 (cos.f64 (.f64 K #s(literal 1/2 binary64))) (.f64 J #s(literal 2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
	67.8%	(.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)))))
▶	74.6%	(.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 U (/.f64 U (.f64 J #s(literal 2 binary64)))) (.f64 (.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)))))))))))
▶	9.3%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
	52.9%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
	45.7%	(.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) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
▶	39.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
	37.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))
▶	53.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
▶	40.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

Compiler

Compiled 526 to 354 computations (32.7% saved)

simplify208.0ms (1.8%)

Memory

-12.7MiB live, 275.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal -2 binary64) J)
cost-diff	0	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
cost-diff	384	(/.f64 K #s(literal 2 binary64))
cost-diff	0	(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
cost-diff	0	(/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U)
cost-diff	0	(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) K)
cost-diff	0	(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
cost-diff	0	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
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	384	(/.f64 (.f64 U (/.f64 U (.f64 J #s(literal 2 binary64)))) (.f64 (.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))))))))
cost-diff	384	(/.f64 K #s(literal 2 binary64))
cost-diff	640	(.f64 #s(literal 2 binary64) (.f64 K #s(literal 1/2 binary64)))
cost-diff	640	(.f64 (.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)))))))

Rules

4 966×	`lower-*.f32`
4 934×	`lower-*.f64`
3 290×	`lower-fma.f32`
3 288×	`lower-fma.f64`
2 992×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	482
0	84	478
1	160	462
2	388	426
3	992	426
4	3862	426
5	5353	426
0	8208	417

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

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

localize163.0ms (1.4%)

Memory

5.2MiB live, 324.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
accuracy	0.08203125	(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
accuracy	6.872306861636425	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
accuracy	56.37552569340239	#s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
accuracy	0.11328125	(/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U)
accuracy	0.25619125976844204	(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
accuracy	7.192985360469474	(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U))
accuracy	37.642164430988885	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
accuracy	0	(*.f64 #s(literal -2 binary64) J)
accuracy	0	(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
accuracy	0.08203125	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
accuracy	29.702535933988678	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
accuracy	0	(neg.f64 U)
accuracy	38.16108347899981	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
accuracy	0.43280531676686745	(+.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	3.6923253624501036	(/.f64 (.f64 U (/.f64 U (.f64 J #s(literal 2 binary64)))) (.f64 (.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))))))))
accuracy	6.872306861636425	(.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 U (/.f64 U (.f64 J #s(literal 2 binary64)))) (.f64 (.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)))))))))))
accuracy	7.758232521255066	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (.f64 J #s(literal 2 binary64)))) (.f64 (.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))))))))))

Samples

93.0ms

256×

valid

Compiler

Compiled 434 to 47 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 27.0ms (39.4% of total)

ival-cos: 18.0ms (26.3% of total)

ival-div: 10.0ms (14.6% of total)

ival-add: 4.0ms (5.8% of total)

ival-pow2: 4.0ms (5.8% of total)

ival-sqrt: 3.0ms (4.4% of total)

exact: 1.0ms (1.5% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

series57.0ms (0.5%)

Memory

-9.5MiB live, 108.9MiB allocated

Counts

22 → 540

Calls

Call 1

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

Outputs
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 J)>
#<alt (+ (* -1/2 (* J (pow K 2))) (* 2 J))>
#<alt (+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))>
#<alt (+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))) (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))>
#<alt (* 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))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))>
#<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)))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))>
#<alt (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<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))))))))>
#<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))))))))>
#<alt (* -1 U)>
#<alt (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))>
#<alt (* 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))>
#<alt (* 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))>
#<alt U>
#<alt (* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))>
#<alt (* -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)))>
#<alt (* -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)))>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))>
#<alt (* 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))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))>
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#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))>
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#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))))>
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#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (+ 1/2 (* 1/2 (cos K)))))))>
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#<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)))))))))>
#<alt (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))>
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#<alt (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))))))>
#<alt (* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3))))))))>
#<alt (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))))))>
#<alt (* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3))))))))>
#<alt (* -1 (* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))))))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))>
#<alt (+ 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)))))))>
#<alt (+ 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)))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))>
#<alt (* 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)))))>
#<alt (* 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))))))>
#<alt (* -1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))>
#<alt (* -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))))))>
#<alt (* -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)))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))>
#<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))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))>
#<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))))))>
#<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)))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))>
#<alt (+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))>
#<alt (+ (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)))))))))))>
#<alt (+ (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)))))))))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt J>
#<alt (+ J (* -1/8 (* J (pow K 2))))>
#<alt (+ J (* (pow K 2) (+ (* -1/8 J) (* 1/384 (* J (pow K 2))))))>
#<alt (+ J (* (pow K 2) (+ (* -1/8 J) (* (pow K 2) (+ (* -1/46080 (* J (pow K 2))) (* 1/384 J))))))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>
#<alt (* J (cos (* 1/2 K)))>

Calls

135 calls:

Time	Variable		Point	Expression
7.0ms	U	@	-inf	(+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U))
3.0ms	K	@	inf	(/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))
2.0ms	J	@	-inf	(sqrt (+ 1 (/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))))
1.0ms	U	@	0	(/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))
1.0ms	J	@	0	(* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2))))))

simplify523.0ms (4.5%)

Memory

19.1MiB live, 501.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 604×	`lower-fma.f64`
11 604×	`lower-fma.f32`
8 840×	`lower-*.f64`
8 840×	`lower-*.f32`
3 540×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	664	13505
1	2168	13138
0	8258	12352

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 523

Calls

Call 1

Inputs
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 J)
(+ (* -1/2 (* J (pow K 2))) (* 2 J))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
K
K
K
K
K
K
K
K
K
K
K
K
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos 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))))))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
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(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) U) (sqrt (+ 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))))))) (* (pow J 2) (+ (* -2 (* (/ (cos (* 1/2 K)) U) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (* 2 (* (/ (* (pow J 2) (* (cos (* 1/2 K)) (+ (* 1/2 (/ (cos K) (pow U 2))) (* 1/2 (/ 1 (pow U 2)))))) U) (sqrt (+ 1/2 (* 1/2 (cos K)))))))))
(+ (* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* (pow J 2) (+ (* -2 (* (/ (cos (* 1/2 K)) U) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (* (pow J 2) (+ (* -4 (* (/ (* (pow J 2) (* (cos (* 1/2 K)) (+ (* 1/2 (/ (cos K) (pow U 2))) (* 1/2 (/ 1 (pow U 2)))))) (pow U 3)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (* 2 (* (/ (* (cos (* 1/2 K)) (+ (* 1/2 (/ (cos K) (pow U 2))) (* 1/2 (/ 1 (pow U 2))))) U) (sqrt (+ 1/2 (* 1/2 (cos K)))))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos K))))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos K))) 2)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1/2 (* 1/2 (cos K))) 2))))))))
(* -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 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 K))) 2)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos 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 K))) 2)))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1/2 (* 1/2 (cos K))) 3)))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 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 (* (* 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))))
(+ (* -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)))))))))
(* -1 (* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))
(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K)))))))))
(* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))))))
(* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3))))))))
(* (* U (cos (* 1/2 K))) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))
(* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))))))
(* -1 (* U (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3))))))))
(* -1 (* U (+ (* -4 (* (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 5)))) (+ (* -2 (* (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2)) (sqrt (+ 1/2 (* 1/2 (cos K)))))) (+ (* -1 (* (cos (* 1/2 K)) (sqrt (/ 1 (+ 1/2 (* 1/2 (cos K))))))) (* 2 (* (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)) (sqrt (pow (+ 1/2 (* 1/2 (cos K))) 3)))))))))
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/128 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 4)))))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1/2 (/ U (* J (cos (* 1/2 K)))))
(* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -1 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 3)) (pow U 3))) (/ (cos (* 1/2 K)) U)))) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (pow K 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
J
(+ J (* -1/8 (* J (pow K 2))))
(+ J (* (pow K 2) (+ (* -1/8 J) (* 1/384 (* J (pow K 2))))))
(+ J (* (pow K 2) (+ (* -1/8 J) (* (pow K 2) (+ (* -1/46080 (* J (pow K 2))) (* 1/384 J))))))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))
(* J (cos (* 1/2 K)))

Outputs
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 J)
(*.f64 #s(literal 2 binary64) J)
(+ (* -1/2 (* J (pow K 2))) (* 2 J))
(fma.f64 #s(literal 2 binary64) J (.f64 #s(literal -1/2 binary64) (.f64 J (*.f64 K K))))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))
(fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/2 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/24 binary64))) (*.f64 #s(literal 2 binary64) J))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal 1/24 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal -1/720 binary64))) (.f64 J #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) J))
(* 2 (* J (+ 1/2 (* 1/2 (cos K)))))
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U
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U
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(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
J
(+ J (* -1/8 (* J (pow K 2))))
(fma.f64 K (.f64 K (.f64 J #s(literal -1/8 binary64))) J)
(+ J (* (pow K 2) (+ (* -1/8 J) (* 1/384 (* J (pow K 2))))))
(fma.f64 (.f64 K K) (fma.f64 J #s(literal -1/8 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal 1/384 binary64))) J)
(+ J (* (pow K 2) (+ (* -1/8 J) (* (pow K 2) (+ (* -1/46080 (* J (pow K 2))) (* 1/384 J))))))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal 1/384 binary64) (.f64 (.f64 J (.f64 K K)) #s(literal -1/46080 binary64))) (.f64 J #s(literal -1/8 binary64))) J)
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))
(* J (cos (* 1/2 K)))
(.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K)))

rewrite403.0ms (3.5%)

Memory

10.3MiB live, 367.3MiB allocated

Rules

5 552×	`lower-fma.f32`
5 550×	`lower-fma.f64`
3 988×	`lower-*.f32`
3 956×	`lower-*.f64`
3 832×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	339
0	84	315
1	276	299
2	1815	287
0	8414	281

Stop Event

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

Counts

22 → 652

Calls

Call 1

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

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

eval368.0ms (3.2%)

Memory: 22.7MiB live, 327.4MiB allocated
Compiler: Compiled 42 048 to 3 593 computations (91.5% saved)

prune312.0ms (2.7%)

Memory

-14.8MiB live, 322.1MiB allocated

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	1 402	22	1 424
Fresh	5	1	6
Picked	3	2	5
Done	0	0	0
Total	1 410	25	1 435

