Maksimov and Kolovsky, Equation (3)

Time bar (total: 10.5s)

analyze460.0ms (4.4%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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 28 to 18 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 278.0ms
ival-pow: 130.0ms (46.8% of total)
ival-mult: 77.0ms (27.7% of total)
ival-div: 27.0ms (9.7% of total)
ival-sqrt: 15.0ms (5.4% of total)
ival-add: 14.0ms (5% of total)
ival-cos: 11.0ms (4% of total)
const: 4.0ms (1.4% of total)
backward-pass: 1.0ms (0.4% of total)

sample1.7s (16.4%)

Results
1.3s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 933.0ms
ival-mult: 334.0ms (35.8% of total)
ival-cos: 200.0ms (21.4% of total)
ival-pow: 130.0ms (13.9% of total)
ival-div: 123.0ms (13.2% of total)
ival-sqrt: 75.0ms (8% of total)
ival-add: 50.0ms (5.4% of total)
const: 18.0ms (1.9% of total)
backward-pass: 3.0ms (0.3% of total)
Bogosity

preprocess126.0ms (1.2%)

Algorithm
2×egg-herbie
Rules
1106×sum3-define
1004×distribute-lft-neg-in
852×*-lowering-*.f32
852×*-lowering-*.f64
824×distribute-rgt-neg-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
075246
1196210
2649210
32301210
44627210
01724
13421
28021
320521
461621
5114521
6158921
7165221
8167021
9168821
10169621
11169821
12169821
0169821
Stop Event
1×iter limit
1×saturated
1×node limit
Calls
Call 1
Inputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
Outputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
Call 2
Inputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
(* (* (* -2 (neg J)) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 (neg J)) (cos (/ K 2)))) 2))))
(* (* (* -2 J) (cos (/ (neg K) 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ (neg K) 2)))) 2))))
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ (neg U) (* (* 2 J) (cos (/ K 2)))) 2))))
(neg (* (* (* -2 (neg J)) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 (neg J)) (cos (/ K 2)))) 2)))))
(neg (* (* (* -2 J) (cos (/ (neg K) 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ (neg K) 2)))) 2)))))
(neg (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ (neg U) (* (* 2 J) (cos (/ K 2)))) 2)))))
(* (* (* -2 K) (cos (/ J 2))) (sqrt (+ 1 (pow (/ U (* (* 2 K) (cos (/ J 2)))) 2))))
(* (* (* -2 U) (cos (/ K 2))) (sqrt (+ 1 (pow (/ J (* (* 2 U) (cos (/ K 2)))) 2))))
(* (* (* -2 J) (cos (/ U 2))) (sqrt (+ 1 (pow (/ K (* (* 2 J) (cos (/ U 2)))) 2))))
Outputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
(* (* (* -2 J) (cos (/ K 2))) (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))))
(* (* (* -2 (neg J)) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 (neg J)) (cos (/ K 2)))) 2))))
(* J (* (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))) (* 2 (cos (/ K 2)))))
(* (* (* -2 J) (cos (/ (neg K) 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ (neg K) 2)))) 2))))
(* (* (* -2 J) (cos (/ K 2))) (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))))
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ (neg U) (* (* 2 J) (cos (/ K 2)))) 2))))
(* (* (* -2 J) (cos (/ K 2))) (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))))
(neg (* (* (* -2 (neg J)) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 (neg J)) (cos (/ K 2)))) 2)))))
(* (* (* -2 J) (cos (/ K 2))) (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))))
(neg (* (* (* -2 J) (cos (/ (neg K) 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ (neg K) 2)))) 2)))))
(* J (* (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))) (* 2 (cos (/ K 2)))))
(neg (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ (neg U) (* (* 2 J) (cos (/ K 2)))) 2)))))
(* J (* (hypot 1 (/ U (* (cos (/ K 2)) (* J 2)))) (* 2 (cos (/ K 2)))))
(* (* (* -2 K) (cos (/ J 2))) (sqrt (+ 1 (pow (/ U (* (* 2 K) (cos (/ J 2)))) 2))))
(* (* (* -2 K) (cos (/ J 2))) (hypot 1 (/ (/ (* U 1/2) K) (cos (/ J 2)))))
(* (* (* -2 U) (cos (/ K 2))) (sqrt (+ 1 (pow (/ J (* (* 2 U) (cos (/ K 2)))) 2))))
(* -2 (* (hypot 1 (/ J (* (cos (/ K 2)) (* 2 U)))) (* (cos (/ K 2)) U)))
(* (* (* -2 J) (cos (/ U 2))) (sqrt (+ 1 (pow (/ K (* (* 2 J) (cos (/ U 2)))) 2))))
(* (* (* -2 J) (cos (* U 1/2))) (hypot 1 (/ (/ K (* J 2)) (cos (* U 1/2)))))
Symmetry

(abs K)

(abs U)

(negabs J)

explain243.0ms (2.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
330-0-(*.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)))))
300-0-(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))))
00-0-(*.f64 #s(literal -2 binary64) J)
00-0-#s(literal -2 binary64)
00-0-#s(literal 2 binary64)
00-0-(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
00-0-J
085(1.1068727283239132e+229 2.4865385187927522e-169 3.0884056131469767e+167)0-(pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
00-0-(/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
00-0-(+.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)))
00-0-U
00-0-(*.f64 #s(literal 2 binary64) J)
0120(30.257764548769057 3.345633507142781e+130 4.5698532151430464e-204)0-(cos.f64 (/.f64 K #s(literal 2 binary64)))
00-0-#s(literal 1 binary64)
00-0-(/.f64 K #s(literal 2 binary64))
00-0-K
00-0-(*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
Results
114.0ms512×0valid
Compiler

Compiled 255 to 53 computations (79.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-mult: 20.0ms (36% of total)
ival-cos: 12.0ms (21.6% of total)
ival-div: 8.0ms (14.4% of total)
ival-pow: 7.0ms (12.6% of total)
ival-sqrt: 4.0ms (7.2% of total)
ival-add: 3.0ms (5.4% of total)
const: 1.0ms (1.8% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 24 to 15 computations (37.5% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶87.7%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
▶76.6%
(*.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 51 to 32 computations (37.3% saved)

simplify97.0ms (0.9%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff0
(*.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)))))
✓cost-diff6528
(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×*-lowering-*.f32
852×*-lowering-*.f64
830×associate-*r/
758×/-lowering-/.f32
758×/-lowering-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025177
155177
2115177
3321177
4800177
51321177
61594177
71904177
82187177
92260177
102260177
112411177
122411177
02411177
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
(* (* -2 J) (cos (/ K 2)))
(* -2 J)
-2
J
(cos (/ K 2))
(/ K 2)
K
2
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
(+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))
1
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
(/ U (* (* 2 J) (cos (/ K 2))))
U
(* (* 2 J) (cos (/ K 2)))
(* 2 J)
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))
(* (* -2 J) (cos (/ K 2)))
(* -2 J)
-2
J
(cos (/ K 2))
(/ K 2)
K
2
(sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2))))))
1
(/ (/ (/ U J) 2) (cos (/ K 2)))
(/ (/ U J) 2)
(/ U J)
U
Outputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
(*.f64 #s(literal -2 binary64) (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(* (* -2 J) (cos (/ K 2)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))
(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
(pow.f64 (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 2 binary64))
(/ U (* (* 2 J) (cos (/ K 2))))
(/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
U
(* (* 2 J) (cos (/ K 2)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))
(* 2 J)
(*.f64 J #s(literal 2 binary64))
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))
(*.f64 #s(literal -2 binary64) (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(* (* -2 J) (cos (/ K 2)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2))))))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(/ (/ (/ U J) 2) (cos (/ K 2)))
(/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ (/ U J) 2)
(/.f64 (/.f64 U J) #s(literal 2 binary64))
(/ U J)
(/.f64 U J)
U

localize212.0ms (2%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (/.f64 U J) #s(literal 2 binary64))
✓accuracy99.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.8%
(/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy87.9%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
✓accuracy99.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.5%
(pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
✓accuracy89.0%
(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))))
✓accuracy87.9%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
Results
163.0ms256×0valid
Compiler

Compiled 189 to 23 computations (87.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-add: 20.0ms (30.9% of total)
ival-mult: 13.0ms (20.1% of total)
ival-div: 11.0ms (17% of total)
compiled-spec: 7.0ms (10.8% of total)
ival-cos: 6.0ms (9.3% of total)
ival-sqrt: 4.0ms (6.2% of total)
ival-pow: 3.0ms (4.6% of total)
const: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series64.0ms (0.6%)

Counts
9 → 252
Calls
Call 1
Inputs
#<alt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))>
#<alt (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))>
#<alt (* (* -2 J) (cos (/ K 2)))>
#<alt (* -2 J)>
#<alt (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))>
#<alt (cos (/ K 2))>
#<alt (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)>
#<alt (/ (/ (/ U J) 2) (cos (/ K 2)))>
#<alt (/ (/ U J) 2)>
Outputs
#<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))))))>
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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))))>
#<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)))>
#<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) (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 (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U J))>
#<alt (+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
#<alt (* 1/2 (/ U J))>
Calls

63 calls:

TimeVariablePointExpression
20.0ms
U
@0
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
5.0ms
K
@0
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
3.0ms
K
@0
(* (* -2 J) (cos (/ K 2)))
3.0ms
K
@-inf
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
2.0ms
K
@inf
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite585.0ms (5.6%)

Algorithm
1×batch-egg-rewrite
Rules
4526×/-lowering-/.f32
4526×/-lowering-/.f64
3914×*-lowering-*.f32
3914×*-lowering-*.f64
1170×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02595
112695
2103195
0855195
Stop Event
1×iter limit
1×node limit
Counts
9 → 565
Calls
Call 1
Inputs
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
(* (* -2 J) (cos (/ K 2)))
(* -2 J)
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))
(cos (/ K 2))
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
(/ (/ (/ U J) 2) (cos (/ K 2)))
(/ (/ U J) 2)
Outputs
(exp.f64 (*.f64 (log1p.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))) #s(literal 1/2 binary64)))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 6 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal -1 binary64))) (sqrt.f64 (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64))))
(/.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K))))))) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))))) #s(literal 1/2 binary64))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64)))))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) (+.f64 (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))) #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) K)))))))) #s(literal 1/2 binary64)))
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(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U (*.f64 #s(literal 2 binary64) J)))))
(/.f64 (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) J))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64))
(/.f64 (/.f64 U #s(literal 2 binary64)) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 U J))))
(/.f64 (exp.f64 (log.f64 U)) (exp.f64 (log.f64 (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(/.f64 (exp.f64 (log.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)))) (exp.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (exp.f64 (log.f64 (/.f64 U J))) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
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(/.f64 (neg.f64 (/.f64 U #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (neg.f64 (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) J)))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -2 binary64))
(pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
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(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U (*.f64 #s(literal 2 binary64) J))) #s(literal -1 binary64))
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(*.f64 (sqrt.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(*.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
(*.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal -2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 U J) #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) U) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) J)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U J)) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 U J))) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(*.f64 (exp.f64 (log.f64 U)) (exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))))
(*.f64 (exp.f64 (log.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)))) (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U #s(literal 2 binary64)))
(*.f64 (/.f64 U (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) J))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) J)) (/.f64 U (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 U #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (/.f64 U J)))
(*.f64 (/.f64 (/.f64 U J) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal -1 binary64) J) #s(literal 2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 J #s(literal -2 binary64))) (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64))) (/.f64 U J))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) U)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) J)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 U J))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 U J) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) J))) (/.f64 (/.f64 U J) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) J))) (/.f64 U (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) J))))
(neg.f64 (/.f64 (/.f64 U J) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 U J)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 U J)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 J U) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) J)) (-.f64 #s(literal 0 binary64) U)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 J (/.f64 U #s(literal 2 binary64))))
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(/.f64 U (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) J))))
(/.f64 U (neg.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) J))))
(/.f64 (/.f64 U J) #s(literal 2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 J U))
(/.f64 (-.f64 #s(literal 0 binary64) U) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) J)))
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(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (/.f64 U J))))
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 J U)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) J))
(/.f64 (/.f64 U #s(literal 2 binary64)) J)
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1/2 binary64))) J)
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(*.f64 (/.f64 U J) #s(literal 1/2 binary64))
(*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64))
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(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 U J) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) J))))
(*.f64 (-.f64 #s(literal 0 binary64) U) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) J))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) #s(literal -1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 U J) #s(literal -2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 U J)))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) J))
(*.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) J))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) U) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) J))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) U) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) J))
(*.f64 (pow.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) J))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 U J)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 U J)) #s(literal -1/2 binary64)))