Accuracy

100.0%

Counts

1 435 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	9.3%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #s(literal -2 binary64)) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
▶	74.6%	(.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 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
	66.4%	(.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 U (/.f64 U (.f64 J #s(literal 2 binary64)))) #s(approx ( (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))) (*.f64 #s(literal 2 binary64) J))))))
	52.9%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
	31.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 #s(approx (pow (cos (* 1/2 K)) 2) (fma.f64 K (.f64 K #s(literal -1/4 binary64)) #s(literal 1 binary64))) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
	41.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) U) (.f64 J #s(literal -2 binary64))) J (neg.f64 U)))
	28.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64)))) (+.f64 #s(literal 0 binary64) (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
	25.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 U (neg.f64 U)) U))
	13.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (neg.f64 (.f64 U (.f64 U U))) (fma.f64 U U #s(literal 0 binary64))))
	53.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64)) (neg.f64 U)))
	25.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 U (neg.f64 U)) (/.f64 #s(literal 1 binary64) U)))
	48.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) K))) (.f64 #s(literal -2 binary64) J)))
▶	28.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))
✓	53.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
	29.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
	30.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
	29.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
✓	40.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
	34.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J J) #s(literal 1/2 binary64)) U)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 J J) U) (neg.f64 U)))))
▶	39.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
▶	29.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	30.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
▶	32.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
	50.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 (neg.f64 U) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))

Compiler

Compiled 922 to 595 computations (35.5% saved)

simplify256.0ms (2.2%)

Memory

-13.7MiB live, 482.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))
cost-diff	192	(+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))
cost-diff	192	(-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64)))
cost-diff	1344	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 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)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
cost-diff	320	(fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (*.f64 J #s(literal -1/192 binary64)))
cost-diff	320	(fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (*.f64 J #s(literal 1/4 binary64)))
cost-diff	0	(/.f64 (*.f64 J J) U)
cost-diff	0	(fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))
cost-diff	0	#s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
cost-diff	0	(*.f64 J #s(literal -2 binary64))
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 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)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
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) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
cost-diff	128	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))
cost-diff	384	(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))

Rules

15 720×	`lower-fma.f32`
15 710×	`lower-fma.f64`
4 600×	`lower-*.f32`
4 570×	`lower-*.f64`
2 864×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	561
0	112	527
1	221	524
2	544	519
3	1521	515
4	4418	512
0	8093	496

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 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #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) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))
#s(literal 1 binary64)
(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
(*.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J)))
U
(/.f64 U (fma.f64 J (cos.f64 K) J))
(fma.f64 J (cos.f64 K) J)
(cos.f64 K)
(*.f64 J #s(literal 2 binary64))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64)))
(*.f64 J #s(literal -2 binary64))
J
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
#s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U)))
(fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))
#s(literal -2 binary64)
(/.f64 (*.f64 J J) U)
(*.f64 J J)
J
U
(neg.f64 U)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64))))
(fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))
(*.f64 K K)
K
(fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (*.f64 J #s(literal 1/4 binary64)))
(.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64))))
(fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (*.f64 J #s(literal -1/192 binary64)))
J
(.f64 (.f64 K K) #s(literal 1/23040 binary64))
#s(literal 1/23040 binary64)
(*.f64 J #s(literal -1/192 binary64))
#s(literal -1/192 binary64)
(*.f64 J #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 J #s(literal -2 binary64))
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(*.f64 #s(literal 1/2 binary64) K)
#s(literal 1/2 binary64)
K
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64)))
#s(literal 0 binary64)
(.f64 (.f64 J J) #s(literal 4 binary64))
(*.f64 J J)
J
#s(literal 4 binary64)
(+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))
(*.f64 J #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) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 U (/.f64 U (.f64 J (*.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) 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 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))))
(sqrt.f64 (fma.f64 U (/.f64 U (.f64 J (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J)))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))
(fma.f64 U (/.f64 U (.f64 J (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J)))) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 U U) (.f64 J (*.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))))
(*.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J)))
(/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J))
U
(/.f64 U (fma.f64 J (cos.f64 K) J))
(fma.f64 J (cos.f64 K) J)
(cos.f64 K)
(*.f64 J #s(literal 2 binary64))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64)))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 #s(literal -2 binary64) J))
(*.f64 J #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) J)
J
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
#s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U)))
(fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))
#s(literal -2 binary64)
(/.f64 (*.f64 J J) U)
(*.f64 J J)
J
U
(neg.f64 U)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 #s(literal -2 binary64) J (.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (*.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64))))
#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 #s(literal -2 binary64) J (.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (*.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64))))))
(fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))
(fma.f64 #s(literal -2 binary64) J (.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (*.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))))
(*.f64 K K)
K
(fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (*.f64 J #s(literal 1/4 binary64)))
(.f64 J (fma.f64 (.f64 K K) (fma.f64 (*.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)))
(.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64))))
(.f64 J (.f64 K (fma.f64 (*.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64))))
(fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (*.f64 J #s(literal -1/192 binary64)))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
J
(.f64 (.f64 K K) #s(literal 1/23040 binary64))
#s(literal 1/23040 binary64)
(*.f64 J #s(literal -1/192 binary64))
#s(literal -1/192 binary64)
(*.f64 J #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 J #s(literal -2 binary64))
(*.f64 #s(literal -2 binary64) J)
#s(literal -2 binary64)
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) K)
(*.f64 K #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
K
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64)))
(.f64 J (.f64 J #s(literal -4 binary64)))
#s(literal 0 binary64)
(.f64 (.f64 J J) #s(literal 4 binary64))
(.f64 J (.f64 J #s(literal 4 binary64)))
(*.f64 J J)
J
#s(literal 4 binary64)
(+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))
(*.f64 J #s(literal 2 binary64))
(*.f64 J #s(literal 2 binary64))
#s(literal 2 binary64)

localize207.0ms (1.8%)

Memory

25.3MiB live, 395.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.006191259768442017	(.f64 (.f64 J J) #s(literal 4 binary64))
accuracy	0.08203125	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))))
accuracy	28.785928485940175	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))
accuracy	29.702535933988678	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))
accuracy	0.4296875	(*.f64 J #s(literal -1/192 binary64))
accuracy	4.239088144143711	(fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (*.f64 J #s(literal -1/192 binary64)))
accuracy	29.702535933988678	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
accuracy	30.083126008854556	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64))))
accuracy	0	(neg.f64 U)
accuracy	7.29060296543944	#s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U)))
accuracy	8.269302731795594	(/.f64 (*.f64 J J) U)
accuracy	37.642164430988885	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
accuracy	0	(*.f64 J #s(literal -2 binary64))
accuracy	27.148936716741023	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64)))
accuracy	29.702535933988678	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
accuracy	0.42559608067893656	(fma.f64 J (cos.f64 K) J)
accuracy	3.6219647344208745	(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
accuracy	6.872306861636425	(.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 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
accuracy	7.758232521255066	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))))

Samples

117.0ms

256×

valid

Compiler

Compiled 445 to 65 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-mult: 39.0ms (42.5% of total)

ival-cos: 15.0ms (16.3% of total)

ival-div: 10.0ms (10.9% of total)

ival-add: 10.0ms (10.9% of total)

const: 6.0ms (6.5% of total)

ival-pow2: 4.0ms (4.4% of total)

ival-sqrt: 3.0ms (3.3% of total)

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

exact: 1.0ms (1.1% of total)

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

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

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

series55.0ms (0.5%)

Memory

-2.9MiB live, 116.6MiB allocated

Counts

25 → 624

Calls

Call 1

Inputs
#<alt (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))>
#<alt (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))>
#<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 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))>
#<alt (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))>
#<alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))>
#<alt #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64)))>
#<alt (*.f64 J #s(literal -2 binary64))>
#<alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))>
#<alt #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U)))>
#<alt (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))>
#<alt (/.f64 (*.f64 J J) U)>
#<alt (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (*.f64 J #s(literal 1/4 binary64)))>
#<alt (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (*.f64 J #s(literal -1/192 binary64)))>
#<alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))>
#<alt #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64))))>
#<alt (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))>
#<alt (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64)))>
#<alt (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))>
#<alt #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))>
#<alt (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))))>
#<alt (fma.f64 J (cos.f64 K) J)>
#<alt (neg.f64 U)>
#<alt (*.f64 J #s(literal -1/192 binary64))>
#<alt (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))))>
#<alt (.f64 (.f64 J J) #s(literal 4 binary64))>

Outputs
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2)))))>
#<alt (+ 1 (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2)))))))>
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#<alt (+ (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)))))) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* 2 J)>
#<alt (+ (* -1/2 (* J (pow K 2))) (* 2 J))>
#<alt (+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))>
#<alt (+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -1/192 J)>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>
#<alt (* 4 (pow J 2))>

Calls

156 calls:

Time	Variable		Point	Expression
4.0ms	K	@	-inf	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2)))))
4.0ms	U	@	0	(/ (* U (/ U (+ (* J (cos K)) J))) (* J 2))
2.0ms	K	@	0	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2)))))
2.0ms	U	@	0	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
1.0ms	U	@	inf	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2)))))

simplify397.0ms (3.4%)

Memory

-3.8MiB live, 471.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 484×	`lower-fma.f64`
11 484×	`lower-fma.f32`
8 708×	`lower-*.f64`
8 708×	`lower-*.f32`
3 542×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	701	13810
1	2294	13434
0	8701	12648