simplify373.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
6680×*-lowering-*.f32
6680×*-lowering-*.f64
1846×/-lowering-/.f32
1846×/-lowering-/.f64
1812×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03895624
113764833
258944626
086104626
Stop Event
1×iter limit
1×node limit
Counts
252 → 252
Calls
Call 1
Inputs
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))))))
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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)))
(+ (* 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))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U J))
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
(* 1/2 (/ U J))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(+ 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)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal -1/128 binary64)) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))))))
(+ 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)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 U U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) (*.f64 U (*.f64 U (-.f64 (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/1024 binary64)) (pow.f64 J #s(literal 6 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 1/128 binary64) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)))))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))
(*.f64 U (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 J (*.f64 U U)))))
(* 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)))))
(*.f64 U (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 J (*.f64 U U)))) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)) (/.f64 (*.f64 J (*.f64 J J)) (pow.f64 U #s(literal 4 binary64))))))
(* 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))))))
(*.f64 U (+.f64 (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 J (*.f64 U U)))) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)) (/.f64 (*.f64 J (*.f64 J J)) (pow.f64 U #s(literal 4 binary64))))) (*.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)) (/.f64 (pow.f64 J #s(literal 5 binary64)) (pow.f64 U #s(literal 6 binary64)))))))
(* -1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 J (*.f64 U U))))))
(* -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))))))
(-.f64 #s(literal 0 binary64) (*.f64 U (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 J (*.f64 U U)))) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)) (/.f64 (*.f64 J (*.f64 J J)) (pow.f64 U #s(literal 4 binary64)))))))
(* -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)))))))
(*.f64 (+.f64 (-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 J (*.f64 U U)))) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)) (/.f64 (*.f64 J (*.f64 J J)) (pow.f64 U #s(literal 4 binary64))))) (*.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)) (/.f64 (pow.f64 J #s(literal 5 binary64)) (pow.f64 U #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) U))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)
(/.f64 (+.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (/.f64 (*.f64 J J) 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)
(/.f64 (+.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (*.f64 J J) (-.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) U) (*.f64 (*.f64 J J) (pow.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) U) #s(literal 3 binary64)))))) 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)
(/.f64 (+.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (*.f64 J J) (+.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) U) (*.f64 J (*.f64 J (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64))) (pow.f64 U #s(literal 5 binary64))) (pow.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) U) #s(literal 3 binary64)))))))) J)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))) (/.f64 (/.f64 (*.f64 #s(literal 1/1024 binary64) (pow.f64 U #s(literal 6 binary64))) (pow.f64 J #s(literal 6 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 6 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 U U)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))) (/.f64 (/.f64 (*.f64 #s(literal 1/1024 binary64) (pow.f64 U #s(literal 6 binary64))) (pow.f64 J #s(literal 6 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 6 binary64))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))))
(+ (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)))))))))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))))) (*.f64 (*.f64 #s(literal 1/32 binary64) (*.f64 K K)) (/.f64 (*.f64 U U) (*.f64 J J)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
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(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 U (*.f64 K K))) J))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 U #s(literal 1/16 binary64)) J) (*.f64 K (*.f64 K (*.f64 (/.f64 U J) #s(literal 5/768 binary64)))))))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 U #s(literal 1/16 binary64)) J) (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 (*.f64 U #s(literal -5/384 binary64)) J) (*.f64 (*.f64 K K) (+.f64 (*.f64 (/.f64 U J) #s(literal -5/3072 binary64)) (*.f64 (/.f64 U J) #s(literal 7/23040 binary64))))) (*.f64 K K))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(* 1/2 (/ U J))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))

eval139.0ms (1.3%)

Compiler

Compiled 28848 to 3199 computations (88.9% saved)

prune162.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New9287935
Fresh000
Picked202
Done000
Total9307937
Accuracy
99.9%
Counts
937 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶38.7%
(-.f64 #s(literal 0 binary64) U)
45.5%
(*.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 #s(literal 2 binary64) K))))) (*.f64 #s(literal 4 binary64) (*.f64 J J)))) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
▶87.7%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
75.0%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
▶32.4%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
▶54.4%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
▶12.4%
U
Compiler

Compiled 264 to 182 computations (31.1% saved)

simplify200.0ms (1.9%)

Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))
✓cost-diff0
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
✓cost-diff320
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))))
✓cost-diff0
(*.f64 J #s(literal -2 binary64))
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) K)
✓cost-diff0
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
✓cost-diff0
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
✓cost-diff0
(-.f64 #s(literal 0 binary64) U)
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
✓cost-diff0
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Rules
2420×*-lowering-*.f32
2420×*-lowering-*.f64
2158×fma-lowering-fma.f32
2158×fma-lowering-fma.f64
2046×fma-define
Iterations

Useful iterations: 10 (0.0ms)

IterNodesCost
035166
192163
2216163
3545159
41417159
52058159
63455159
74389159
84671159
94765159
106249157
117125157
08232157
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))
(* (* -2 J) (/ 1 (/ 1 (cos (/ K 2)))))
(* -2 J)
-2
J
(/ 1 (/ 1 (cos (/ K 2))))
1
(/ 1 (cos (/ K 2)))
(cos (/ K 2))
(/ K 2)
K
2
(sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2))))))
(/ (/ (/ U J) 2) (cos (/ K 2)))
(/ (/ U J) 2)
(/ U J)
U
U
(- 0 U)
0
U
(* (cos (* 1/2 K)) (* J -2))
(cos (* 1/2 K))
(* 1/2 K)
1/2
K
(* J -2)
J
-2
(* (sqrt (+ 1 (/ (* (* U U) 1/4) (* J J)))) (* J -2))
(sqrt (+ 1 (/ (* (* U U) 1/4) (* J J))))
(+ 1 (/ (* (* U U) 1/4) (* J J)))
1
(/ (* (* U U) 1/4) (* J J))
(* (* U U) 1/4)
(* U U)
U
1/4
(* J J)
J
(* J -2)
-2
Outputs
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(* (* -2 J) (/ 1 (/ 1 (cos (/ K 2)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(/ 1 (/ 1 (cos (/ K 2))))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(/ 1 (cos (/ K 2)))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2))))))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/ (/ (/ U J) 2) (cos (/ K 2)))
(/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ (/ U J) 2)
(/.f64 U (*.f64 J #s(literal 2 binary64)))
(/ U J)
(/.f64 U J)
U
U
(- 0 U)
(-.f64 #s(literal 0 binary64) U)
0
#s(literal 0 binary64)
U
(* (cos (* 1/2 K)) (* J -2))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(* 1/2 K)
(*.f64 K #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
K
(* J -2)
(*.f64 #s(literal -2 binary64) J)
J
-2
#s(literal -2 binary64)
(* (sqrt (+ 1 (/ (* (* U U) 1/4) (* J J)))) (* J -2))
(*.f64 J (*.f64 #s(literal -2 binary64) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 J #s(literal 2 binary64))))))
(sqrt (+ 1 (/ (* (* U U) 1/4) (* J J))))
(hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 J #s(literal 2 binary64))))
(+ 1 (/ (* (* U U) 1/4) (* J J)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 U U) (*.f64 (*.f64 J J) #s(literal 4 binary64))))
1
#s(literal 1 binary64)
(/ (* (* U U) 1/4) (* J J))
(/.f64 (*.f64 U U) (*.f64 (*.f64 J J) #s(literal 4 binary64)))
(* (* U U) 1/4)
(*.f64 U (*.f64 U #s(literal 1/4 binary64)))
(* U U)
(*.f64 U U)
U
1/4
#s(literal 1/4 binary64)
(* J J)
(*.f64 J J)
J
(* J -2)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)

localize208.0ms (2%)

Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 J #s(literal -2 binary64))
✓accuracy89.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))))
✓accuracy87.9%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
✓accuracy68.3%
(/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))
✓accuracy100.0%
(*.f64 J #s(literal -2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) K)
✓accuracy100.0%
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
✓accuracy99.8%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) U)
✓accuracy99.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
✓accuracy99.8%
(/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy87.9%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
Results
150.0ms256×0valid
Compiler

Compiled 196 to 33 computations (83.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 67.0ms
ival-mult: 26.0ms (38.9% of total)
ival-div: 13.0ms (19.4% of total)
ival-cos: 11.0ms (16.4% of total)
compiled-spec: 8.0ms (12% of total)
ival-sqrt: 4.0ms (6% of total)
ival-add: 3.0ms (4.5% of total)
ival-sub: 1.0ms (1.5% of total)
const: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series47.0ms (0.4%)

Counts
14 → 288
Calls
Call 1
Inputs
#<alt (/ 1 (/ 1 (cos (/ K 2))))>
#<alt (* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))>
#<alt (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2)))))>
#<alt (* -2 J)>
#<alt (- 0 U)>
#<alt (* (cos (* 1/2 K)) (* J -2))>
#<alt (cos (* 1/2 K))>
#<alt (* 1/2 K)>
#<alt (* J -2)>
#<alt (sqrt (+ 1 (/ (* (* U U) 1/4) (* J J))))>
#<alt (* (sqrt (+ 1 (/ (* (* U U) 1/4) (* J J)))) (* J -2))>
#<alt (+ 1 (/ (* (* U U) 1/4) (* J J)))>
#<alt (/ (* (* U U) 1/4) (* J J))>
#<alt (/ (/ (/ U J) 2) (cos (/ K 2)))>
Outputs
#<alt 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 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 (* -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 (* -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 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 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 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 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 (* 1/2 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>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (pow J 4))) (* 1/8 (/ 1 (pow J 2))))))>
#<alt (+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (pow J 6))) (* 1/128 (/ 1 (pow J 4))))) (* 1/8 (/ 1 (pow J 2))))))>
#<alt (* 1/2 (/ U J))>
#<alt (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))>
#<alt (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))>
#<alt (* -1/2 (/ U J))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))>
#<alt (* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))))>
#<alt (* 1/2 (/ U J))>
#<alt (/ (+ (* 1/2 U) (/ (pow J 2) U)) J)>
#<alt (/ (+ (* 1/2 U) (* (pow J 2) (+ (* -1 (/ (pow J 2) (pow U 3))) (/ 1 U)))) J)>
#<alt (/ (+ (* 1/2 U) (* (pow J 2) (+ (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 5))) (/ 1 (pow U 3)))) (/ 1 U)))) J)>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* -1/4 (/ (pow U 2) J)))>
#<alt (+ (* -2 J) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (pow J 3))) (* 1/4 (/ 1 J)))))>
#<alt (+ (* -2 J) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (pow J 5))) (* 1/64 (/ 1 (pow J 3))))) (* 1/4 (/ 1 J)))))>
#<alt (* -1 U)>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))>
#<alt (* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1))>
#<alt U>
#<alt (* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))>
#<alt (* -1 (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1)))>
#<alt (* -1 (* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1)))>
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (pow J 2) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))))>
#<alt (+ (* -1 U) (* (pow J 2) (- (* (pow J 2) (+ (* -4 (/ (pow J 2) (pow U 5))) (* 2 (/ 1 (pow U 3))))) (* 2 (/ 1 U)))))>
#<alt (* -2 J)>
#<alt (* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))>
#<alt (* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (* 1/64 (/ (pow U 4) (pow J 4)))) 2))>
#<alt (* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (+ (* -1/512 (/ (pow U 6) (pow J 6))) (* 1/64 (/ (pow U 4) (pow J 4))))) 2))>
#<alt (* -2 J)>
#<alt (* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))>
#<alt (* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (+ (* 1/512 (/ (pow U 6) (pow J 6))) (* 1/4 (/ (pow U 2) (pow J 2))))))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U J))>
#<alt (+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
Calls

72 calls:

TimeVariablePointExpression
27.0ms
J
@0
(* (sqrt (+ 1 (/ (* (* U U) 1/4) (* J J)))) (* J -2))
6.0ms
U
@0
(+ 1 (/ (* (* U U) 1/4) (* J J)))
1.0ms
U
@inf
(sqrt (+ 1 (/ (* (* U U) 1/4) (* J J))))
0.0ms
U
@0
(sqrt (+ 1 (/ (* (* U U) 1/4) (* J J))))
0.0ms
U
@inf
(+ 1 (/ (* (* U U) 1/4) (* J J)))

rewrite319.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
4358×*-lowering-*.f32
4358×*-lowering-*.f64
3794×/-lowering-/.f32
3794×/-lowering-/.f64
1952×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035106
1178103
21486103
08385103
Stop Event
1×iter limit
1×node limit
Counts
14 → 308
Calls
Call 1
Inputs
(/ 1 (/ 1 (cos (/ K 2))))
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ (/ U J) 2) (cos (/ K 2))) (/ (/ (/ U J) 2) (cos (/ K 2)))))))
(* (* -2 J) (/ 1 (/ 1 (cos (/ K 2)))))
(* -2 J)
(- 0 U)
(* (cos (* 1/2 K)) (* J -2))
(cos (* 1/2 K))
(* 1/2 K)
(* J -2)
(sqrt (+ 1 (/ (* (* U U) 1/4) (* J J))))
(* (sqrt (+ 1 (/ (* (* U U) 1/4) (* J J)))) (* J -2))
(+ 1 (/ (* (* U U) 1/4) (* J J)))
(/ (* (* U U) 1/4) (* J J))
(/ (/ (/ U J) 2) (cos (/ K 2)))
Outputs
(exp.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U J)))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 J U)))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (/.f64 U J)))
(/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))
(/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
(/.f64 (/.f64 U J) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 U J)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U (*.f64 #s(literal 2 binary64) J)))))
(/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) J)))
(/.f64 (/.f64 (/.f64 U J) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (neg.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (*.f64 U #s(literal 1 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 (/.f64 U J) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) #s(literal 1 binary64)) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (*.f64 U #s(literal -1 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) J) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (*.f64 (/.f64 U J) #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) #s(literal -1 binary64)) (*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 U (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) J))
(/.f64 (*.f64 (/.f64 U J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -2 binary64))
(/.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U (*.f64 #s(literal 2 binary64) J))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 U J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U (*.f64 #s(literal 2 binary64) J))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U J)) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 J U)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U (*.f64 #s(literal 2 binary64) J)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (pow.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)))
(*.f64 U (/.f64 (/.f64 #s(literal 1 binary64) J) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 U (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) J) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(*.f64 (/.f64 U J) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 U J) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 U J) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 U J) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 U J) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 2 binary64)))
(*.f64 (/.f64 (/.f64 U J) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U J)) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) U) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) J)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 U J))) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 U J) #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 U J) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (/.f64 U (*.f64 #s(literal 2 binary64) J)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))

simplify337.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
6122×*-lowering-*.f32
6122×*-lowering-*.f64
1930×+-lowering-+.f64
1930×+-lowering-+.f32
1806×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04293810
114663356
256713233
083423233
Stop Event
1×iter limit
1×node limit
Counts
288 → 288
Calls
Call 1
Inputs
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(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 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* -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 U 2) (pow J 2))))
(+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (pow J 4))) (* 1/8 (/ 1 (pow J 2))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (pow J 6))) (* 1/128 (/ 1 (pow J 4))))) (* 1/8 (/ 1 (pow J 2))))))
(* 1/2 (/ U J))
(* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))
(* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))
(* -1/2 (/ U J))
(* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))))
(* 1/2 (/ U J))
(/ (+ (* 1/2 U) (/ (pow J 2) U)) J)
(/ (+ (* 1/2 U) (* (pow J 2) (+ (* -1 (/ (pow J 2) (pow U 3))) (/ 1 U)))) J)
(/ (+ (* 1/2 U) (* (pow J 2) (+ (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 5))) (/ 1 (pow U 3)))) (/ 1 U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))
(* -2 J)
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (pow J 3))) (* 1/4 (/ 1 J)))))
(+ (* -2 J) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (pow J 5))) (* 1/64 (/ 1 (pow J 3))))) (* 1/4 (/ 1 J)))))
(* -1 U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1)))
(* -1 U)
(+ (* -2 (/ (pow J 2) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))))
(+ (* -1 U) (* (pow J 2) (- (* (pow J 2) (+ (* -4 (/ (pow J 2) (pow U 5))) (* 2 (/ 1 (pow U 3))))) (* 2 (/ 1 U)))))
(* -2 J)
(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
(* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (* 1/64 (/ (pow U 4) (pow J 4)))) 2))
(* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (+ (* -1/512 (/ (pow U 6) (pow J 6))) (* 1/64 (/ (pow U 4) (pow J 4))))) 2))
(* -2 J)
(* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))
(* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (* 1/4 (/ (pow U 2) (pow J 2)))))))
(* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (+ (* 1/512 (/ (pow U 6) (pow J 6))) (* 1/4 (/ (pow U 2) (pow J 2))))))))
1
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
1
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
1
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U J))
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64)))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64)))))))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (*.f64 J J) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)))) U) U)
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))) U) (*.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64)) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U))))))) 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) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))) U) (*.f64 (*.f64 J J) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 J J) #s(literal -4 binary64)) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64))) (pow.f64 U #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 4 binary64))) (*.f64 U (*.f64 U U))))))) U)
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(*.f64 J (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 J J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(*.f64 J (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 J J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) (/.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #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 (+.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -2 binary64)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 J J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 U #s(literal 6 binary64))) (pow.f64 J #s(literal 6 binary64))) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64))))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(*.f64 (+.f64 (*.f64 (/.f64 (/.f64 U J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) (neg.f64 J))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(*.f64 (+.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (+.f64 (*.f64 (/.f64 (/.f64 U J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64))))) (neg.f64 J))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(*.f64 (+.f64 (+.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (+.f64 (*.f64 (/.f64 (/.f64 U J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 3 binary64))))) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 J #s(literal 6 binary64))) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 5 binary64)))) (neg.f64 J))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))) (*.f64 #s(literal -2 binary64) J))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(*.f64 #s(literal -2 binary64) (+.f64 (*.f64 J (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))))) (*.f64 (*.f64 K K) (+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))) (*.f64 #s(literal -1/8 binary64) J)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))))) (/.f64 (*.f64 #s(literal 1/32 binary64) (*.f64 U U)) J))))))
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U
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(*.f64 (+.f64 (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 J #s(literal 4 binary64))))) (neg.f64 J))
(* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (+ (* 1/512 (/ (pow U 6) (pow J 6))) (* 1/4 (/ (pow U 2) (pow J 2))))))))
(*.f64 (+.f64 #s(literal 2 binary64) (+.f64 (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))) (+.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 J #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 U #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 J #s(literal 6 binary64)))))) (neg.f64 J))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/.f64 (+.f64 (*.f64 J J) (*.f64 U (*.f64 U #s(literal 1/4 binary64)))) (*.f64 J J))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/.f64 (+.f64 (*.f64 J J) (*.f64 U (*.f64 U #s(literal 1/4 binary64)))) (*.f64 J J))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/.f64 (+.f64 (*.f64 J J) (*.f64 U (*.f64 U #s(literal 1/4 binary64)))) (*.f64 J J))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J)))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(*.f64 U (*.f64 U (/.f64 #s(literal 1/4 binary64) (*.f64 J J))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (*.f64 K (*.f64 K (/.f64 (*.f64 U #s(literal 1/16 binary64)) J))))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (*.f64 (*.f64 K K) (+.f64 (*.f64 (*.f64 K K) (*.f64 (/.f64 U J) #s(literal 5/768 binary64))) (/.f64 (*.f64 U #s(literal 1/16 binary64)) J))))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (*.f64 K (*.f64 K (+.f64 (/.f64 (*.f64 U #s(literal 1/16 binary64)) J) (*.f64 (*.f64 K K) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 U J) #s(literal -5/3072 binary64)) (*.f64 (/.f64 U J) #s(literal 7/23040 binary64))) (*.f64 (*.f64 K K) #s(literal -1/2 binary64))) (*.f64 (/.f64 U J) #s(literal 5/768 binary64))))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) U) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))

eval117.0ms (1.1%)

Compiler

Compiled 12858 to 1409 computations (89% saved)

prune75.0ms (0.7%)

Pruning

19 alts after pruning (16 fresh and 3 done)

PrunedKeptTotal
New59815613
Fresh112
Picked235
Done000
Total60119620
Accuracy
100.0%
Counts
620 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶54.3%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
54.3%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
36.8%
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
▶31.8%
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
10.4%
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 J J) U) U)))))
39.4%
(*.f64 (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 J #s(literal -2 binary64)))
45.5%
(*.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 #s(literal 2 binary64) K))))) (*.f64 #s(literal 4 binary64) (*.f64 J J)))) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
21.6%
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U)))))) J) (*.f64 J #s(literal -2 binary64)))
10.6%
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
29.1%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))) (*.f64 J #s(literal -2 binary64)))
28.9%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))) (*.f64 J #s(literal -2 binary64)))
▶29.1%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
10.0%
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
✓32.4%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
▶47.6%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
✓54.4%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
30.6%
(*.f64 #s(literal -2 binary64) J)
▶38.7%
(neg.f64 U)
✓12.4%
U
Compiler

Compiled 622 to 434 computations (30.2% saved)

simplify165.0ms (1.6%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J))))
✓cost-diff0
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
✓cost-diff0
(+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))
✓cost-diff0
(*.f64 J J)
✓cost-diff0
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
✓cost-diff128
(*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U)))))
✓cost-diff0
(*.f64 K K)
✓cost-diff0
(*.f64 #s(literal -1/8 binary64) (*.f64 K K))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K)))
✓cost-diff128
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
✓cost-diff-64
(neg.f64 U)
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff128
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Rules
3180×*-lowering-*.f32
3180×*-lowering-*.f64
1632×sum3-define
1458×fma-lowering-fma.f32
1458×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
035196
198187
2254183
3686174
41719170
52602170
64995170
08115170
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (* -2 J) (/ 1 (cos (/ K 2))))
(* -2 J)
-2
J
(/ 1 (cos (/ K 2)))
1
(cos (/ K 2))
(/ K 2)
K
2
(neg U)
U
(* (+ 1 (* -1/8 (* K K))) (* J -2))
(+ 1 (* -1/8 (* K K)))
1
(* -1/8 (* K K))
-1/8
(* K K)
K
(* J -2)
J
-2
(- (* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))) U)
(* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))
(* J J)
J
(+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))
(/ -2 U)
-2
U
(/ (* 2 (* J J)) (* U (* U U)))
(* 2 (* J J))
2
(* U (* U U))
(* U U)
(* (sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J)))) (* J -2))
(sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J))))
(+ 1 (* (/ U J) (/ (* U 1/4) J)))
1
(* (/ U J) (/ (* U 1/4) J))
(/ U J)
U
J
(/ (* U 1/4) J)
(* U 1/4)
1/4
(* J -2)
-2
Outputs
(/ (* -2 J) (/ 1 (cos (/ K 2))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(/ 1 (cos (/ K 2)))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(neg U)
(-.f64 #s(literal 0 binary64) U)
U
(* (+ 1 (* -1/8 (* K K))) (* J -2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 (*.f64 K K) #s(literal 1/4 binary64))))
(+ 1 (* -1/8 (* K K)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K)))
1
#s(literal 1 binary64)
(* -1/8 (* K K))
(*.f64 #s(literal -1/8 binary64) (*.f64 K K))
-1/8
#s(literal -1/8 binary64)
(* K K)
(*.f64 K K)
K
(* J -2)
(*.f64 #s(literal -2 binary64) J)
J
-2
#s(literal -2 binary64)
(- (* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))) U)
(-.f64 (/.f64 (*.f64 (*.f64 J J) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U U)))) U) U)
(* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))
(/.f64 (*.f64 (*.f64 J J) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U U)))) U)
(* J J)
(*.f64 J J)
J
(+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))
(+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))
(/ -2 U)
(/.f64 #s(literal -2 binary64) U)
-2
#s(literal -2 binary64)
U
(/ (* 2 (* J J)) (* U (* U U)))
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U)))
(* 2 (* J J))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
2
#s(literal 2 binary64)
(* U (* U U))
(*.f64 U (*.f64 U U))
(* U U)
(*.f64 U U)
(* (sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J)))) (* J -2))
(*.f64 (*.f64 #s(literal -2 binary64) J) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 U (*.f64 (/.f64 U J) #s(literal 1/4 binary64))) J))))
(sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 U (*.f64 (/.f64 U J) #s(literal 1/4 binary64))) J)))
(+ 1 (* (/ U J) (/ (* U 1/4) J)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 U (*.f64 (/.f64 U J) #s(literal 1/4 binary64))) J))
1
#s(literal 1 binary64)
(* (/ U J) (/ (* U 1/4) J))
(/.f64 (*.f64 U (*.f64 (/.f64 U J) #s(literal 1/4 binary64))) J)
(/ U J)
(/.f64 U J)
U
J
(/ (* U 1/4) J)
(*.f64 (/.f64 U J) #s(literal 1/4 binary64))
(* U 1/4)
(*.f64 U #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* J -2)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)

localize260.0ms (2.5%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (*.f64 U #s(literal 1/4 binary64)) J)
✓accuracy99.6%
(*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J))
✓accuracy89.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J))))
✓accuracy87.9%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (*.f64 J J))
✓accuracy99.9%
(*.f64 U (*.f64 U U))
✓accuracy84.7%
(*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U)))))
✓accuracy73.3%
(/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U)))
✓accuracy100.0%
(*.f64 K K)
✓accuracy100.0%
(*.f64 J #s(literal -2 binary64))
✓accuracy99.7%
(*.f64 #s(literal -1/8 binary64) (*.f64 K K))
✓accuracy94.1%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
✓accuracy100.0%
(neg.f64 U)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.7%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Results
140.0ms256×0valid
Compiler