Stop Event

1×	iter limit
1×	node limit

Counts

624 → 620

Calls

Call 1

Inputs
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* 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) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
1
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
1
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
1
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 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) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K))))))
(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* -1 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))))
(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* 1/4 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))
(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 5) (pow (sqrt 1/2) 5))) (sqrt (pow (+ 1 (cos K)) 5)))) (* 1/4 (* (/ (cos (* 1/2 K)) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K))))) (* 1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1 (cos K)) 2)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K))))) (+ (* -1/64 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1 (cos K)) 3)))) (* 1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1 (cos K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (+ (* -1/64 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (- (* -1 (cos K)) 1) 3)))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (+ J (* J (cos K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/2 (/ (cos (* 1/2 K)) (+ J (* J (cos K))))) (* 1/16 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (pow (+ J (* J (cos K))) 2)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/2 (/ (cos (* 1/2 K)) (+ J (* J (cos K))))) (* (pow U 2) (+ (* -1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (pow (+ J (* J (cos K))) 3)))) (* 1/16 (/ (cos (* 1/2 K)) (* J (pow (+ J (* J (cos K))) 2)))))))))
(* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* U (* (cos (* 1/2 K)) (sqrt 1/2)))))
(* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2)))))))
(* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3))))))))
(* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (* (pow J 7) (pow (+ J (* J (cos K))) 5))) (/ (cos (* 1/2 K)) (* (pow U 6) (pow (sqrt 1/2) 5))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3)))))))))
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U
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U
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1
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(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/128 (/ (pow U 2) (* (pow J 3) (pow (+ J (* J (cos K))) 3)))) (* 1/32 (/ 1 (* (pow J 2) (pow (+ J (* J (cos K))) 2)))))) (* 1/4 (/ 1 (* J (+ J (* J (cos K)))))))))
(* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (* U (sqrt 1/2)))
(* U (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))
(* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))
(* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/16 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 5))) (/ 1 (* (pow U 6) (pow (sqrt 1/2) 5))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))))
(* -1 (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (* U (sqrt 1/2))))
(* -1 (* U (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))
(* -1 (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))))
(* -1 (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/16 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 5))) (/ 1 (* (pow U 6) (pow (sqrt 1/2) 5))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))))
(* (/ (* U (sqrt 1/2)) J) (sqrt (/ 1 (+ 1 (cos K)))))
(/ (+ (* 1/2 (* (/ (pow J 2) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K)))))) J)
(/ (+ (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ (pow J 2) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))) (* 1/2 (* (/ 1 (* U (sqrt 1/2))) (sqrt (+ 1 (cos K)))))))) J)
(/ (+ (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K))))) (* (pow J 2) (+ (* 1/2 (* (/ 1 (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ 1 (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))) (* 1/16 (* (/ (pow J 2) (* (pow U 5) (pow (sqrt 1/2) 5))) (sqrt (pow (+ 1 (cos K)) 5))))))))) J)
1
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(+ 1 (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (+ 1 (cos K)) 2)))) (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))))
(+ 1 (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (+ 1 (cos K)) 2)))) (+ (* 1/128 (/ (pow U 6) (* (pow J 6) (pow (+ 1 (cos K)) 3)))) (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))))
1
(+ 1 (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 1 (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))) (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2))))))
(+ 1 (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (* -1/128 (/ (pow U 6) (* (pow J 6) (pow (- (* -1 (cos K)) 1) 3)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* 2 J)
(+ (* -1/2 (* J (pow K 2))) (* 2 J))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -1/192 J)
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))
(* 4 (pow J 2))

Outputs
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (*.f64 J J))
(+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) (.f64 (/.f64 (.f64 U U) (.f64 J J)) (.f64 #s(literal 1/16 binary64) (*.f64 K K))))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))
(fma.f64 (.f64 K K) (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 K K) (.f64 #s(literal 1/96 binary64) (.f64 U U))) (.f64 J J))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 U U)) (*.f64 J J)))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) (.f64 (.f64 K K) (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 K (.f64 K (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 13/5760 binary64) (.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal -1/192 binary64)))) (/.f64 (.f64 (.f64 U U) #s(literal -1/48 binary64)) (.f64 J J))) (.f64 K K)) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 U U)) (.f64 J J)))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (+.f64 (cos.f64 K) #s(literal 1 binary64))) (.f64 J J)) (*.f64 J J))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (+.f64 (cos.f64 K) #s(literal 1 binary64))) (.f64 J J)) (*.f64 J J))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (+.f64 (cos.f64 K) #s(literal 1 binary64))) (.f64 J J)) (*.f64 J J))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J)))) #s(literal 1 binary64))
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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
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(* -2 (* J (cos (* 1/2 K))))
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(* -2 J)
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(* -2 J)
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(* -2 (* J (cos (* 1/2 K))))
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(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
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(* -2 (* J (cos (* 1/2 K))))
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(* -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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(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* -2 (* J (cos (* 1/2 K))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))
(* 4 (pow J 2))
(.f64 J (.f64 J #s(literal 4 binary64)))

rewrite437.0ms (3.8%)

Memory

5.3MiB live, 522.7MiB allocated

Rules

6 276×	`lower-*.f32`
6 246×	`lower-*.f64`
5 828×	`lower-fma.f32`
5 818×	`lower-fma.f64`
3 470×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	441
0	112	410
1	407	401
2	3121	397
0	11417	390

Stop Event

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

Counts

25 → 855

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (.f64 U U)) (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))))
(/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 J #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J)))))
(/.f64 (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64))))
(/.f64 (.f64 U U) (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J)))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J))))
(/.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 2 binary64))
(/.f64 (.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64)) (*.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)))) (*.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (*.f64 J (fma.f64 J (cos.f64 K) J)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)))) (.f64 J #s(literal 2 binary64)))
(/.f64 (neg.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J)))) #s(literal -2 binary64))
(/.f64 (*.f64 (/.f64 U J) (/.f64 U (fma.f64 J (cos.f64 K) J))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 U U) (/.f64 #s(literal 1/2 binary64) J)) (fma.f64 J (cos.f64 K) J))
(/.f64 (.f64 U (/.f64 U (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J)))) J)
(/.f64 (/.f64 (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J)) #s(literal 2 binary64)) J)
(pow.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J)))) #s(literal -1 binary64))
(.f64 U (/.f64 U (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))))
(.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) (/.f64 U (.f64 J #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (/.f64 #s(literal 1/2 binary64) J))
(.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (*.f64 J (fma.f64 J (cos.f64 K) J))))
(.f64 (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (/.f64 #s(literal 1/2 binary64) J))
(.f64 (/.f64 U J) (/.f64 U (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))))
(.f64 (/.f64 U (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))) (/.f64 U J))
(.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)))
(.f64 (/.f64 #s(literal 1/2 binary64) J) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 U U) (*.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1/2 binary64))
(.f64 (/.f64 U (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))) U)
(.f64 (.f64 #s(literal 1 binary64) U) (/.f64 U (.f64 (.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J))) (/.f64 #s(literal 1/2 binary64) J))
(*.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) J))
(*.f64 (/.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) J) (/.f64 U #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) J) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 U J)) (/.f64 U (*.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))))
(.f64 (/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (*.f64 J J) #s(literal 4 binary64)))
(.f64 (/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 (.f64 J J) #s(literal 4 binary64))) (*.f64 J #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 J (/.f64 U (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) U) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) U) #s(literal -1 binary64)) (pow.f64 (/.f64 J (/.f64 U (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 J (cos.f64 K) J)))
(+.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))))
(+.f64 #s(literal 1 binary64) (.f64 (neg.f64 U) (/.f64 U (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J)))))
(+.f64 #s(literal 1 binary64) (.f64 (neg.f64 (/.f64 U J)) (/.f64 U (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J)))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))) (/.f64 (pow.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (*.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))))
(fma.f64 U (/.f64 U (.f64 (.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(fma.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) (/.f64 U (*.f64 J #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J)) (/.f64 #s(literal 1/2 binary64) J) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(fma.f64 (neg.f64 (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J))) (/.f64 #s(literal 1/2 binary64) J) #s(literal 1 binary64))
(fma.f64 (/.f64 U J) (/.f64 U (*.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(fma.f64 (/.f64 U (*.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))) (/.f64 U J) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) J) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 U (.f64 (.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))) U #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) U) (/.f64 U (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (/.f64 #s(literal 1/2 binary64) J) #s(literal 1 binary64))
(fma.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) J) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) J) (/.f64 U #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) J) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (/.f64 U J)) (/.f64 U (.f64 #s(literal 2 binary64) (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (.f64 J J) #s(literal 4 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 (.f64 J J) #s(literal 4 binary64))) (.f64 J #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (/.f64 J (/.f64 U (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) U) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) U) #s(literal -1 binary64)) (pow.f64 (/.f64 J (/.f64 U (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (.f64 U U)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) (-.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 2 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64))))
(/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64)) (fma.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) (-.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))
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(fma.f64 (neg.f64 J) (*.f64 J #s(literal 4 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 J #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 16 binary64) (pow.f64 (/.f64 (.f64 J J) (.f64 J #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -4 binary64) (*.f64 J J) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 J #s(literal 2 binary64)) #s(literal -2 binary64)) J #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 (*.f64 J J) J) #s(literal 2 binary64)) #s(literal 4 binary64) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 J J) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 J #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 J #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 J #s(literal 4 binary64)) J) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 (*.f64 J J) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) J) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 #s(literal 4 binary64) J) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 J J) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64))) #s(literal 2 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (neg.f64 J) #s(literal 2 binary64)) #s(literal 4 binary64) #s(literal 0 binary64))
(neg.f64 (.f64 (.f64 J J) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64))))
(/.f64 (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64)) (.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)))
(/.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64)))
(/.f64 (.f64 (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64))) (.f64 (.f64 J (*.f64 J J)) #s(literal 8 binary64)))
(/.f64 (-.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) #s(literal 0 binary64)) (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) #s(literal 0 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64)))
(/.f64 (.f64 (.f64 J #s(literal 2 binary64)) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (*.f64 J J) #s(literal 4 binary64)))
(/.f64 (.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (.f64 J (*.f64 J J)) #s(literal 8 binary64)))
(pow.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 J #s(literal 2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) J) #s(literal -2 binary64))
(pow.f64 (/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) #s(literal -1 binary64))
(.f64 J (.f64 J #s(literal 4 binary64)))
(.f64 J (.f64 #s(literal 2 binary64) (*.f64 J #s(literal 2 binary64))))
(.f64 J (neg.f64 (.f64 J #s(literal 4 binary64))))
(.f64 J (.f64 #s(literal -2 binary64) (*.f64 J #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 J (*.f64 J #s(literal 2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 J J) #s(literal 4 binary64)))
(.f64 #s(literal -2 binary64) (.f64 J (*.f64 J #s(literal 2 binary64))))
(.f64 (.f64 J (*.f64 J #s(literal 2 binary64))) #s(literal 2 binary64))
(.f64 (.f64 J (*.f64 J #s(literal 2 binary64))) #s(literal -2 binary64))
(.f64 (.f64 J J) #s(literal 4 binary64))
(.f64 (.f64 J J) #s(literal -4 binary64))
(.f64 (.f64 J J) (pow.f64 (/.f64 (.f64 J #s(literal 4 binary64)) (.f64 J #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 #s(literal 4 binary64) (.f64 J J))
(.f64 #s(literal 4 binary64) (neg.f64 (.f64 J J)))
(.f64 #s(literal 4 binary64) (pow.f64 (/.f64 (.f64 J J) J) #s(literal 2 binary64)))
(*.f64 #s(literal 4 binary64) (pow.f64 (neg.f64 J) #s(literal 2 binary64)))
(.f64 (.f64 J #s(literal 2 binary64)) (*.f64 J #s(literal 2 binary64)))
(.f64 (neg.f64 (.f64 J J)) #s(literal 4 binary64))
(.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 J J) (*.f64 J J)) #s(literal 16 binary64))))
(.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 J J) #s(literal 4 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (*.f64 J J) #s(literal 4 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 J J) #s(literal 4 binary64)))
(.f64 (.f64 J #s(literal 4 binary64)) J)
(.f64 (.f64 (*.f64 J #s(literal 2 binary64)) #s(literal 2 binary64)) J)
(.f64 (neg.f64 J) (.f64 J #s(literal 4 binary64)))
(.f64 (.f64 (.f64 J J) (.f64 J J)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 J #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (.f64 (.f64 (.f64 J J) (*.f64 J J)) #s(literal 16 binary64)))
(.f64 #s(literal 16 binary64) (pow.f64 (/.f64 (.f64 J J) (*.f64 J #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 #s(literal -4 binary64) (.f64 J J))
(.f64 (.f64 (*.f64 J #s(literal 2 binary64)) #s(literal -2 binary64)) J)
(.f64 (pow.f64 (/.f64 (.f64 J J) J) #s(literal 2 binary64)) #s(literal 4 binary64))
(.f64 (pow.f64 (/.f64 J J) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 J #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 J #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 J #s(literal 4 binary64)) J) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 J J) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) J) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 4 binary64) J) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 J J) #s(literal 2 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64))) #s(literal 2 binary64)) (.f64 (*.f64 J J) #s(literal 4 binary64)))
(*.f64 (pow.f64 (neg.f64 J) #s(literal 2 binary64)) #s(literal 4 binary64))

eval224.0ms (1.9%)

Memory: -11.3MiB live, 496.9MiB allocated
Compiler: Compiled 41 795 to 2 963 computations (92.9% saved)

prune186.0ms (1.6%)

Memory

6.2MiB live, 483.0MiB allocated

Pruning

33 alts after pruning (30 fresh and 3 done)

	Pruned	Kept	Total
New	1 542	19	1 561
Fresh	7	11	18
Picked	4	1	5
Done	0	2	2
Total	1 553	33	1 586

Accuracy

100.0%

Counts

1 586 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.6%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))))
	9.3%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #s(literal -2 binary64)) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
	66.4%	(.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 U (/.f64 U (.f64 J #s(literal 2 binary64)))) #s(approx ( (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))) (*.f64 #s(literal 2 binary64) J))))))
	52.9%	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 #s(approx (+ 1 (/ ( U (/ U (+ (* J (cos K)) J))) (* J 2))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
▶	44.3%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
	31.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 #s(approx (pow (cos (* 1/2 K)) 2) (fma.f64 K (.f64 K #s(literal -1/4 binary64)) #s(literal 1 binary64))) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
	41.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) U) (.f64 J #s(literal -2 binary64))) J (neg.f64 U)))
	28.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64)))) (+.f64 #s(literal 0 binary64) (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
	25.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 U (neg.f64 U)) (/.f64 #s(literal 1 binary64) U)))
	28.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (*.f64 J #s(literal 2 binary64)))))
✓	53.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
	30.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
	29.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
✓	40.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
	34.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J J) #s(literal 1/2 binary64)) U)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 J J) U) (neg.f64 U)))))
▶	41.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
	30.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal 1/2 binary64) (.f64 J (.f64 J (/.f64 (.f64 K K) U))) (-.f64 (/.f64 (.f64 (*.f64 J J) #s(literal -2 binary64)) U) U))))
	29.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (/ (- 0 (* (* J J) 4)) (+ 0 (* J 2)))) (fma.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	18.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64))) (.f64 J (-.f64 (.f64 (.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)))) (.f64 J (-.f64 (.f64 (.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
▶	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	30.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	14.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (*.f64 J J) #s(literal 4 binary64)))))
	0.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (.f64 (.f64 J J) (*.f64 J J)) #s(literal 16 binary64)))))
	1.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J (*.f64 J J)) #s(literal 8 binary64)))))
	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
	32.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
	3.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) J) #s(literal 2 binary64))))
	3.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) #s(literal 2 binary64)) (/.f64 #s(literal 4 binary64) J))))
▶	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))
✓	32.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) J)) #s(literal -1 binary64)))))
	50.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 (neg.f64 U) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))

Compiler

Compiled 1 272 to 774 computations (39.2% saved)

simplify202.0ms (1.7%)

Memory

-1.3MiB live, 397.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* -2 J) (cos (/ K 2))) (*.f64 J #s(literal -2 binary64)))
cost-diff	0	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
cost-diff	128	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))
cost-diff	384	(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
cost-diff	0	(*.f64 K K)
cost-diff	0	(fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 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)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
cost-diff	0	(*.f64 (/.f64 J U) #s(literal -2 binary64))
cost-diff	0	(fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))
cost-diff	0	#s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U)))
cost-diff	0	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
cost-diff	0	(*.f64 J #s(literal 2 binary64))
cost-diff	0	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 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)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 J (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64))
cost-diff	0	(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))))
cost-diff	128	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))
cost-diff	384	(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))

Rules

5 394×	`lower-fma.f32`
5 386×	`lower-fma.f64`
4 890×	`lower-*.f32`
4 862×	`lower-*.f64`
3 474×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	632
0	100	618
1	194	618
2	391	618
3	832	618
4	1794	618
5	3814	618
6	6405	618
0	8123	600

Stop Event

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

Calls

Call 1

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

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

localize232.0ms (2%)

Memory

17.1MiB live, 541.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	3.6219647344208736	(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
accuracy	6.872306861636425	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
accuracy	7.758232521255066	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))))
accuracy	27.148936716741023	#s(approx (* (* -2 J) (cos (/ K 2))) (*.f64 J #s(literal -2 binary64)))
accuracy	8.535139220356903	(.f64 J (.f64 (*.f64 K K) #s(literal 1/23040 binary64)))
accuracy	29.702535933988678	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
accuracy	30.083126008854556	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64))))
accuracy	32.27954179648344	#s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (*.f64 K K) #s(literal 1/23040 binary64))))
accuracy	0.0078125	(*.f64 (/.f64 J U) #s(literal -2 binary64))
accuracy	0.0703125	(fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))
accuracy	7.29060296543944	#s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U)))
accuracy	37.642164430988885	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
accuracy	0	(*.f64 J #s(literal 2 binary64))
accuracy	29.702535933988678	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))
accuracy	60.15095487799351	#s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64)))
accuracy	0.42559608067893673	(fma.f64 J (cos.f64 K) J)
accuracy	3.6219647344208736	(/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))
accuracy	6.872306861636425	(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))))
accuracy	7.758232521255066	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64)))))

Samples

138.0ms

256×

valid

Compiler

Compiled 480 to 64 computations (86.7% saved)

Precisions

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

ival-mult: 42.0ms (44.4% of total)

ival-cos: 19.0ms (20.1% of total)

ival-div: 9.0ms (9.5% of total)

ival-add: 8.0ms (8.5% of total)

const: 6.0ms (6.3% of total)

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

ival-sqrt: 3.0ms (3.2% of total)

exact: 1.0ms (1.1% of total)

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

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

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

series45.0ms (0.4%)

Memory

-16.0MiB live, 105.5MiB allocated

Counts

21 → 588

Calls

Call 1

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

Outputs
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))>
#<alt (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))>
#<alt (/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2)))))>
#<alt (+ 1 (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2)))))))>
#<alt (+ 1 (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K))))))>
#<alt (+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* -1 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))))>
#<alt (+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* 1/4 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))>
#<alt (+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 5) (pow (sqrt 1/2) 5))) (sqrt (pow (+ 1 (cos K)) 5)))) (* 1/4 (* (/ (cos (* 1/2 K)) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K))))) (* 1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1 (cos K)) 2)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K))))) (+ (* -1/64 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1 (cos K)) 3)))) (* 1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1 (cos K)) 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (* 2 (cos (* 1/2 K))))))>
#<alt (* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (* 2 (cos (* 1/2 K)))))))>
#<alt (* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (+ (* -1/64 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (- (* -1 (cos K)) 1) 3)))) (* 2 (cos (* 1/2 K))))))))>
#<alt (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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))))))))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (+ J (* J (cos K))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/2 (/ (cos (* 1/2 K)) (+ J (* J (cos K))))) (* 1/16 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (pow (+ J (* J (cos K))) 2)))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/2 (/ (cos (* 1/2 K)) (+ J (* J (cos K))))) (* (pow U 2) (+ (* -1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (pow (+ J (* J (cos K))) 3)))) (* 1/16 (/ (cos (* 1/2 K)) (* J (pow (+ J (* J (cos K))) 2)))))))))>
#<alt (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* U (* (cos (* 1/2 K)) (sqrt 1/2)))))>
#<alt (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2)))))))>
#<alt (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3))))))))>
#<alt (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (* (pow J 7) (pow (+ J (* J (cos K))) 5))) (/ (cos (* 1/2 K)) (* (pow U 6) (pow (sqrt 1/2) 5))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3)))))))))>
#<alt (* 2 (* (sqrt (/ J (+ J (* J (cos K))))) (* U (* (cos (* 1/2 K)) (sqrt 1/2)))))>
#<alt (* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))))))>
#<alt (* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3)))))))))>
#<alt (* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (* (pow J 7) (pow (+ J (* J (cos K))) 5))) (/ (cos (* 1/2 K)) (* (pow U 6) (pow (sqrt 1/2) 5))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3))))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))>
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#<alt (* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))))))>
#<alt (* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3)))))))))>
#<alt (* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (* (pow J 7) (pow (+ J (* J (cos K))) 5))) (/ (cos (* 1/2 K)) (* (pow U 6) (pow (sqrt 1/2) 5))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3))))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (* J (+ J (* J (cos K)))))))>
#<alt (+ 1 (* (pow U 2) (+ (* -1/32 (/ (pow U 2) (* (pow J 2) (pow (+ J (* J (cos K))) 2)))) (* 1/4 (/ 1 (* J (+ J (* J (cos K)))))))))>
#<alt (+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/128 (/ (pow U 2) (* (pow J 3) (pow (+ J (* J (cos K))) 3)))) (* 1/32 (/ 1 (* (pow J 2) (pow (+ J (* J (cos K))) 2)))))) (* 1/4 (/ 1 (* J (+ J (* J (cos K)))))))))>
#<alt (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (* U (sqrt 1/2)))>
#<alt (* U (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))>
#<alt (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))>
#<alt (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/16 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 5))) (/ 1 (* (pow U 6) (pow (sqrt 1/2) 5))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))))>
#<alt (* -1 (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (* U (sqrt 1/2))))>
#<alt (* -1 (* U (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))>
#<alt (* -1 (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))))>
#<alt (* -1 (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/16 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 5))) (/ 1 (* (pow U 6) (pow (sqrt 1/2) 5))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))))>
#<alt (* (/ (* U (sqrt 1/2)) J) (sqrt (/ 1 (+ 1 (cos K)))))>
#<alt (/ (+ (* 1/2 (* (/ (pow J 2) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K)))))) J)>
#<alt (/ (+ (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ (pow J 2) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))) (* 1/2 (* (/ 1 (* U (sqrt 1/2))) (sqrt (+ 1 (cos K)))))))) J)>
#<alt (/ (+ (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K))))) (* (pow J 2) (+ (* 1/2 (* (/ 1 (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ 1 (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))) (* 1/16 (* (/ (pow J 2) (* (pow U 5) (pow (sqrt 1/2) 5))) (sqrt (pow (+ 1 (cos K)) 5))))))))) J)>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))>
#<alt (+ 1 (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (+ 1 (cos K)) 2)))) (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))))>
#<alt (+ 1 (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (+ 1 (cos K)) 2)))) (+ (* 1/128 (/ (pow U 6) (* (pow J 6) (pow (+ 1 (cos K)) 3)))) (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))>
#<alt (+ 1 (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))) (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2))))))>
#<alt (+ 1 (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (* -1/128 (/ (pow U 6) (* (pow J 6) (pow (- (* -1 (cos K)) 1) 3)))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))>
#<alt (+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))>
#<alt (+ (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) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))))))))>
#<alt (+ (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)))))) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* J (+ 1 (cos K)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* -1 (* J (- (* -1 (cos K)) 1)))>
#<alt (* 2 J)>
#<alt (+ (* -1/2 (* J (pow K 2))) (* 2 J))>
#<alt (+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))>
#<alt (+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (+ J (* J (cos K)))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* J (- (* 1/23040 (pow K 2)) 1/192))>
#<alt (* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))>
#<alt (* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))>
#<alt (* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))>
#<alt (* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))>
#<alt (* -1/192 J)>
#<alt (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))>
#<alt (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))>
#<alt (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))>
#<alt (* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))>
#<alt (* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))>
#<alt (* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))>
#<alt (* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>
#<alt (* 1/23040 (* J (pow K 2)))>