Compiled 228 to 36 computations (84.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-mult: 20.0ms (42.1% of total)
ival-div: 12.0ms (25.2% of total)
ival-cos: 6.0ms (12.6% of total)
ival-add: 4.0ms (8.4% of total)
ival-sqrt: 2.0ms (4.2% of total)
ival-sub: 1.0ms (2.1% of total)
const: 1.0ms (2.1% of total)
ival-neg: 1.0ms (2.1% of total)
backward-pass: 0.0ms (0% of total)

series22.0ms (0.2%)

Counts
22 → 396
Calls
Call 1
Inputs
#<alt (/ (* -2 J) (/ 1 (cos (/ K 2))))>
#<alt (* -2 J)>
#<alt (/ 1 (cos (/ K 2)))>
#<alt (cos (/ K 2))>
#<alt (neg U)>
#<alt (* (+ 1 (* -1/8 (* K K))) (* J -2))>
#<alt (+ 1 (* -1/8 (* K K)))>
#<alt (* -1/8 (* K K))>
#<alt (* K K)>
#<alt (* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))>
#<alt (- (* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))) U)>
#<alt (* J J)>
#<alt (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))>
#<alt (* (sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J)))) (* J -2))>
#<alt (sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J))))>
#<alt (+ 1 (* (/ U J) (/ (* U 1/4) J)))>
#<alt (* (/ U J) (/ (* U 1/4) J))>
#<alt (* J -2)>
#<alt (/ (* 2 (* J J)) (* U (* U U)))>
#<alt (* U (* U U))>
#<alt (* 2 (* J J))>
#<alt (/ (* U 1/4) J)>
Outputs
#<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 (* -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>
#<alt (+ 1 (* 1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 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 (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (* 1/4 (* J (pow K 2)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* 1/4 (* J (pow K 2)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt (* -2 (* J (+ 1 (* -1/8 (pow K 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (* -1/8 (pow K 2))>
#<alt (* (pow K 2) (- (/ 1 (pow K 2)) 1/8))>
#<alt (* (pow K 2) (- (/ 1 (pow K 2)) 1/8))>
#<alt (* (pow K 2) (- (/ 1 (pow K 2)) 1/8))>
#<alt (* -1/8 (pow K 2))>
#<alt (* (pow K 2) (- (/ 1 (pow K 2)) 1/8))>
#<alt (* (pow K 2) (- (/ 1 (pow K 2)) 1/8))>
#<alt (* (pow K 2) (- (/ 1 (pow K 2)) 1/8))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (* -1/8 (pow K 2))>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (pow K 2)>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U))))>
#<alt (* 2 (/ (pow J 4) (pow U 3)))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* 2 (/ (pow J 4) (pow U 3)))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* 2 (/ (pow J 4) (pow U 3)))>
#<alt (/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))>
#<alt (/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))>
#<alt (/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (/ (+ (* -2 (pow J 2)) (* 2 (/ (pow J 4) (pow U 2)))) U)>
#<alt (/ (+ (* -2 (pow J 2)) (* 2 (/ (pow J 4) (pow U 2)))) U)>
#<alt (/ (+ (* -2 (pow J 2)) (* 2 (/ (pow J 4) (pow U 2)))) U)>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -1 (/ (+ (* -2 (/ (pow J 4) (pow U 2))) (* 2 (pow J 2))) U))>
#<alt (* -1 (/ (+ (* -2 (/ (pow J 4) (pow U 2))) (* 2 (pow J 2))) U))>
#<alt (* -1 (/ (+ (* -2 (/ (pow J 4) (pow U 2))) (* 2 (pow J 2))) U))>
#<alt (* -1 U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (- (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))) U)>
#<alt (- (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))) U)>
#<alt (* 2 (/ (pow J 4) (pow U 3)))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))>
#<alt (* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))>
#<alt (* 2 (/ (pow J 4) (pow U 3)))>
#<alt (* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))>
#<alt (* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))>
#<alt (* 2 (/ (pow J 4) (pow U 3)))>
#<alt (/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))>
#<alt (/ (+ (* 2 (pow J 4)) (* (pow U 2) (+ (* -2 (pow J 2)) (* -1 (pow U 2))))) (pow U 3))>
#<alt (/ (+ (* 2 (pow J 4)) (* (pow U 2) (+ (* -2 (pow J 2)) (* -1 (pow U 2))))) (pow U 3))>
#<alt (* -1 U)>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))>
#<alt (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))>
#<alt (* -1 U)>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -1 (* U (+ 1 (+ (* -2 (/ (pow J 4) (pow U 4))) (* 2 (/ (pow J 2) (pow U 2)))))))>
#<alt (* -1 (* U (+ 1 (+ (* -2 (/ (pow J 4) (pow U 4))) (* 2 (/ (pow J 2) (pow U 2)))))))>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (/ (+ (* -2 (pow U 2)) (* 2 (pow J 2))) (pow U 3))>
#<alt (/ (+ (* -2 (pow U 2)) (* 2 (pow J 2))) (pow U 3))>
#<alt (/ (+ (* -2 (pow U 2)) (* 2 (pow J 2))) (pow U 3))>
#<alt (/ -2 U)>
#<alt (/ (- (* 2 (/ (pow J 2) (pow U 2))) 2) U)>
#<alt (/ (- (* 2 (/ (pow J 2) (pow U 2))) 2) U)>
#<alt (/ (- (* 2 (/ (pow J 2) (pow U 2))) 2) U)>
#<alt (/ -2 U)>
#<alt (* -1 (/ (+ 2 (* -2 (/ (pow J 2) (pow U 2)))) U))>
#<alt (* -1 (/ (+ 2 (* -2 (/ (pow J 2) (pow U 2)))) U))>
#<alt (* -1 (/ (+ 2 (* -2 (/ (pow J 2) (pow U 2)))) U))>
#<alt (/ -2 U)>
#<alt (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))>
#<alt (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))>
#<alt (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* -1/4 (/ (pow U 2) J)))>
#<alt (+ (* -2 J) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (pow J 3))) (* 1/4 (/ 1 J)))))>
#<alt (+ (* -2 J) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (pow J 5))) (* 1/64 (/ 1 (pow J 3))))) (* 1/4 (/ 1 J)))))>
#<alt (* -1 U)>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))>
#<alt (* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1))>
#<alt U>
#<alt (* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))>
#<alt (* -1 (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1)))>
#<alt (* -1 (* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1)))>
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (pow J 2) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))))>
#<alt (+ (* -1 U) (* (pow J 2) (- (* (pow J 2) (+ (* -4 (/ (pow J 2) (pow U 5))) (* 2 (/ 1 (pow U 3))))) (* 2 (/ 1 U)))))>
#<alt (* -2 J)>
#<alt (* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))>
#<alt (* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (* 1/64 (/ (pow U 4) (pow J 4)))) 2))>
#<alt (* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (+ (* -1/512 (/ (pow U 6) (pow J 6))) (* 1/64 (/ (pow U 4) (pow J 4))))) 2))>
#<alt (* -2 J)>
#<alt (* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))>
#<alt (* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (+ (* 1/512 (/ (pow U 6) (pow J 6))) (* 1/4 (/ (pow U 2) (pow J 2))))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (pow J 4))) (* 1/8 (/ 1 (pow J 2))))))>
#<alt (+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (pow J 6))) (* 1/128 (/ 1 (pow J 4))))) (* 1/8 (/ 1 (pow J 2))))))>
#<alt (* 1/2 (/ U J))>
#<alt (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))>
#<alt (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))>
#<alt (* -1/2 (/ U J))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))>
#<alt (* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))))>
#<alt (* 1/2 (/ U J))>
#<alt (/ (+ (* 1/2 U) (/ (pow J 2) U)) J)>
#<alt (/ (+ (* 1/2 U) (* (pow J 2) (+ (* -1 (/ (pow J 2) (pow U 3))) (/ 1 U)))) J)>
#<alt (/ (+ (* 1/2 U) (* (pow J 2) (+ (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 5))) (/ 1 (pow U 3)))) (/ 1 U)))) J)>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))>
#<alt (/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt 1>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<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 (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (* 2 (/ (pow J 2) (pow U 3)))>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (pow U 3)>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 2 (pow J 2))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
#<alt (* 1/4 (/ U J))>
Calls

99 calls:

TimeVariablePointExpression
3.0ms
J
@inf
(/ (* 2 (* J J)) (* U (* U U)))
1.0ms
J
@0
(* (+ 1 (* -1/8 (* K K))) (* J -2))
1.0ms
J
@0
(* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))
1.0ms
J
@inf
(* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))
1.0ms
U
@0
(* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))

rewrite393.0ms (3.7%)

Algorithm
1×batch-egg-rewrite
Rules
3542×/-lowering-/.f32
3542×/-lowering-/.f64
3502×*-lowering-*.f32
3502×*-lowering-*.f64
2072×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035155
1199146
21884146
08761146
Stop Event
1×iter limit
1×node limit
Counts
22 → 649
Calls
Call 1
Inputs
(/ (* -2 J) (/ 1 (cos (/ K 2))))
(* -2 J)
(/ 1 (cos (/ K 2)))
(cos (/ K 2))
(neg U)
(* (+ 1 (* -1/8 (* K K))) (* J -2))
(+ 1 (* -1/8 (* K K)))
(* -1/8 (* K K))
(* K K)
(* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U)))))
(- (* (* J J) (+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))) U)
(* J J)
(+ (/ -2 U) (/ (* 2 (* J J)) (* U (* U U))))
(* (sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J)))) (* J -2))
(sqrt (+ 1 (* (/ U J) (/ (* U 1/4) J))))
(+ 1 (* (/ U J) (/ (* U 1/4) J)))
(* (/ U J) (/ (* U 1/4) J))
(* J -2)
(/ (* 2 (* J J)) (* U (* U U)))
(* U (* U U))
(* 2 (* J J))
(/ (* U 1/4) J)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(neg.f64 (*.f64 #s(literal 2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64))))
(/.f64 (*.f64 J #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 J #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 J #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 J (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 J (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (/.f64 J (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 J #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (*.f64 J #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (/.f64 J #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 J #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 (/.f64 J #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 (/.f64 J #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 J #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -1 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 J (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 (/.f64 J #s(literal 1 binary64)) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 J (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(/.f64 (*.f64 J #s(literal 2 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 J #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J)) #s(literal -1 binary64))
(*.f64 #s(literal -2 binary64) J)
(*.f64 #s(literal -2 binary64) (/.f64 J #s(literal 1 binary64)))
(*.f64 J #s(literal -2 binary64))
(*.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(cos.f64 (/.f64 K #s(literal -2 binary64)))
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(pow.f64 (/.f64 (/.f64 (*.f64 U (*.f64 U U)) (*.f64 J (*.f64 J #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 U U) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 J J) U))) #s(literal -1 binary64))
(*.f64 #s(literal -2 binary64) (/.f64 (neg.f64 (*.f64 J J)) (*.f64 U (*.f64 U U))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 U (*.f64 U U))))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) (*.f64 U (*.f64 U U))))
(*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U (*.f64 U U)))))
(*.f64 (*.f64 J J) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U U)))))
(*.f64 (*.f64 J J) (/.f64 #s(literal 2 binary64) (*.f64 U (*.f64 U U))))
(*.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (neg.f64 (*.f64 J J)) (*.f64 U U)))
(*.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 J J) (neg.f64 (*.f64 U U))))
(*.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U U))))
(*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U)))))
(*.f64 (*.f64 J #s(literal 2 binary64)) (*.f64 J (/.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U U)))))
(*.f64 (*.f64 J #s(literal 2 binary64)) (/.f64 J (*.f64 U (*.f64 U U))))
(*.f64 (/.f64 #s(literal 2 binary64) U) (/.f64 (*.f64 J J) (*.f64 U U)))
(*.f64 (/.f64 (*.f64 J J) (*.f64 U U)) (/.f64 #s(literal 2 binary64) U))
(*.f64 (/.f64 J U) (/.f64 (*.f64 J #s(literal 2 binary64)) (*.f64 U U)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U U))) (*.f64 J (*.f64 J #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 U (*.f64 U U))) (pow.f64 (/.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (*.f64 J J))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) (*.f64 U U)))
(*.f64 (/.f64 #s(literal 1 binary64) U) (pow.f64 (/.f64 (*.f64 U U) (*.f64 J (*.f64 J #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 J J) U)) (/.f64 #s(literal 1 binary64) (*.f64 U U)))
(*.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 J J) U)) (/.f64 (/.f64 #s(literal 1 binary64) U) U))
(*.f64 (*.f64 J (/.f64 J (*.f64 U (*.f64 U U)))) #s(literal 2 binary64))
(*.f64 (/.f64 J (*.f64 U U)) (/.f64 (*.f64 J #s(literal 2 binary64)) U))
(*.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) (/.f64 (*.f64 J J) U))
(*.f64 (/.f64 (*.f64 J J) U) (/.f64 #s(literal 2 binary64) (*.f64 U U)))
(*.f64 (/.f64 (*.f64 J J) U) (/.f64 (/.f64 #s(literal 2 binary64) U) U))
(*.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) U) (/.f64 J (*.f64 U U)))
(*.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) U) (/.f64 (/.f64 J U) U))
(*.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) (*.f64 U U)) (/.f64 J U))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 U U)) (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 J J) U)))
(*.f64 (/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) (*.f64 U U)) (/.f64 #s(literal 1 binary64) U))
(*.f64 (pow.f64 (/.f64 U (*.f64 J J)) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 U U) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 U U) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 U (*.f64 J J)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 U U) J) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 U U) (*.f64 J #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 J U))
(*.f64 (/.f64 (*.f64 J J) #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) (*.f64 U (*.f64 U U))))
(*.f64 (/.f64 (neg.f64 (*.f64 J J)) #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (*.f64 U (*.f64 U U))))
(*.f64 (/.f64 (neg.f64 (*.f64 J J)) U) (/.f64 #s(literal 2 binary64) (neg.f64 (*.f64 U U))))
(*.f64 (/.f64 #s(literal -1 binary64) U) (/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) (neg.f64 (*.f64 U U))))
(*.f64 (/.f64 (neg.f64 (*.f64 J #s(literal 2 binary64))) U) (/.f64 J (neg.f64 (*.f64 U U))))
(*.f64 (/.f64 (neg.f64 (*.f64 J #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 J (*.f64 U (*.f64 U U))))
(*.f64 (/.f64 #s(literal -2 binary64) (*.f64 U U)) (/.f64 (*.f64 J J) (-.f64 #s(literal 0 binary64) U)))
(*.f64 (/.f64 (*.f64 J J) (pow.f64 U #s(literal 3/2 binary64))) (/.f64 #s(literal 2 binary64) (pow.f64 U #s(literal 3/2 binary64))))
(*.f64 (/.f64 (neg.f64 (*.f64 J J)) (*.f64 U U)) (/.f64 #s(literal -2 binary64) U))
(*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 U #s(literal 3/2 binary64))) (/.f64 (*.f64 J J) (pow.f64 U #s(literal 3/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 U U)) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U))
(*.f64 (/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) (pow.f64 U #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 U #s(literal 3/2 binary64))))
(*.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) (pow.f64 U #s(literal 3/2 binary64))) (/.f64 J (pow.f64 U #s(literal 3/2 binary64))))
(*.f64 (/.f64 (neg.f64 (*.f64 J #s(literal 2 binary64))) (*.f64 U U)) (/.f64 J (-.f64 #s(literal 0 binary64) U)))
(*.f64 (/.f64 J (pow.f64 U #s(literal 3/2 binary64))) (/.f64 (*.f64 J #s(literal 2 binary64)) (pow.f64 U #s(literal 3/2 binary64))))
(*.f64 (/.f64 (*.f64 J J) (-.f64 #s(literal 0 binary64) U)) (/.f64 #s(literal -2 binary64) (*.f64 U U)))
(*.f64 (/.f64 (*.f64 J J) (neg.f64 (*.f64 U U))) (/.f64 #s(literal -2 binary64) U))
(*.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (*.f64 U U))) (/.f64 (neg.f64 (*.f64 J J)) U))
(*.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) U)) (/.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 U U)))
(*.f64 (/.f64 (*.f64 J #s(literal 2 binary64)) (neg.f64 (*.f64 U U))) (/.f64 (-.f64 #s(literal 0 binary64) J) U))
(*.f64 (/.f64 (/.f64 #s(literal 2 binary64) U) U) (/.f64 (*.f64 J J) U))
(exp.f64 (*.f64 (log.f64 U) #s(literal 3 binary64)))
(pow.f64 U #s(literal 3 binary64))
(pow.f64 (*.f64 U U) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 U #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 U)) #s(literal 3 binary64))
(*.f64 U (*.f64 U U))
(*.f64 (*.f64 U U) U)
(*.f64 (pow.f64 U #s(literal 3/2 binary64)) (pow.f64 U #s(literal 3/2 binary64)))
(*.f64 J (*.f64 J #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(*.f64 (*.f64 J J) #s(literal 2 binary64))
(*.f64 (*.f64 J #s(literal 2 binary64)) J)
(exp.f64 (*.f64 (log.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) J)) (*.f64 #s(literal -1/4 binary64) (/.f64 U J)))
(neg.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 U J)))
(neg.f64 (/.f64 (*.f64 U #s(literal -1/4 binary64)) J))
(/.f64 #s(literal 1 binary64) (/.f64 J (*.f64 U #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64))))))
(/.f64 (*.f64 U #s(literal 1/4 binary64)) J)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64))) #s(literal 1 binary64))))
(/.f64 (*.f64 U #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) J))
(/.f64 (*.f64 (*.f64 U #s(literal 1/4 binary64)) #s(literal 1 binary64)) J)
(/.f64 (neg.f64 (*.f64 U #s(literal -1/4 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) J)))
(/.f64 (neg.f64 (*.f64 (*.f64 U #s(literal 1/4 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) J))
(/.f64 (neg.f64 (neg.f64 (*.f64 U #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) J))))
(pow.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 J (*.f64 U #s(literal 1/4 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 U J)))
(*.f64 U (/.f64 #s(literal 1/4 binary64) J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(*.f64 (*.f64 U #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) J))
(*.f64 (*.f64 U #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) J)))
(*.f64 (/.f64 #s(literal 1 binary64) J) (*.f64 U #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) J) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 U #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/4 binary64) J) U)
(*.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 #s(literal 0 binary64) U) J))
(*.f64 (/.f64 U #s(literal 1 binary64)) (/.f64 #s(literal 1/4 binary64) J))
(*.f64 (/.f64 U #s(literal -1 binary64)) (/.f64 #s(literal -1/4 binary64) J))

simplify330.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
3974×*-lowering-*.f32
3974×*-lowering-*.f64
3266×+-lowering-+.f64
3266×+-lowering-+.f32
1552×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03043594
19313118
230193019
370243015
080583015
Stop Event
1×iter limit
1×node limit
Counts
396 → 396
Calls
Call 1
Inputs
(* -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) (+ 1/8 (* 5/384 (pow K 2)))))
(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(* 1/4 (* J (pow K 2)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* 1/4 (* J (pow K 2)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* -1/8 (pow K 2)))
(* -1/8 (pow K 2))
(* (pow K 2) (- (/ 1 (pow K 2)) 1/8))
(* (pow K 2) (- (/ 1 (pow K 2)) 1/8))
(* (pow K 2) (- (/ 1 (pow K 2)) 1/8))
(* -1/8 (pow K 2))
(* (pow K 2) (- (/ 1 (pow K 2)) 1/8))
(* (pow K 2) (- (/ 1 (pow K 2)) 1/8))
(* (pow K 2) (- (/ 1 (pow K 2)) 1/8))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(* -1/8 (pow K 2))
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(pow K 2)
(* -2 (/ (pow J 2) U))
(* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U))))
(* 2 (/ (pow J 4) (pow U 3)))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* 2 (/ (pow J 4) (pow U 3)))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* 2 (/ (pow J 4) (pow U 3)))
(/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))
(/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))
(/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))
(* -2 (/ (pow J 2) U))
(/ (+ (* -2 (pow J 2)) (* 2 (/ (pow J 4) (pow U 2)))) U)
(/ (+ (* -2 (pow J 2)) (* 2 (/ (pow J 4) (pow U 2)))) U)
(/ (+ (* -2 (pow J 2)) (* 2 (/ (pow J 4) (pow U 2)))) U)
(* -2 (/ (pow J 2) U))
(* -1 (/ (+ (* -2 (/ (pow J 4) (pow U 2))) (* 2 (pow J 2))) U))
(* -1 (/ (+ (* -2 (/ (pow J 4) (pow U 2))) (* 2 (pow J 2))) U))
(* -1 (/ (+ (* -2 (/ (pow J 4) (pow U 2))) (* 2 (pow J 2))) U))
(* -1 U)
(- (* -2 (/ (pow J 2) U)) U)
(- (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))) U)
(- (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))) U)
(* 2 (/ (pow J 4) (pow U 3)))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))
(* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))
(* 2 (/ (pow J 4) (pow U 3)))
(* (pow J 4) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))
(* (pow J 4) (- (+ (* -1 (/ U (pow J 4))) (* 2 (/ 1 (pow U 3)))) (/ 2 (* (pow J 2) U))))
(* 2 (/ (pow J 4) (pow U 3)))
(/ (+ (* -2 (* (pow J 2) (pow U 2))) (* 2 (pow J 4))) (pow U 3))
(/ (+ (* 2 (pow J 4)) (* (pow U 2) (+ (* -2 (pow J 2)) (* -1 (pow U 2))))) (pow U 3))
(/ (+ (* 2 (pow J 4)) (* (pow U 2) (+ (* -2 (pow J 2)) (* -1 (pow U 2))))) (pow U 3))
(* -1 U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))
(* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))
(* -1 U)
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -1 (* U (+ 1 (+ (* -2 (/ (pow J 4) (pow U 4))) (* 2 (/ (pow J 2) (pow U 2)))))))
(* -1 (* U (+ 1 (+ (* -2 (/ (pow J 4) (pow U 4))) (* 2 (/ (pow J 2) (pow U 2)))))))
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(* 2 (/ (pow J 2) (pow U 3)))
(/ (+ (* -2 (pow U 2)) (* 2 (pow J 2))) (pow U 3))
(/ (+ (* -2 (pow U 2)) (* 2 (pow J 2))) (pow U 3))
(/ (+ (* -2 (pow U 2)) (* 2 (pow J 2))) (pow U 3))
(/ -2 U)
(/ (- (* 2 (/ (pow J 2) (pow U 2))) 2) U)
(/ (- (* 2 (/ (pow J 2) (pow U 2))) 2) U)
(/ (- (* 2 (/ (pow J 2) (pow U 2))) 2) U)
(/ -2 U)
(* -1 (/ (+ 2 (* -2 (/ (pow J 2) (pow U 2)))) U))
(* -1 (/ (+ 2 (* -2 (/ (pow J 2) (pow U 2)))) U))
(* -1 (/ (+ 2 (* -2 (/ (pow J 2) (pow U 2)))) U))
(/ -2 U)
(- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))
(- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))
(- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))
(* 2 (/ (pow J 2) (pow U 3)))
(* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* 2 (/ (pow J 2) (pow U 3)))
(* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* (pow J 2) (- (* 2 (/ 1 (pow U 3))) (* 2 (/ 1 (* (pow J 2) U)))))
(* -2 J)
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (pow J 3))) (* 1/4 (/ 1 J)))))
(+ (* -2 J) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (pow J 5))) (* 1/64 (/ 1 (pow J 3))))) (* 1/4 (/ 1 J)))))
(* -1 U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (pow J 6) (pow U 6))) (+ (* -2 (/ (pow J 2) (pow U 2))) (* 2 (/ (pow J 4) (pow U 4))))) 1)))
(* -1 U)
(+ (* -2 (/ (pow J 2) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))))
(+ (* -1 U) (* (pow J 2) (- (* (pow J 2) (+ (* -4 (/ (pow J 2) (pow U 5))) (* 2 (/ 1 (pow U 3))))) (* 2 (/ 1 U)))))
(* -2 J)
(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
(* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (* 1/64 (/ (pow U 4) (pow J 4)))) 2))
(* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (+ (* -1/512 (/ (pow U 6) (pow J 6))) (* 1/64 (/ (pow U 4) (pow J 4))))) 2))
(* -2 J)
(* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))
(* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (* 1/4 (/ (pow U 2) (pow J 2)))))))
(* -1 (* J (+ 2 (+ (* -1/64 (/ (pow U 4) (pow J 4))) (+ (* 1/512 (/ (pow U 6) (pow J 6))) (* 1/4 (/ (pow U 2) (pow J 2))))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (pow J 4))) (* 1/8 (/ 1 (pow J 2))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (pow J 6))) (* 1/128 (/ 1 (pow J 4))))) (* 1/8 (/ 1 (pow J 2))))))
(* 1/2 (/ U J))
(* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))
(* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))
(* -1/2 (/ U J))
(* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ (pow J 5) (pow U 6))) (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))))
(* 1/2 (/ U J))
(/ (+ (* 1/2 U) (/ (pow J 2) U)) J)
(/ (+ (* 1/2 U) (* (pow J 2) (+ (* -1 (/ (pow J 2) (pow U 3))) (/ 1 U)))) J)
(/ (+ (* 1/2 U) (* (pow J 2) (+ (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 5))) (/ 1 (pow U 3)))) (/ 1 U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (pow J 2))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (* 1/8 (/ (pow U 2) (pow J 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (pow J 4))) (+ (* 1/1024 (/ (pow U 6) (pow J 6))) (* 1/8 (/ (pow U 2) (pow J 2))))))
1
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* (pow U 2) (+ (* 1/4 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
(/ (+ (* 1/4 (pow U 2)) (pow J 2)) (pow J 2))
1
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
1
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(* 2 (/ (pow J 2) (pow U 3)))
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(pow U 3)
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 2 (pow J 2))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
(* 1/4 (/ U J))
Outputs
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (+.f64 (*.f64 J #s(literal 1/4 binary64)) (*.f64 (*.f64 J (*.f64 K K)) (+.f64 #s(literal -1/192 binary64) (*.f64 #s(literal 1/23040 binary64) (*.f64 K K)))))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal 1/8 binary64)))
(+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) #s(literal 5/384 binary64))) K) K))
(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64))))))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64)))))))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* 1/4 (* J (pow K 2)))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* 1/4 (* J (pow K 2)))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(* -2 (* J (+ 1 (* -1/8 (pow K 2)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
1
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(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(* 2 (/ (pow J 2) (pow U 3)))
(*.f64 J (*.f64 J (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 U U)) U)))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(pow U 3)
(*.f64 U (*.f64 U U))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 2 (pow J 2))
(*.f64 #s(literal 2 binary64) (*.f64 J J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))
(* 1/4 (/ U J))
(*.f64 #s(literal 1/4 binary64) (/.f64 U J))