Calls

147 calls:

Time	Variable		Point	Expression
19.0ms	U	@	-inf	(* (* (* J (cos (* K 1/2))) -2) (sqrt (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2)))))
3.0ms	K	@	-inf	(+ (* (* K K) (+ (* K (* K (+ (* J (* (* K K) 1/23040)) (* J -1/192)))) (* J 1/4))) (* J -2))
1.0ms	J	@	inf	(* (/ J U) -2)
0.0ms	U	@	inf	(* (/ J U) -2)
0.0ms	J	@	0	(+ (* (* K K) (+ (* K (* K (+ (* J (* (* K K) 1/23040)) (* J -1/192)))) (* J 1/4))) (* J -2))

simplify342.0ms (2.9%)

Memory

32.1MiB live, 664.6MiB allocated

Algorithm

1×	egg-herbie

Rules

11 672×	`lower-fma.f64`
11 672×	`lower-fma.f32`
8 804×	`lower-*.f64`
8 804×	`lower-*.f32`
3 658×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	710	14301
1	2324	13964
0	8397	13132

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 585

Calls

Call 1

Inputs
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1))))
(* 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) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
1
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/2 (/ 1 (* J (+ J (* J (cos K)))))) (/ 1 (pow U 2))))
(* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
(/ (+ (* 1/2 (/ (pow U 2) (+ 1 (cos K)))) (pow J 2)) (pow J 2))
1
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(+ 1 (* 1/2 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
1
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 1 (* -1/2 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 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) (+ (* -1/2 (* (pow K 2) (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (+ (* -1/2 (* (pow K 2) (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))))))) (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K))))))
(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* -1 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))))
(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* 1/4 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))
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(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* 1/4 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))
(+ (* -2 (* (* U (* (cos (* 1/2 K)) (sqrt 1/2))) (sqrt (/ 1 (+ 1 (cos K)))))) (* (pow J 2) (+ (* -1 (* (/ (cos (* 1/2 K)) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ (* (pow J 2) (cos (* 1/2 K))) (* (pow U 5) (pow (sqrt 1/2) 5))) (sqrt (pow (+ 1 (cos K)) 5)))) (* 1/4 (* (/ (cos (* 1/2 K)) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K))))) (* 1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1 (cos K)) 2)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (+ 1 (cos K))))) (+ (* -1/64 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (+ 1 (cos K)) 3)))) (* 1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (+ 1 (cos K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/16 (/ (* (pow U 4) (cos (* 1/2 K))) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (+ (* -1/64 (/ (* (pow U 6) (cos (* 1/2 K))) (* (pow J 6) (pow (- (* -1 (cos K)) 1) 3)))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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 (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/2 (/ (* (pow U 2) (cos (* 1/2 K))) (+ J (* J (cos K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/2 (/ (cos (* 1/2 K)) (+ J (* J (cos K))))) (* 1/16 (/ (* (pow U 2) (cos (* 1/2 K))) (* J (pow (+ J (* J (cos K))) 2)))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/2 (/ (cos (* 1/2 K)) (+ J (* J (cos K))))) (* (pow U 2) (+ (* -1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (* (pow J 2) (pow (+ J (* J (cos K))) 3)))) (* 1/16 (/ (cos (* 1/2 K)) (* J (pow (+ J (* J (cos K))) 2)))))))))
(* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* U (* (cos (* 1/2 K)) (sqrt 1/2)))))
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(* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3))))))))
(* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (* (pow J 7) (pow (+ J (* J (cos K))) 5))) (/ (cos (* 1/2 K)) (* (pow U 6) (pow (sqrt 1/2) 5))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3)))))))))
(* 2 (* (sqrt (/ J (+ J (* J (cos K))))) (* U (* (cos (* 1/2 K)) (sqrt 1/2)))))
(* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))))))
(* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 3)))))))))
(* -1 (* U (+ (* -2 (* (sqrt (/ J (+ J (* J (cos K))))) (* (cos (* 1/2 K)) (sqrt 1/2)))) (+ (* -1 (* (sqrt (* (pow J 3) (+ J (* J (cos K))))) (/ (cos (* 1/2 K)) (* (pow U 2) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (* (pow J 7) (pow (+ J (* J (cos K))) 5))) (/ (cos (* 1/2 K)) (* (pow U 6) (pow (sqrt 1/2) 5))))) (* 1/4 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 3))) (/ (cos (* 1/2 K)) (* (pow U 4) (pow (sqrt 1/2) 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 (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
1
(+ 1 (* 1/4 (/ (pow U 2) (* J (+ J (* J (cos K)))))))
(+ 1 (* (pow U 2) (+ (* -1/32 (/ (pow U 2) (* (pow J 2) (pow (+ J (* J (cos K))) 2)))) (* 1/4 (/ 1 (* J (+ J (* J (cos K)))))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/128 (/ (pow U 2) (* (pow J 3) (pow (+ J (* J (cos K))) 3)))) (* 1/32 (/ 1 (* (pow J 2) (pow (+ J (* J (cos K))) 2)))))) (* 1/4 (/ 1 (* J (+ J (* J (cos K)))))))))
(* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (* U (sqrt 1/2)))
(* U (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))
(* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))
(* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/16 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 5))) (/ 1 (* (pow U 6) (pow (sqrt 1/2) 5))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))))
(* -1 (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (* U (sqrt 1/2))))
(* -1 (* U (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))
(* -1 (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2))))))
(* -1 (* U (+ (* -1/8 (* (sqrt (* (pow J 3) (pow (+ J (* J (cos K))) 3))) (/ 1 (* (pow U 4) (pow (sqrt 1/2) 3))))) (+ (* 1/16 (* (sqrt (* (pow J 5) (pow (+ J (* J (cos K))) 5))) (/ 1 (* (pow U 6) (pow (sqrt 1/2) 5))))) (+ (* 1/2 (* (sqrt (* J (+ J (* J (cos K))))) (/ 1 (* (pow U 2) (sqrt 1/2))))) (* (sqrt (/ 1 (* J (+ J (* J (cos K)))))) (sqrt 1/2)))))))
(* (/ (* U (sqrt 1/2)) J) (sqrt (/ 1 (+ 1 (cos K)))))
(/ (+ (* 1/2 (* (/ (pow J 2) (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K)))))) J)
(/ (+ (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ (pow J 2) (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))) (* 1/2 (* (/ 1 (* U (sqrt 1/2))) (sqrt (+ 1 (cos K)))))))) J)
(/ (+ (* (* U (sqrt 1/2)) (sqrt (/ 1 (+ 1 (cos K))))) (* (pow J 2) (+ (* 1/2 (* (/ 1 (* U (sqrt 1/2))) (sqrt (+ 1 (cos K))))) (* (pow J 2) (+ (* -1/8 (* (/ 1 (* (pow U 3) (pow (sqrt 1/2) 3))) (sqrt (pow (+ 1 (cos K)) 3)))) (* 1/16 (* (/ (pow J 2) (* (pow U 5) (pow (sqrt 1/2) 5))) (sqrt (pow (+ 1 (cos K)) 5))))))))) J)
1
(+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))
(+ 1 (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (+ 1 (cos K)) 2)))) (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K)))))))
(+ 1 (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (+ 1 (cos K)) 2)))) (+ (* 1/128 (/ (pow U 6) (* (pow J 6) (pow (+ 1 (cos K)) 3)))) (* 1/4 (/ (pow U 2) (* (pow J 2) (+ 1 (cos K))))))))
1
(+ 1 (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))))
(+ 1 (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))) (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2))))))
(+ 1 (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (- (* -1 (cos K)) 1)))) (+ (* -1/32 (/ (pow U 4) (* (pow J 4) (pow (- (* -1 (cos K)) 1) 2)))) (* -1/128 (/ (pow U 6) (* (pow J 6) (pow (- (* -1 (cos K)) 1) 3)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* J (+ 1 (cos K)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(* 2 J)
(+ (* -1/2 (* J (pow K 2))) (* 2 J))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(+ J (* J (cos K)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(* -1/192 J)
(+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))
(+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))
(+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))
(* 1/23040 (* J (pow K 2)))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(* 1/23040 (* J (pow K 2)))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))
(* 1/23040 (* J (pow K 2)))

Outputs
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
(* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 U U)) (*.f64 J (fma.f64 J (cos.f64 K) J)))
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U
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U
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(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
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(* -2 J)
(*.f64 J #s(literal -2 binary64))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(fma.f64 #s(literal 1/4 binary64) (.f64 J (.f64 K K)) (*.f64 J #s(literal -2 binary64)))
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(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
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(fma.f64 K (.f64 K (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 K K)) (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)) (.f64 J (.f64 J (.f64 J J)))))) (/.f64 (.f64 #s(literal 1/32 binary64) (.f64 U U)) (.f64 J J))))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))
(+ (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)))))) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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) (- (* -1/2 (+ (* -1/2880 (/ (pow U 2) (pow J 2))) (+ (* 1/384 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/2 (+ (* -1/32 (/ (pow U 2) (pow J 2))) (* 1/96 (/ (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)))))))))))))
(fma.f64 K (.f64 K (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) #s(literal 1/32 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))) (+.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)) (.f64 J (.f64 J (.f64 J J)))))) (.f64 (.f64 K K) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 13/5760 binary64) (.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal -1/192 binary64))) (.f64 (.f64 #s(literal -1/32 binary64) (.f64 U U)) (/.f64 (fma.f64 (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1/96 binary64) (/.f64 (.f64 #s(literal -1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)) (.f64 J (.f64 J (.f64 J J)))))) (.f64 (.f64 J J) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))))))))))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(sqrt (+ 1 (* 1/2 (/ (pow U 2) (* J (+ J (* J (cos K))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)))
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (+ 1 (cos K)))
(fma.f64 J (cos.f64 K) J)
(* -1 (* J (- (* -1 (cos K)) 1)))
(neg.f64 (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(neg.f64 (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(neg.f64 (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J)))
(* -1 (* J (- (* -1 (cos K)) 1)))
(neg.f64 (fma.f64 (neg.f64 (cos.f64 K)) J (neg.f64 J)))
(* 2 J)
(*.f64 #s(literal 2 binary64) J)
(+ (* -1/2 (* J (pow K 2))) (* 2 J))
(fma.f64 #s(literal 2 binary64) J (.f64 J (.f64 #s(literal -1/2 binary64) (*.f64 K K))))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* 1/24 (* J (pow K 2))))))
(fma.f64 (.f64 (fma.f64 J #s(literal -1/2 binary64) (.f64 J (.f64 (.f64 K K) #s(literal 1/24 binary64)))) K) K (*.f64 #s(literal 2 binary64) J))
(+ (* 2 J) (* (pow K 2) (+ (* -1/2 J) (* (pow K 2) (+ (* -1/720 (* J (pow K 2))) (* 1/24 J))))))
(fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 J #s(literal 1/24 binary64) (.f64 J (.f64 (.f64 K K) #s(literal -1/720 binary64)))) (.f64 J #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) J))
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(+ J (* J (cos K)))
(fma.f64 J (cos.f64 K) J)
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* J (- (* 1/23040 (pow K 2)) 1/192))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(neg.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal -1/23040 binary64) #s(literal 1/192 binary64))))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(neg.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal -1/23040 binary64) #s(literal 1/192 binary64))))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(neg.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal -1/23040 binary64) #s(literal 1/192 binary64))))
(* -1 (* J (+ 1/192 (* -1/23040 (pow K 2)))))
(neg.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal -1/23040 binary64) #s(literal 1/192 binary64))))
(* -1/192 J)
(*.f64 J #s(literal -1/192 binary64))
(+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))
(.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (/.f64 J (.f64 K K)) (.f64 J #s(literal 1/23040 binary64))))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (/.f64 J (.f64 K K)) (.f64 J #s(literal 1/23040 binary64))))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (/.f64 J (.f64 K K)) (.f64 J #s(literal 1/23040 binary64))))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (/.f64 J (.f64 K K)) (.f64 J #s(literal 1/23040 binary64))))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (/.f64 J (.f64 K K)) (.f64 J #s(literal 1/23040 binary64))))
(* (pow K 2) (+ (* -1/192 (/ J (pow K 2))) (* 1/23040 J)))
(.f64 (.f64 K K) (fma.f64 #s(literal -1/192 binary64) (/.f64 J (.f64 K K)) (.f64 J #s(literal 1/23040 binary64))))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(* 1/23040 (* J (pow K 2)))
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))

rewrite309.0ms (2.7%)

Memory

-22.1MiB live, 380.2MiB allocated

Rules

5 946×	`lower-*.f32`
5 918×	`lower-*.f64`
4 262×	`lower-fma.f32`
4 254×	`lower-fma.f64`
3 752×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	439
0	100	429
1	346	429
2	2357	425
0	8914	417

Stop Event

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

Counts

21 → 258

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (.f64 U U)) (fma.f64 J (cos.f64 K) J))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 J #s(literal -2 binary64))))
(neg.f64 (/.f64 (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal 2 binary64))))
(/.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) (.f64 J #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J)))))
(/.f64 (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (.f64 J #s(literal -2 binary64)))
(/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64))))
(/.f64 (.f64 U U) (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J)))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (/.f64 (.f64 J #s(literal 2 binary64)) (*.f64 U U)) (fma.f64 J (cos.f64 K) J))))
(/.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 2 binary64))
(/.f64 (.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)) #s(literal 1 binary64)) (*.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (*.f64 J (fma.f64 J (cos.f64 K) J)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (/.f64 (.f64 U U) (fma.f64 J (cos.f64 K) J)))) (neg.f64 (.f64 J #s(literal -2 binary64))))
(/.f64 (neg.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J)))) #s(literal -2 binary64))
(/.f64 (*.f64 (/.f64 U J) (/.f64 U (fma.f64 J (cos.f64 K) J))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 U U) (/.f64 #s(literal 1/2 binary64) J)) (fma.f64 J (cos.f64 K) J))
(/.f64 (.f64 U (.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) #s(literal 1/2 binary64))) J)
(/.f64 (/.f64 (/.f64 (*.f64 U U) (fma.f64 J (cos.f64 K) J)) #s(literal 2 binary64)) J)
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(.f64 (sqrt.f64 (fma.f64 (pow.f64 (/.f64 (.f64 U U) (.f64 J (fma.f64 J (cos.f64 K) J))) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) (-.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 U U) (.f64 (fma.f64 J (cos.f64 K) J) (*.f64 J #s(literal 2 binary64))))))))
(.f64 (pow.f64 (fma.f64 U (/.f64 U (.f64 (.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 U (/.f64 U (.f64 (*.f64 J #s(literal 2 binary64)) (fma.f64 J (cos.f64 K) J))) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 J (*.f64 J (cos.f64 K)))
(+.f64 (*.f64 J (cos.f64 K)) J)
(-.f64 (/.f64 (.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K))))) (-.f64 (.f64 J (cos.f64 K)) J)) (/.f64 (.f64 J J) (-.f64 (*.f64 J (cos.f64 K)) J)))
(fma.f64 J (cos.f64 K) J)
(fma.f64 (cos.f64 K) J J)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (.f64 J (-.f64 J (.f64 J (cos.f64 K))))) (fma.f64 J (.f64 J J) (pow.f64 (*.f64 J (cos.f64 K)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 J (cos.f64 K)) J) (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (neg.f64 (*.f64 J J)))))
(/.f64 (fma.f64 J (.f64 J J) (pow.f64 (.f64 J (cos.f64 K)) #s(literal 3 binary64))) (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (.f64 J (-.f64 J (*.f64 J (cos.f64 K))))))
(/.f64 (fma.f64 J (.f64 J J) (pow.f64 (.f64 J (cos.f64 K)) #s(literal 3 binary64))) (fma.f64 J J (-.f64 (.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K))))) (.f64 J (.f64 J (cos.f64 K))))))
(/.f64 (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (neg.f64 (.f64 J J))) (-.f64 (*.f64 J (cos.f64 K)) J))
(/.f64 (neg.f64 (fma.f64 J (.f64 J J) (pow.f64 (.f64 J (cos.f64 K)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (.f64 J (-.f64 J (*.f64 J (cos.f64 K)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (neg.f64 (.f64 J J)))) (neg.f64 (-.f64 (*.f64 J (cos.f64 K)) J)))
(/.f64 (-.f64 (.f64 J J) (.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))))) (-.f64 J (.f64 J (cos.f64 K))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K))))) (-.f64 (.f64 J (cos.f64 K)) J)) (.f64 (-.f64 (.f64 J (cos.f64 K)) J) (.f64 J J))) (.f64 (-.f64 (.f64 J (cos.f64 K)) J) (-.f64 (.f64 J (cos.f64 K)) J)))
(pow.f64 (/.f64 (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (.f64 J (-.f64 J (.f64 J (cos.f64 K))))) (fma.f64 J (.f64 J J) (pow.f64 (*.f64 J (cos.f64 K)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 J (cos.f64 K)) J) (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (neg.f64 (*.f64 J J)))) #s(literal -1 binary64))
(.f64 (fma.f64 J (.f64 J J) (pow.f64 (.f64 J (cos.f64 K)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (.f64 J (-.f64 J (.f64 J (cos.f64 K)))))))
(.f64 (fma.f64 (.f64 J J) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) K)))) (neg.f64 (.f64 J J))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 J (cos.f64 K)) J)))
(*.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64)) J)
#s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (*.f64 K #s(literal 1/23040 binary64)))))
(.f64 J (.f64 K (*.f64 K #s(literal 1/23040 binary64))))
(.f64 K (.f64 (*.f64 K #s(literal 1/23040 binary64)) J))
(.f64 (.f64 K K) (*.f64 #s(literal 1/23040 binary64) J))
(.f64 #s(literal 1/23040 binary64) (.f64 J (*.f64 K K)))
(.f64 (.f64 K (*.f64 K #s(literal 1/23040 binary64))) J)
(.f64 (.f64 J (*.f64 K K)) #s(literal 1/23040 binary64))
(.f64 (.f64 J K) (*.f64 K #s(literal 1/23040 binary64)))
(.f64 (.f64 J #s(literal 1/23040 binary64)) (*.f64 K K))

eval172.0ms (1.5%)

Memory: 9.5MiB live, 229.5MiB allocated
Compiler: Compiled 35 171 to 1 791 computations (94.9% saved)

prune155.0ms (1.3%)

Memory

11.9MiB live, 257.3MiB allocated

Pruning

36 alts after pruning (30 fresh and 6 done)

	Pruned	Kept	Total
New	1 136	8	1 144
Fresh	3	22	25
Picked	2	3	5
Done	0	3	3
Total	1 141	36	1 177