eval169.0ms (1.6%)

Compiler

Compiled 24872 to 2841 computations (88.6% saved)

prune204.0ms (1.9%)

Pruning

25 alts after pruning (19 fresh and 6 done)

PrunedKeptTotal
New1075131088
Fresh5611
Picked235
Done033
Total1082251107
Accuracy
100.0%
Counts
1107 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
54.2%
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
29.1%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
28.8%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
✓54.3%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
▶29.0%
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
▶54.3%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
▶36.8%
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
35.4%
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
10.4%
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U))))
28.9%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
45.5%
(*.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 #s(literal 2 binary64) K))))) (*.f64 #s(literal 4 binary64) (*.f64 J J)))) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
23.8%
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
10.6%
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
29.0%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
▶10.0%
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
16.8%
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
✓32.4%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
✓47.6%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
✓54.4%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
29.1%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
2.8%
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
▶30.6%
(*.f64 #s(literal -2 binary64) J)
✓38.7%
(neg.f64 U)
13.8%
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64)))
✓12.4%
U
Compiler

Compiled 811 to 565 computations (30.3% saved)

simplify144.0ms (1.4%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64))))))))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
✓cost-diff0
(+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))
✓cost-diff0
(-.f64 #s(literal 0 binary64) U)
✓cost-diff256
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))
✓cost-diff256
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
✓cost-diff0
(*.f64 J J)
✓cost-diff0
(*.f64 #s(literal -2 binary64) (*.f64 J J))
✓cost-diff0
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U)
✓cost-diff0
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff128
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
Rules
2050×*-lowering-*.f32
2050×*-lowering-*.f64
1988×sum3-define
1538×fma-lowering-fma.f32
1538×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
038222
1107206
2335206
31019204
42927195
56253195
08038195
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))
1
(/ (/ 1 (cos (/ K 2))) (* -2 J))
(/ 1 (cos (/ K 2)))
(cos (/ K 2))
(/ K 2)
K
2
(* -2 J)
-2
J
(* -2 J)
-2
J
(- (/ (* -2 (* J J)) U) U)
(/ (* -2 (* J J)) U)
(* -2 (* J J))
-2
(* J J)
J
U
(* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))
(* (- 0 U) (+ (/ 1/2 J) (/ J (* U U))))
(- 0 U)
0
U
(+ (/ 1/2 J) (/ J (* U U)))
(/ 1/2 J)
1/2
J
(/ J (* U U))
(* U U)
(* J -2)
-2
(/ (* -2 J) (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))))
(* -2 J)
-2
J
(+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))))
1
(* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))
K
(* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))
(+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))
1/8
(* (* K K) (+ 5/384 (* (* K K) 61/46080)))
(* K K)
(+ 5/384 (* (* K K) 61/46080))
5/384
(* (* K K) 61/46080)
61/46080
Outputs
(/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
1
#s(literal 1 binary64)
(/ (/ 1 (cos (/ K 2))) (* -2 J))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ 1 (cos (/ K 2)))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(- (/ (* -2 (* J J)) U) U)
(-.f64 (/.f64 (/.f64 J (/.f64 #s(literal -1/2 binary64) J)) U) U)
(/ (* -2 (* J J)) U)
(/.f64 (/.f64 J (/.f64 #s(literal -1/2 binary64) J)) U)
(* -2 (* J J))
(/.f64 J (/.f64 #s(literal -1/2 binary64) J))
-2
#s(literal -2 binary64)
(* J J)
(*.f64 J J)
J
U
(* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))
(+.f64 U (/.f64 (*.f64 J (*.f64 #s(literal 2 binary64) J)) U))
(* (- 0 U) (+ (/ 1/2 J) (/ J (* U U))))
(-.f64 (/.f64 U (/.f64 J #s(literal -1/2 binary64))) (/.f64 J U))
(- 0 U)
(-.f64 #s(literal 0 binary64) U)
0
#s(literal 0 binary64)
U
(+ (/ 1/2 J) (/ J (* U U)))
(+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (/.f64 J U) U))
(/ 1/2 J)
(/.f64 #s(literal 1/2 binary64) J)
1/2
#s(literal 1/2 binary64)
J
(/ J (* U U))
(/.f64 (/.f64 J U) U)
(* U U)
(*.f64 U U)
(* J -2)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
(/ (* -2 J) (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))))
(/.f64 (/.f64 J #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64))))))))
1
#s(literal 1 binary64)
(* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))
(*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))
K
(* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))
(*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))
(+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))
(+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64))))))
1/8
#s(literal 1/8 binary64)
(* (* K K) (+ 5/384 (* (* K K) 61/46080)))
(*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))
(* K K)
(*.f64 K K)
(+ 5/384 (* (* K K) 61/46080))
(+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))
5/384
#s(literal 5/384 binary64)
(* (* K K) 61/46080)
(*.f64 (*.f64 K K) #s(literal 61/46080 binary64))
61/46080
#s(literal 61/46080 binary64)

localize184.0ms (1.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64))))))
✓accuracy99.8%
(*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64))))
✓accuracy99.1%
(*.f64 (*.f64 K K) #s(literal 61/46080 binary64))
✓accuracy98.8%
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
✓accuracy100.0%
(+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))
✓accuracy87.8%
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
✓accuracy86.6%
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))
✓accuracy83.9%
(/.f64 J (*.f64 U U))
✓accuracy100.0%
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
✓accuracy100.0%
(*.f64 J J)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) (*.f64 J J))
✓accuracy85.5%
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.7%
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))
✓accuracy99.4%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
Results
129.0ms256×0valid
Compiler

Compiled 263 to 39 computations (85.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 55.0ms
ival-mult: 18.0ms (32.7% of total)
ival-div: 14.0ms (25.4% of total)
...c/correct-round.rkt:119:19: 9.0ms (16.3% of total)
ival-cos: 6.0ms (10.9% of total)
ival-add: 5.0ms (9.1% of total)
ival-sub: 2.0ms (3.6% of total)
const: 1.0ms (1.8% of total)
backward-pass: 0.0ms (0% of total)

series27.0ms (0.3%)

Counts
20 → 348
Calls
Call 1
Inputs
#<alt (/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))>
#<alt (/ (/ 1 (cos (/ K 2))) (* -2 J))>
#<alt (/ 1 (cos (/ K 2)))>
#<alt (cos (/ K 2))>
#<alt (* -2 J)>
#<alt (- (/ (* -2 (* J J)) U) U)>
#<alt (/ (* -2 (* J J)) U)>
#<alt (* -2 (* J J))>
#<alt (* J J)>
#<alt (* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))>
#<alt (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U))))>
#<alt (- 0 U)>
#<alt (+ (/ 1/2 J) (/ J (* U U)))>
#<alt (/ (* -2 J) (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))))>
#<alt (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))))>
#<alt (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))>
#<alt (/ J (* U U))>
#<alt (* (* K K) 61/46080)>
#<alt (* (* K K) (+ 5/384 (* (* K K) 61/46080)))>
#<alt (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))>
Outputs
#<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 (/ -1/2 J)>
#<alt (- (* -1/16 (/ (pow K 2) J)) (* 1/2 (/ 1 J)))>
#<alt (- (* (pow K 2) (- (* -5/768 (/ (pow K 2) J)) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))>
#<alt (- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (/ (pow K 2) J)) (* 5/768 (/ 1 J)))) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt (/ -1/2 (* J (cos (* 1/2 K))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (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 U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)>
#<alt (/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)>
#<alt (/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)>
#<alt (* -1 U)>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* -1 U)>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (* -2 (pow J 2))>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (* 2 (/ (pow J 2) U))>
#<alt (/ (+ (* 2 (pow J 2)) (pow U 2)) U)>
#<alt (/ (+ (* 2 (pow J 2)) (pow U 2)) U)>
#<alt (/ (+ (* 2 (pow J 2)) (pow U 2)) U)>
#<alt U>
#<alt (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2)))))>
#<alt (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2)))))>
#<alt (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2)))))>
#<alt U>
#<alt (* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))>
#<alt (* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))>
#<alt (* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))>
#<alt U>
#<alt (+ U (* 2 (/ (pow J 2) U)))>
#<alt (+ U (* 2 (/ (pow J 2) U)))>
#<alt (+ U (* 2 (/ (pow J 2) U)))>
#<alt (* 2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))>
#<alt (* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))>
#<alt (* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))>
#<alt (* 2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))>
#<alt (* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))>
#<alt (* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))>
#<alt (* -1 (/ J U))>
#<alt (/ (+ (* -1 J) (* -1/2 (/ (pow U 2) J))) U)>
#<alt (/ (+ (* -1 J) (* -1/2 (/ (pow U 2) J))) U)>
#<alt (/ (+ (* -1 J) (* -1/2 (/ (pow U 2) J))) U)>
#<alt (* -1/2 (/ U J))>
#<alt (* U (- (* -1 (/ J (pow U 2))) (* 1/2 (/ 1 J))))>
#<alt (* U (- (* -1 (/ J (pow U 2))) (* 1/2 (/ 1 J))))>
#<alt (* U (- (* -1 (/ J (pow U 2))) (* 1/2 (/ 1 J))))>
#<alt (* -1/2 (/ U J))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))>
#<alt (* -1/2 (/ U J))>
#<alt (/ (+ (* -1 (/ (pow J 2) U)) (* -1/2 U)) J)>
#<alt (/ (+ (* -1 (/ (pow J 2) U)) (* -1/2 U)) J)>
#<alt (/ (+ (* -1 (/ (pow J 2) U)) (* -1/2 U)) J)>
#<alt (* -1 (/ J U))>
#<alt (* J (- (* -1/2 (/ U (pow J 2))) (/ 1 U)))>
#<alt (* J (- (* -1/2 (/ U (pow J 2))) (/ 1 U)))>
#<alt (* J (- (* -1/2 (/ U (pow J 2))) (/ 1 U)))>
#<alt (* -1 (/ J U))>
#<alt (* -1 (* J (+ (* 1/2 (/ U (pow J 2))) (/ 1 U))))>
#<alt (* -1 (* J (+ (* 1/2 (/ U (pow J 2))) (/ 1 U))))>
#<alt (* -1 (* J (+ (* 1/2 (/ U (pow J 2))) (/ 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 (/ 1/2 J)>
#<alt (/ (+ 1/2 (/ (pow J 2) (pow U 2))) J)>
#<alt (/ (+ 1/2 (/ (pow J 2) (pow U 2))) J)>
#<alt (/ (+ 1/2 (/ (pow J 2) (pow U 2))) J)>
#<alt (/ J (pow U 2))>
#<alt (* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (/ J (pow U 2))>
#<alt (* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))>
#<alt (/ J (pow U 2))>
#<alt (/ (+ J (* 1/2 (/ (pow U 2) J))) (pow U 2))>
#<alt (/ (+ J (* 1/2 (/ (pow U 2) J))) (pow U 2))>
#<alt (/ (+ J (* 1/2 (/ (pow U 2) J))) (pow U 2))>
#<alt (/ 1/2 J)>
#<alt (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))>
#<alt (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))>
#<alt (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))>
#<alt (/ 1/2 J)>
#<alt (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))>
#<alt (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))>
#<alt (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* 2 (* (pow K 2) (+ (* -1/64 J) (* 5/384 J)))))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* 2 (* (pow K 2) (+ (* -1/8 (+ (* -1/64 J) (* 5/384 J))) (+ (* -5/3072 J) (* 61/46080 J))))) (* 2 (+ (* -1/64 J) (* 5/384 J))))))))>
#<alt (* -92160/61 (/ J (pow K 6)))>
#<alt (/ (+ (* -92160/61 J) (* 55296000/3721 (/ J (pow K 2)))) (pow K 6))>
#<alt (/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2))))) (pow K 6))>
#<alt (/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -159252480000/226981 J) (+ (* -600/61 (+ (* -16588800000/226981 J) (* 265420800/3721 J))) (* 2123366400/3721 J))) (pow K 6))) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2)))))) (pow K 6))>
#<alt (* -92160/61 (/ J (pow K 6)))>
#<alt (/ (+ (* -92160/61 J) (* 55296000/3721 (/ J (pow K 2)))) (pow K 6))>
#<alt (/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2))))) (pow K 6))>
#<alt (/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -159252480000/226981 J) (+ (* -600/61 (+ (* -16588800000/226981 J) (* 265420800/3721 J))) (* 2123366400/3721 J))) (pow K 6))) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2)))))) (pow K 6))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))>
#<alt (* 61/46080 (pow K 6))>
#<alt (* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (+ (* 5/384 (/ 1 (pow K 2))) (/ 1 (pow K 6))))))>
#<alt (* 61/46080 (pow K 6))>
#<alt (* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (+ (* 5/384 (/ 1 (pow K 2))) (/ 1 (pow K 6))))))>
#<alt (* 1/8 (pow K 2))>
#<alt (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2))))>
#<alt (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))>
#<alt (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))>
#<alt (* 61/46080 (pow K 6))>
#<alt (* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* 61/46080 (pow K 6))>
#<alt (* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (/ J (pow U 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 61/46080 (pow K 2))>
#<alt (* 5/384 (pow K 2))>
#<alt (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))>
#<alt (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))>
#<alt (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))>
#<alt (* 61/46080 (pow K 4))>
#<alt (* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* 61/46080 (pow K 4))>
#<alt (* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* 1/8 K)>
#<alt (* K (+ 1/8 (* 5/384 (pow K 2))))>
#<alt (* K (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))>
#<alt (* K (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))>
#<alt (* 61/46080 (pow K 5))>
#<alt (* (pow K 5) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* (pow K 5) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* (pow K 5) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))>
#<alt (* 61/46080 (pow K 5))>
#<alt (* (pow K 5) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))>
#<alt (* -1 (* (pow K 5) (- (* -1 (/ (+ 5/384 (* 1/8 (/ 1 (pow K 2)))) (pow K 2))) 61/46080)))>
#<alt (* -1 (* (pow K 5) (- (* -1 (/ (+ 5/384 (* 1/8 (/ 1 (pow K 2)))) (pow K 2))) 61/46080)))>
Calls