Accuracy

100.0%

Counts

1 177 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.8%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) (/.f64 U (*.f64 J #s(literal 2 binary64))) #s(literal 1 binary64))))
	66.4%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ ( J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64))))))
	52.9%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 #s(approx (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
	9.3%	(.f64 (.f64 (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))) #s(literal -2 binary64)) #s(approx (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (/.f64 (.f64 U #s(literal -1/2 binary64)) (.f64 J (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
	48.6%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64))))))
	2.8%	(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) #s(approx (sqrt (+ 1 (/ ( U (/ U (+ (* J (cos K)) J))) (* J 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 J (fma.f64 J (cos.f64 K) J)))) (neg.f64 (*.f64 U (sqrt.f64 #s(literal 1/2 binary64)))))))
	31.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 #s(approx (pow (cos (* 1/2 K)) 2) (fma.f64 K (.f64 K #s(literal -1/4 binary64)) #s(literal 1 binary64))) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
	41.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) U) (.f64 J #s(literal -2 binary64))) J (neg.f64 U)))
	28.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) (.f64 (.f64 J J) #s(literal 4 binary64)))) (+.f64 #s(literal 0 binary64) (.f64 (.f64 J #s(literal 2 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
	10.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (*.f64 U U)) #s(literal -1 binary64)) (neg.f64 U)))
	25.3%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 U (neg.f64 U)) (/.f64 #s(literal 1 binary64) U)))
	28.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (*.f64 J #s(literal 2 binary64)))))
✓	53.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
	30.2%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
	29.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
✓	40.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))
	34.5%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J J) #s(literal 1/2 binary64)) U)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 J J) U) (neg.f64 U)))))
✓	41.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
	31.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 J (.f64 J (.f64 K K))) U) (-.f64 (.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U))))
	29.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (/ (- 0 (* (* J J) 4)) (+ 0 (* J 2)))) (fma.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	18.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64))) (.f64 J (-.f64 (.f64 (.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)))) (.f64 J (-.f64 (.f64 (.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
✓	29.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	30.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
	16.6%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (-.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (fma.f64 (.f64 K K) #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (.f64 K #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (.f64 (.f64 K K) (.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(approx (+ ( J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (.f64 K #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))))))) (-.f64 (.f64 J #s(literal -2 binary64)) (.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (.f64 K #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))))))))
	14.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (*.f64 J J) #s(literal 4 binary64)))))
	0.7%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (.f64 (.f64 J J) (*.f64 J J)) #s(literal 16 binary64)))))
	1.0%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J (*.f64 J J)) #s(literal 8 binary64)))))
	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
	32.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
	3.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) J) #s(literal 2 binary64))))
	3.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) #s(literal 2 binary64)) (/.f64 #s(literal 4 binary64) J))))
✓	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))
✓	32.1%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
	3.9%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) J)) #s(literal -1 binary64)))))
	29.8%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* K (* K (+ (* J (* (* K K) 1/23040)) (* J -1/192)))) (* J 1/4))) (* J -2)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
	50.4%	#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 (neg.f64 U) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))

Compiler

Compiled 1 955 to 703 computations (64% saved)

regimes124.0ms (1.1%)

Memory

13.2MiB live, 260.5MiB allocated

Counts

61 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

6 calls:

23.0ms	U
22.0ms	(/.f64 K #s(literal 2 binary64))
20.0ms	(cos.f64 (/.f64 K #s(literal 2 binary64)))
19.0ms	(.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)))))
18.0ms	K

Results

Accuracy	Segments	Branch
87.2%	2	`J`
77.0%	1	`K`
88.7%	2	`U`
99.9%	3	`(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))`
77.0%	1	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
77.0%	1	`(/.f64 K #s(literal 2 binary64))`

Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes21.0ms (0.2%)

Memory

-10.4MiB live, 28.3MiB allocated

Counts

59 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

16.0ms

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

Results

Accuracy	Segments	Branch
99.7%	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)

regimes31.0ms (0.3%)

Memory

-20.2MiB live, 23.7MiB allocated

Counts

55 → 3

Calls

Call 1

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

Calls

1 calls:

27.0ms

(*.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
90.7%	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)

regimes37.0ms (0.3%)

Memory

8.3MiB live, 46.9MiB allocated

Counts

54 → 3

Calls

Call 1

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

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

Calls

2 calls:

19.0ms

14.0ms

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

Results

Accuracy	Segments	Branch
83.1%	2	`U`
89.3%	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)

regimes17.0ms (0.1%)

Memory

-4.1MiB live, 34.1MiB allocated

Counts

47 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

14.0ms

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

Results

Accuracy	Segments	Branch
89.3%	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)

regimes30.0ms (0.3%)

Memory

20.9MiB live, 59.2MiB allocated

Counts

46 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

14.0ms

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
75.5%	2	`J`
84.1%	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 31 to 20 computations (35.5% saved)

regimes72.0ms (0.6%)

Memory

-3.2MiB live, 110.0MiB allocated

Counts

42 → 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))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 U (neg.f64 U)) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) J) #s(literal 2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(literal 1/4 binary64))) (*.f64 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 (cos ( 1/2 K)) (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 U (neg.f64 U)) (/.f64 #s(literal 1 binary64) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (neg.f64 (.f64 U (.f64 U U))) (fma.f64 U U #s(literal 0 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) #s(literal 2 binary64)) (/.f64 #s(literal 4 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* K (* K (+ (* J (* (* K K) 1/23040)) (* J -1/192)))) (* J 1/4))) (* J -2)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (*.f64 J J) #s(literal 4 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 #s(approx (pow (cos (* 1/2 K)) 2) (fma.f64 K (.f64 K #s(literal -1/4 binary64)) #s(literal 1 binary64))) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (/ (- 0 (* (* J J) 4)) (+ 0 (* J 2)))) (fma.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (*.f64 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 (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J (*.f64 J J)) #s(literal 8 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal 1/2 binary64) (.f64 J (.f64 J (/.f64 (.f64 K K) U))) (-.f64 (/.f64 (.f64 (*.f64 J J) #s(literal -2 binary64)) U) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 J (.f64 J (.f64 K K))) U) (-.f64 (.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J J) #s(literal 1/2 binary64)) U)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 J J) U) (neg.f64 U)))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J (.f64 J J)) (.f64 (.f64 J (.f64 J J)) #s(literal 64 binary64))) (/.f64 #s(literal 1/2 binary64) J)) (.f64 (.f64 (.f64 J J) (*.f64 J J)) #s(literal 16 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64))) (.f64 J (-.f64 (.f64 (.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)))) (.f64 J (-.f64 (.f64 (.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) K))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 J (cos.f64 (.f64 #s(literal 1/2 binary64) K))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)) U) (.f64 J #s(literal -2 binary64))) J (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (*.f64 J #s(literal 2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J J) #s(literal 4 binary64))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64))))))
(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 #s(approx (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (-.f64 (.f64 (.f64 J J) #s(literal 4 binary64)) (.f64 (fma.f64 (.f64 K K) #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (.f64 K #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (.f64 (.f64 K K) (.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(approx (+ ( J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (.f64 K #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))))))) (-.f64 (.f64 J #s(literal -2 binary64)) (.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 K (.f64 K #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))))))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U (fma.f64 J (cos.f64 K) J))) (*.f64 J #s(literal 2 binary64))))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(approx (sqrt (+ 1 (pow (/ U ( (* 2 J) (cos (/ K 2)))) 2))) (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 #s(approx (+ 1 (/ ( U (/ U (+ (* J (cos K)) J))) (* J 2))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) #s(approx (sqrt (+ 1 (/ ( U (/ U (+ (* J (cos K)) J))) (* J 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 J (fma.f64 J (cos.f64 K) J)))) (neg.f64 (*.f64 U (sqrt.f64 #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))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 #s(approx (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64)))))
(.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))

Calls

5 calls:

15.0ms	(/.f64 K #s(literal 2 binary64))
15.0ms	(cos.f64 (/.f64 K #s(literal 2 binary64)))
14.0ms	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
12.0ms	U
12.0ms	K

Results

Accuracy	Segments	Branch
67.3%	3	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
64.8%	2	`K`
64.8%	2	`(/.f64 K #s(literal 2 binary64))`
75.9%	4	`U`
81.7%	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 48 to 34 computations (29.2% saved)

regimes15.0ms (0.1%)

Memory

-10.3MiB live, 26.0MiB allocated

Counts

36 → 4

Calls

Call 1

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

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
79.7%	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)

regimes30.0ms (0.3%)

Memory

8.2MiB live, 58.1MiB allocated

Counts

30 → 3

Calls

Call 1

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

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

Calls

3 calls:

11.0ms

9.0ms

8.0ms

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

Results

Accuracy	Segments	Branch
62.1%	2	`U`
59.2%	2	`J`
68.7%	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 35 to 23 computations (34.3% saved)

regimes54.0ms (0.5%)

Memory

-12.9MiB live, 100.5MiB allocated

Counts

27 → 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))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (*.f64 U (neg.f64 U)) U))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) J) #s(literal 2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 K (.f64 K (.f64 J #s(literal 1/4 binary64))) (*.f64 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 (cos ( 1/2 K)) (fma.f64 K (.f64 K #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (.f64 U (neg.f64 U)) (/.f64 #s(literal 1 binary64) U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (/.f64 (neg.f64 (.f64 U (.f64 U U))) (fma.f64 U U #s(literal 0 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (.f64 (/.f64 (.f64 J J) #s(literal 2 binary64)) (/.f64 #s(literal 4 binary64) J))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 #s(approx (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (*.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) #s(approx (+ (* (* K K) (+ (* K (* K (+ (* J (* (* K K) 1/23040)) (* J -1/192)))) (* J 1/4))) (* J -2)) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 J (.f64 J J)) #s(literal 8 binary64))) (.f64 (*.f64 J J) #s(literal 4 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (fma.f64 (/.f64 #s(approx (pow (cos (* 1/2 K)) 2) (fma.f64 K (.f64 K #s(literal -1/4 binary64)) #s(literal 1 binary64))) U) (.f64 #s(literal -2 binary64) (*.f64 J J)) (neg.f64 U)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (/ (- 0 (* (* J J) 4)) (+ 0 (* J 2)))) (fma.f64 (.f64 K K) (.f64 J (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal 1/23040 binary64) #s(literal -1/192 binary64)) #s(literal 1/4 binary64))) (*.f64 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 (cos ( 1/2 K)) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) (fma.f64 (.f64 K K) #s(literal -1/46080 binary64) #s(literal 1/384 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (/.f64 (.f64 (.f64 (.f64 J J) (.f64 J J)) #s(literal 16 binary64)) (.f64 (.f64 J (*.f64 J J)) #s(literal 8 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K #s(approx (+ (* J (* (* K K) 1/23040)) (* J -1/192)) (.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64))))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (fma.f64 (.f64 K K) (fma.f64 K (.f64 K (fma.f64 J (.f64 (.f64 K K) #s(literal 1/23040 binary64)) (.f64 J #s(literal -1/192 binary64)))) (.f64 J #s(literal 1/4 binary64))) (*.f64 J #s(literal -2 binary64)))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal 1/2 binary64) (.f64 J (.f64 J (/.f64 (.f64 K K) U))) (-.f64 (/.f64 (.f64 (*.f64 J J) #s(literal -2 binary64)) U) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 J (.f64 J (.f64 K K))) U) (-.f64 (.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 K (.f64 K (/.f64 (.f64 (.f64 J J) #s(literal 1/2 binary64)) U)) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 J J) U) (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 (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal -2 binary64))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (sqrt.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))) (.f64 #s(literal -2 binary64) J)))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (+ (* (/ (pow (cos (* 1/2 K)) 2) U) (* -2 (* J J))) (neg U)) (fma.f64 J (*.f64 (/.f64 J U) #s(literal -2 binary64)) (neg.f64 U))))
#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) #s(approx (* (cos (* 1/2 K)) (* -2 J)) (*.f64 J #s(literal 2 binary64))))

Calls

6 calls:

10.0ms	J
10.0ms	K
9.0ms	(.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
8.0ms	(/.f64 K #s(literal 2 binary64))
8.0ms	U

Results

Accuracy	Segments	Branch
56.0%	3	`J`
57.3%	3	`U`
51.3%	4	`K`
51.3%	4	`(/.f64 K #s(literal 2 binary64))`
49.2%	3	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
62.1%	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 52 to 37 computations (28.8% saved)

regimes48.0ms (0.4%)

Memory

11.0MiB live, 66.8MiB allocated

Counts

22 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

34.0ms

7.0ms

6.0ms

(*.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
51.3%	2	`J`
54.3%	2	`U`
54.2%	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 35 to 23 computations (34.3% saved)

regimes7.0ms (0.1%)

Memory

-27.0MiB live, 10.3MiB allocated

Counts

11 → 2

Calls

Call 1

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

Outputs

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
54.0%	2	`U`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes8.0ms (0.1%)

Memory

29.3MiB live, 29.3MiB 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	(/.f64 K #s(literal 2 binary64))
1.0ms	J
1.0ms	U
1.0ms	K

Results

Accuracy	Segments	Branch
40.4%	1	`(cos.f64 (/.f64 K #s(literal 2 binary64)))`
40.4%	1	`K`
40.4%	1	`(/.f64 K #s(literal 2 binary64))`
40.4%	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)))))`
40.4%	1	`J`
40.4%	1	`U`

Compiler

Compiled 52 to 37 computations (28.8% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	3.8945029103034964e+281	+inf
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	3.8945029103034964e+281	+inf
0.0ms	-inf	-7.643036816478099e+307

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	3.8945029103034964e+281	+inf
0.0ms	-inf	-7.643036816478099e+307

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	3.8945029103034964e+281	+inf
0.0ms	-inf	-7.643036816478099e+307

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	3.8945029103034964e+281	+inf
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	-8.794087770162267e-249	-1.8485177797281971e-252
0.0ms	-1.1020301962357374e-18	-2.7751984717859863e-20
0.0ms	-4.295382467672704e+156	-3.849689606064345e+156
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	-8.794087770162267e-249	-1.8485177797281971e-252
0.0ms	-3.3622690058313925e+186	-1.8711769126501112e+186
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch4.0ms (0%)

Memory

-34.5MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	-9.489647154664387e-259	3.4464966949742837e-293
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	-9.489647154664387e-259	3.4464966949742837e-293
0.0ms	-1.6030267841438493e-127	-3.209410775648038e-130
0.0ms	-3.849689606064345e+156	-2.323728586954805e+156
0.0ms	-inf	-7.643036816478099e+307

Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch18.0ms (0.2%)

Memory

32.5MiB live, 32.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	3.522330752968222e-17	5.550244072007836e-15

Samples

12.0ms

112×

valid

Compiler

Compiled 198 to 128 computations (35.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 3.0ms (33.3% of total)

ival-cos: 2.0ms (22.2% of total)

ival-div: 1.0ms (11.1% of total)

ival-sqrt: 1.0ms (11.1% of total)

ival-pow2: 1.0ms (11.1% of total)

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

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

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

exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	3.522330752968222e-17	5.550244072007836e-15

Compiler

Compiled 142 to 100 computations (29.6% saved)

simplify25.0ms (0.2%)

Memory

3.8MiB live, 42.9MiB allocated

Algorithm

1×	egg-herbie

Rules

64×	`*-commutative_binary64`
20×	`+-commutative_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`
14×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	172	1975
1	210	1975
2	228	1975
3	248	1975
4	258	1975
5	263	1975
6	264	1975

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 500000000000000016391122991431049124285352641510746782131666788720471301598687167963967189336205896526908748790912075409350817338455347847996995550646521260562389402122810032907636636177574798245164274456255150314546300696222417826065474282413002311039392838405427552850632350105600 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))))
(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 500000000000000016391122991431049124285352641510746782131666788720471301598687167963967189336205896526908748790912075409350817338455347847996995550646521260562389402122810032907636636177574798245164274456255150314546300696222417826065474282413002311039392838405427552850632350105600 binary64)) (.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (fma.f64 (/.f64 U (fma.f64 J (cos.f64 K) J)) (/.f64 U (.f64 J #s(literal 2 binary64))) #s(literal 1 binary64)))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))))
(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 500000000000000016391122991431049124285352641510746782131666788720471301598687167963967189336205896526908748790912075409350817338455347847996995550646521260562389402122810032907636636177574798245164274456255150314546300696222417826065474282413002311039392838405427552850632350105600 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))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))))
(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 500000000000000016391122991431049124285352641510746782131666788720471301598687167963967189336205896526908748790912075409350817338455347847996995550646521260562389402122810032907636636177574798245164274456255150314546300696222417826065474282413002311039392838405427552850632350105600 binary64)) (.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64)))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (neg.f64 U) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (.f64 J J) (*.f64 U U))) #s(literal -1 binary64))))))
(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 500000000000000016391122991431049124285352641510746782131666788720471301598687167963967189336205896526908748790912075409350817338455347847996995550646521260562389402122810032907636636177574798245164274456255150314546300696222417826065474282413002311039392838405427552850632350105600 binary64)) (.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64)))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (/ (* U (/ U (* J 2))) (* (* J 2) (+ 1/2 (* 1/2 (cos (* 2 (* K 1/2)))))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64)))) (.f64 (neg.f64 U) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))))
(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)) (.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ ( J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64)))))))
(if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -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 -3999999999999999933436720892766886858241489100069882145468030457841873670004050218125911507783754967004949553377452420270138029392658294933862041481304342528 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (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 -1298074214633707/1298074214633706907132624082305024 binary64)) (.f64 (.f64 (.f64 J (cos.f64 (.f64 K #s(literal 1/2 binary64)))) #s(literal -2 binary64)) (sqrt.f64 #s(approx (+ 1 (/ (* U (/ U (+ (* J (cos K)) J))) (* J 2))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 U U) (.f64 J J)) #s(literal 1 binary64))))) (if (<=.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (.f64 (.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -5038209258419659/1007641851683931820587806291420968258893675472328417820220872324040744595635843008946260940337480903424595632540239579541935629958157893251896932560850028184716008537290582817399466548302510149103210893455908181007667595468047259786297601506742546990374638711734272 binary64)) (.f64 #s(approx (* (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64)))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))))))
(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 -1999999999999999959234088337507430342214258903733683304135264237914896909571122220072342892220791970157205022783259144237767019517472760523037789559840158117208617709883954451835865006080 binary64)) #s(approx ( (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (.f64 #s(literal -2 binary64) J))) (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 -5038209258419659/1007641851683931820587806291420968258893675472328417820220872324040744595635843008946260940337480903424595632540239579541935629958157893251896932560850028184716008537290582817399466548302510149103210893455908181007667595468047259786297601506742546990374638711734272 binary64)) (.f64 #s(approx ( (* -2 J) (cos (/ K 2))) (.f64 J #s(literal -2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 U (/.f64 U #s(approx (+ (* J (cos K)) J) (.f64 #s(literal 2 binary64) J)))) (.f64 J #s(literal 2 binary64)))))) #s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))))))
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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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#s(approx (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) (neg.f64 U))

soundness1.8s (15.9%)

Memory

-6.6MiB live, 1 324.9MiB allocated

Rules

19 354×	`lower-fma.f64`
19 354×	`lower-fma.f32`
11 672×	`lower-fma.f64`
11 672×	`lower-fma.f32`
11 604×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	439
0	100	429
1	346	429
2	2357	425
0	8914	417
0	360	3717
1	1153	3609
2	4514	3477
0	8499	3319
0	664	13505
1	2168	13138
0	8258	12352
0	73	441
0	112	410
1	407	401
2	3121	397
0	11417	390
0	710	14301
1	2324	13964
0	8397	13132
0	701	13810
1	2294	13434
0	8701	12648
0	53	339
0	84	315
1	276	299
2	1815	287
0	8414	281
0	17	66
0	28	66
1	79	66
2	432	66
3	4364	66
0	8129	66

Stop Event

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

Compiler

Compiled 2 432 to 902 computations (62.9% saved)

preprocess203.0ms (1.8%)

Memory: 34.0MiB live, 300.9MiB allocated
Remove: (abs K)
Compiler: Compiled 3 340 to 604 computations (81.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze341.0ms (2.9%)

sample1.9s (16.2%)

explain230.0ms (2%)

preprocess135.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify45.0ms (0.4%)

localize61.0ms (0.5%)

series35.0ms (0.3%)

simplify418.0ms (3.6%)

rewrite336.0ms (2.9%)

eval128.0ms (1.1%)

prune151.0ms (1.3%)

simplify208.0ms (1.8%)

localize163.0ms (1.4%)

series57.0ms (0.5%)

simplify523.0ms (4.5%)

rewrite403.0ms (3.5%)

eval368.0ms (3.2%)

prune312.0ms (2.7%)

simplify256.0ms (2.2%)

localize207.0ms (1.8%)

series55.0ms (0.5%)

simplify397.0ms (3.4%)

rewrite437.0ms (3.8%)

eval224.0ms (1.9%)

prune186.0ms (1.6%)

simplify202.0ms (1.7%)

localize232.0ms (2%)

series45.0ms (0.4%)

simplify342.0ms (2.9%)

rewrite309.0ms (2.7%)

eval172.0ms (1.5%)

prune155.0ms (1.3%)

regimes124.0ms (1.1%)

regimes21.0ms (0.2%)

regimes31.0ms (0.3%)

regimes37.0ms (0.3%)

regimes17.0ms (0.1%)

regimes30.0ms (0.3%)

regimes72.0ms (0.6%)

regimes15.0ms (0.1%)

regimes30.0ms (0.3%)

regimes54.0ms (0.5%)

regimes48.0ms (0.4%)

regimes7.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch4.0ms (0%)

bsearch1.0ms (0%)

bsearch18.0ms (0.2%)

bsearch1.0ms (0%)

simplify25.0ms (0.2%)

soundness1.8s (15.9%)

preprocess203.0ms (1.8%)

end0.0ms (0%)

Profiling