87 calls:

TimeVariablePointExpression
3.0ms
J
@inf
(/ (* -2 J) (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))))
2.0ms
J
@0
(/ (* -2 J) (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))))
1.0ms
U
@0
(* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))
1.0ms
J
@inf
(* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))
1.0ms
J
@0
(* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))

rewrite344.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
3638×/-lowering-/.f32
3638×/-lowering-/.f64
3232×*-lowering-*.f32
3232×*-lowering-*.f64
1934×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038164
1242151
22472151
08836151
Stop Event
1×iter limit
1×node limit
Counts
20 → 679
Calls
Call 1
Inputs
(/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))
(/ (/ 1 (cos (/ K 2))) (* -2 J))
(/ 1 (cos (/ K 2)))
(cos (/ K 2))
(* -2 J)
(- (/ (* -2 (* J J)) U) U)
(/ (* -2 (* J J)) U)
(* -2 (* J J))
(* J J)
(* (* (- 0 U) (+ (/ 1/2 J) (/ J (* U U)))) (* J -2))
(* (- 0 U) (+ (/ 1/2 J) (/ J (* U U))))
(- 0 U)
(+ (/ 1/2 J) (/ J (* U U)))
(/ (* -2 J) (+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))))
(+ 1 (* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))))
(* K (* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080))))))
(/ J (* U U))
(* (* K K) 61/46080)
(* (* K K) (+ 5/384 (* (* K K) 61/46080)))
(* K (+ 1/8 (* (* K K) (+ 5/384 (* (* K K) 61/46080)))))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) J))
(/.f64 (/.f64 J #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 J #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)))
(*.f64 #s(literal 2 binary64) (/.f64 J (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 J (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal -2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J) #s(literal -1 binary64)))
(*.f64 J (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 J (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J)))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (/.f64 J (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -2 binary64))
(*.f64 (/.f64 J #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 J #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64)) J)
(*.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) J) #s(literal -2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 J #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) J)
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(*.f64 (/.f64 J #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 J #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 J (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 J (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) J) #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 J #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (/.f64 J #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 J #s(literal 1/2 binary64)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 J (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (neg.f64 (/.f64 J #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 J #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) J) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 J (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 J #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 J #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (neg.f64 (neg.f64 (/.f64 J #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) J)
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal 1 binary64) J))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) J))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (neg.f64 (*.f64 #s(literal 1 binary64) J)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J) #s(literal -2 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) J)) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))) (neg.f64 (-.f64 #s(literal 0 binary64) J)))
(/.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)) #s(literal 2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 J (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal 1/2 binary64) J) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J)) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) J)))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
(*.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
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(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 K (*.f64 K K))) (*.f64 (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))) (*.f64 K (*.f64 K K))))) (neg.f64 (+.f64 (*.f64 (*.f64 K #s(literal 1/8 binary64)) (*.f64 K #s(literal 1/8 binary64))) (-.f64 (*.f64 (*.f64 K (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))) (*.f64 K (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))) (*.f64 (*.f64 K #s(literal 1/8 binary64)) (*.f64 K (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 K #s(literal 1/8 binary64)) (*.f64 K #s(literal 1/8 binary64))) (*.f64 (*.f64 K (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))) (*.f64 K (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))) (neg.f64 (-.f64 (*.f64 K #s(literal 1/8 binary64)) (*.f64 K (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))))))
(/.f64 (neg.f64 (*.f64 K (+.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))))))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (-.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) #s(literal 1/8 binary64))))))
(/.f64 (neg.f64 (*.f64 K (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))) (neg.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))))) K)) (neg.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (-.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) #s(literal 1/8 binary64))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))) K)) (neg.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))))
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))) K)

simplify238.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
5058×*-lowering-*.f32
5058×*-lowering-*.f64
1866×+-lowering-+.f64
1866×+-lowering-+.f32
1376×associate-*r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503076
17782645
224812581
372002581
081702581
Stop Event
1×iter limit
1×node limit
Counts
348 → 348
Calls
Call 1
Inputs
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(/ -1/2 J)
(- (* -1/16 (/ (pow K 2) J)) (* 1/2 (/ 1 J)))
(- (* (pow K 2) (- (* -5/768 (/ (pow K 2) J)) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))
(- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (/ (pow K 2) J)) (* 5/768 (/ 1 J)))) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
1
(+ 1 (* 1/8 (pow K 2)))
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(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(* -2 J)
(* -2 J)
(* -2 J)
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(* -1 U)
(- (* -2 (/ (pow J 2) U)) U)
(- (* -2 (/ (pow J 2) U)) U)
(- (* -2 (/ (pow J 2) U)) U)
(* -2 (/ (pow J 2) U))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* -2 (/ (pow J 2) U))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
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(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(* -1 U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
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(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* -1 U)
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -2 (/ (pow J 2) U))
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(* -2 (pow J 2))
(* -2 (pow J 2))
(* -2 (pow J 2))
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(* -2 (pow J 2))
(* -2 (pow J 2))
(* -2 (pow J 2))
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(* 2 (/ (pow J 2) U))
(/ (+ (* 2 (pow J 2)) (pow U 2)) U)
(/ (+ (* 2 (pow J 2)) (pow U 2)) U)
(/ (+ (* 2 (pow J 2)) (pow U 2)) U)
U
(* U (+ 1 (* 2 (/ (pow J 2) (pow U 2)))))
(* U (+ 1 (* 2 (/ (pow J 2) (pow U 2)))))
(* U (+ 1 (* 2 (/ (pow J 2) (pow U 2)))))
U
(* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))
(* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))
(* -1 (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1)))
U
(+ U (* 2 (/ (pow J 2) U)))
(+ U (* 2 (/ (pow J 2) U)))
(+ U (* 2 (/ (pow J 2) U)))
(* 2 (/ (pow J 2) U))
(* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))
(* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))
(* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))
(* 2 (/ (pow J 2) U))
(* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))
(* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))
(* (pow J 2) (+ (* 2 (/ 1 U)) (/ U (pow J 2))))
(* -1 (/ J U))
(/ (+ (* -1 J) (* -1/2 (/ (pow U 2) J))) U)
(/ (+ (* -1 J) (* -1/2 (/ (pow U 2) J))) U)
(/ (+ (* -1 J) (* -1/2 (/ (pow U 2) J))) U)
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(* U (- (* -1 (/ J (pow U 2))) (* 1/2 (/ 1 J))))
(* U (- (* -1 (/ J (pow U 2))) (* 1/2 (/ 1 J))))
(* U (- (* -1 (/ J (pow U 2))) (* 1/2 (/ 1 J))))
(* -1/2 (/ U J))
(* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* -1 (* U (+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))))
(* -1/2 (/ U J))
(/ (+ (* -1 (/ (pow J 2) U)) (* -1/2 U)) J)
(/ (+ (* -1 (/ (pow J 2) U)) (* -1/2 U)) J)
(/ (+ (* -1 (/ (pow J 2) U)) (* -1/2 U)) J)
(* -1 (/ J U))
(* J (- (* -1/2 (/ U (pow J 2))) (/ 1 U)))
(* J (- (* -1/2 (/ U (pow J 2))) (/ 1 U)))
(* J (- (* -1/2 (/ U (pow J 2))) (/ 1 U)))
(* -1 (/ J U))
(* -1 (* J (+ (* 1/2 (/ U (pow J 2))) (/ 1 U))))
(* -1 (* J (+ (* 1/2 (/ U (pow J 2))) (/ 1 U))))
(* -1 (* J (+ (* 1/2 (/ U (pow J 2))) (/ 1 U))))
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(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
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(* -1 U)
(* -1 U)
(* -1 U)
(/ 1/2 J)
(/ (+ 1/2 (/ (pow J 2) (pow U 2))) J)
(/ (+ 1/2 (/ (pow J 2) (pow U 2))) J)
(/ (+ 1/2 (/ (pow J 2) (pow U 2))) J)
(/ J (pow U 2))
(* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(/ J (pow U 2))
(* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(* J (+ (* 1/2 (/ 1 (pow J 2))) (/ 1 (pow U 2))))
(/ J (pow U 2))
(/ (+ J (* 1/2 (/ (pow U 2) J))) (pow U 2))
(/ (+ J (* 1/2 (/ (pow U 2) J))) (pow U 2))
(/ (+ J (* 1/2 (/ (pow U 2) J))) (pow U 2))
(/ 1/2 J)
(+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))
(+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))
(+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))
(/ 1/2 J)
(+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))
(+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))
(+ (* 1/2 (/ 1 J)) (/ J (pow U 2)))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 (/ J (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* 2 (* (pow K 2) (+ (* -1/64 J) (* 5/384 J)))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* 2 (* (pow K 2) (+ (* -1/8 (+ (* -1/64 J) (* 5/384 J))) (+ (* -5/3072 J) (* 61/46080 J))))) (* 2 (+ (* -1/64 J) (* 5/384 J))))))))
(* -92160/61 (/ J (pow K 6)))
(/ (+ (* -92160/61 J) (* 55296000/3721 (/ J (pow K 2)))) (pow K 6))
(/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2))))) (pow K 6))
(/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -159252480000/226981 J) (+ (* -600/61 (+ (* -16588800000/226981 J) (* 265420800/3721 J))) (* 2123366400/3721 J))) (pow K 6))) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2)))))) (pow K 6))
(* -92160/61 (/ J (pow K 6)))
(/ (+ (* -92160/61 J) (* 55296000/3721 (/ J (pow K 2)))) (pow K 6))
(/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2))))) (pow K 6))
(/ (+ (* -92160/61 J) (+ (* 2 (/ (+ (* -159252480000/226981 J) (+ (* -600/61 (+ (* -16588800000/226981 J) (* 265420800/3721 J))) (* 2123366400/3721 J))) (pow K 6))) (+ (* 2 (/ (+ (* -16588800000/226981 J) (* 265420800/3721 J)) (pow K 4))) (* 55296000/3721 (/ J (pow K 2)))))) (pow K 6))
1
(+ 1 (* 1/8 (pow K 2)))
(+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))
(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(* 61/46080 (pow K 6))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (+ (* 5/384 (/ 1 (pow K 2))) (/ 1 (pow K 6))))))
(* 61/46080 (pow K 6))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (+ (* 5/384 (/ 1 (pow K 2))) (/ 1 (pow K 6))))))
(* 1/8 (pow K 2))
(* (pow K 2) (+ 1/8 (* 5/384 (pow K 2))))
(* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(* 61/46080 (pow K 6))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* 61/46080 (pow K 6))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(/ J (pow U 2))
(/ J (pow U 2))
(/ J (pow U 2))
(/ J (pow U 2))
(/ J (pow U 2))
(/ J (pow U 2))
(/ J (pow U 2))
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(/ J (pow U 2))
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(/ J (pow U 2))
(/ J (pow U 2))
(* 61/46080 (pow K 2))
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(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 61/46080 (pow K 2))
(* 5/384 (pow K 2))
(* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))
(* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))
(* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))
(* 61/46080 (pow K 4))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* 61/46080 (pow K 4))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* 1/8 K)
(* K (+ 1/8 (* 5/384 (pow K 2))))
(* K (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(* K (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(* 61/46080 (pow K 5))
(* (pow K 5) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* (pow K 5) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* (pow K 5) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(* 61/46080 (pow K 5))
(* (pow K 5) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(* -1 (* (pow K 5) (- (* -1 (/ (+ 5/384 (* 1/8 (/ 1 (pow K 2)))) (pow K 2))) 61/46080)))
(* -1 (* (pow K 5) (- (* -1 (/ (+ 5/384 (* 1/8 (/ 1 (pow K 2)))) (pow K 2))) 61/46080)))
Outputs
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (+.f64 (*.f64 J #s(literal 1/4 binary64)) (*.f64 (*.f64 K K) (*.f64 J (+.f64 (*.f64 (*.f64 K K) #s(literal 1/23040 binary64)) #s(literal -1/192 binary64)))))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 J)
(/.f64 #s(literal -1/2 binary64) J)
(- (* -1/16 (/ (pow K 2) J)) (* 1/2 (/ 1 J)))
(+.f64 (/.f64 #s(literal -1/2 binary64) J) (/.f64 (*.f64 (*.f64 K K) #s(literal -1/16 binary64)) J))
(- (* (pow K 2) (- (* -5/768 (/ (pow K 2) J)) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))
(+.f64 (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 (*.f64 K K) #s(literal -5/768 binary64)) J) (/.f64 #s(literal -1/16 binary64) J))) (/.f64 #s(literal -1/2 binary64) J))
(- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (/ (pow K 2) J)) (* 5/768 (/ 1 J)))) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))
(+.f64 (*.f64 (*.f64 K K) (+.f64 (*.f64 (*.f64 K K) (+.f64 (*.f64 (/.f64 (*.f64 K K) J) #s(literal -61/92160 binary64)) (/.f64 #s(literal -5/768 binary64) J))) (/.f64 #s(literal -1/16 binary64) J))) (/.f64 #s(literal -1/2 binary64) J))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal 1/8 binary64)))
(+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) #s(literal 5/384 binary64))))))
(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64)))))))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64)))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(- (* -2 (/ (pow J 2) U)) U)
(-.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)
(- (* -2 (/ (pow J 2) U)) U)
(-.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)
(- (* -2 (/ (pow J 2) U)) U)
(-.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/.f64 (-.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/.f64 (-.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/.f64 (-.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)))
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)))
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)))
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U) U)))
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 #s(literal -2 binary64) J)) U)
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(* -2 (pow J 2))
(*.f64 J (*.f64 #s(literal -2 binary64) J))
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(* 2 (/ (pow J 2) U))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
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(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (+ (* 5/384 (/ 1 (pow K 2))) (/ 1 (pow K 6))))))
(+.f64 (*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K))))))) #s(literal 1 binary64))
(* 61/46080 (pow K 6))
(*.f64 #s(literal 61/46080 binary64) (pow.f64 K #s(literal 6 binary64)))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (+ (* 5/384 (/ 1 (pow K 2))) (/ 1 (pow K 6))))))
(+.f64 (*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K))))))) #s(literal 1 binary64))
(* 1/8 (pow K 2))
(*.f64 (*.f64 K K) #s(literal 1/8 binary64))
(* (pow K 2) (+ 1/8 (* 5/384 (pow K 2))))
(*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) #s(literal 5/384 binary64)))))
(* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(* 61/46080 (pow K 6))
(*.f64 #s(literal 61/46080 binary64) (pow.f64 K #s(literal 6 binary64)))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))))
(* 61/46080 (pow K 6))
(*.f64 #s(literal 61/46080 binary64) (pow.f64 K #s(literal 6 binary64)))
(* (pow K 6) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))))
(* (pow K 6) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (pow.f64 K #s(literal 6 binary64)) (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(/ J (pow U 2))
(/.f64 J (*.f64 U U))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 61/46080 (pow K 2))
(*.f64 K (*.f64 K #s(literal 61/46080 binary64)))
(* 5/384 (pow K 2))
(*.f64 (*.f64 K K) #s(literal 5/384 binary64))
(* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))
(*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))
(* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))
(*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))
(* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))
(*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))
(* 61/46080 (pow K 4))
(*.f64 K (*.f64 #s(literal 61/46080 binary64) (*.f64 K (*.f64 K K))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K (*.f64 K (*.f64 K K))) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K (*.f64 K (*.f64 K K))) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K (*.f64 K (*.f64 K K))) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* 61/46080 (pow K 4))
(*.f64 K (*.f64 #s(literal 61/46080 binary64) (*.f64 K (*.f64 K K))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K (*.f64 K (*.f64 K K))) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K (*.f64 K (*.f64 K K))) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* (pow K 4) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K (*.f64 K (*.f64 K K))) (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))))
(* 1/8 K)
(*.f64 K #s(literal 1/8 binary64))
(* K (+ 1/8 (* 5/384 (pow K 2))))
(*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) #s(literal 5/384 binary64))))
(* K (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(* K (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2))))))
(*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(* 61/46080 (pow K 5))
(*.f64 #s(literal 61/46080 binary64) (pow.f64 K #s(literal 5 binary64)))
(* (pow K 5) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))) (pow.f64 K #s(literal 5 binary64)))
(* (pow K 5) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))) (pow.f64 K #s(literal 5 binary64)))
(* (pow K 5) (+ 61/46080 (+ (/ 1/8 (pow K 4)) (* 5/384 (/ 1 (pow K 2))))))
(*.f64 (+.f64 #s(literal 61/46080 binary64) (+.f64 (/.f64 #s(literal 5/384 binary64) (*.f64 K K)) (/.f64 #s(literal 1/8 binary64) (*.f64 K (*.f64 K (*.f64 K K)))))) (pow.f64 K #s(literal 5 binary64)))
(* 61/46080 (pow K 5))
(*.f64 #s(literal 61/46080 binary64) (pow.f64 K #s(literal 5 binary64)))
(* (pow K 5) (+ 61/46080 (* 5/384 (/ 1 (pow K 2)))))
(*.f64 (+.f64 #s(literal 61/46080 binary64) (/.f64 #s(literal 5/384 binary64) (*.f64 K K))) (pow.f64 K #s(literal 5 binary64)))
(* -1 (* (pow K 5) (- (* -1 (/ (+ 5/384 (* 1/8 (/ 1 (pow K 2)))) (pow K 2))) 61/46080)))
(*.f64 (pow.f64 K #s(literal 5 binary64)) (+.f64 #s(literal 61/46080 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -5/384 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 K K)))))
(* -1 (* (pow K 5) (- (* -1 (/ (+ 5/384 (* 1/8 (/ 1 (pow K 2)))) (pow K 2))) 61/46080)))
(*.f64 (pow.f64 K #s(literal 5 binary64)) (+.f64 #s(literal 61/46080 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -5/384 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 K K)))))

eval155.0ms (1.5%)

Compiler

Compiled 23686 to 2661 computations (88.8% saved)

prune156.0ms (1.5%)

Pruning

32 alts after pruning (24 fresh and 8 done)

PrunedKeptTotal
New1040151055
Fresh5914
Picked325
Done066
Total1048321080
Accuracy
100.0%
Counts
1080 → 32
Alt Table
Click to see full alt table
StatusAccuracyProgram
2.6%
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
29.1%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
28.8%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
✓54.3%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓29.0%
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
54.3%
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
54.3%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
30.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
54.2%
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J)))
35.4%
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
39.2%
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
28.9%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
45.5%
(*.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 #s(literal 2 binary64) K))))) (*.f64 #s(literal 4 binary64) (*.f64 J J)))) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
23.8%
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
2.4%
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U)))) (*.f64 (*.f64 U U) (*.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
2.2%
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 U (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J))))) (*.f64 J #s(literal -2 binary64)))
3.7%
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J)))) (*.f64 J #s(literal -2 binary64)))
2.5%
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
29.0%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
5.2%
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J U)) (/.f64 (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U))) U)) (*.f64 J #s(literal -2 binary64)))
10.2%
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (*.f64 (/.f64 J U) (/.f64 #s(literal 1 binary64) U)))) (*.f64 J #s(literal -2 binary64)))
16.8%
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
14.9%
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
✓32.4%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
✓47.6%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
✓54.4%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
11.9%
(*.f64 U (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U U))))))
29.1%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
2.8%
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
✓30.6%
(*.f64 #s(literal -2 binary64) J)
✓38.7%
(neg.f64 U)
✓12.4%
U
Compiler

Compiled 1519 to 663 computations (56.4% saved)

regimes149.0ms (1.4%)

Counts
52 → 3
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
(*.f64 U (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 J J) U) U)))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (*.f64 (/.f64 J U) (/.f64 #s(literal 1 binary64) U)))) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J U)) (/.f64 (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U))) U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U)))))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U)))) (*.f64 (*.f64 U U) (*.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 U (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
(*.f64 (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 J #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #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) (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 #s(literal 2 binary64) K))))) (*.f64 #s(literal 4 binary64) (*.f64 J J)))) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
Outputs
(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)))))
U
Calls

6 calls:

38.0ms
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
30.0ms
J
20.0ms
(/.f64 K #s(literal 2 binary64))
16.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
15.0ms
K
Results
AccuracySegmentsBranch
90.2%2J
87.7%1K
91.2%2U
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)))))
87.7%1(cos.f64 (/.f64 K #s(literal 2 binary64)))
87.7%1(/.f64 K #s(literal 2 binary64))
Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes21.0ms (0.2%)

Counts
50 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
(*.f64 U (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 J J) U) U)))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (*.f64 (/.f64 J U) (/.f64 #s(literal 1 binary64) U)))) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J U)) (/.f64 (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U))) U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U)))))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U)))) (*.f64 (*.f64 U U) (*.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 U (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
(*.f64 (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 J #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
Outputs
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
Calls

1 calls:

15.0ms
U
Results
AccuracySegmentsBranch
91.2%2U
Compiler

Compiled 4 to 3 computations (25% saved)

regimes81.0ms (0.8%)

Counts
48 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
(*.f64 U (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 J J) U) U)))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (*.f64 (/.f64 J U) (/.f64 #s(literal 1 binary64) U)))) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J U)) (/.f64 (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U))) U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U)))))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U)))) (*.f64 (*.f64 U U) (*.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 U (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
(*.f64 (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 J #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64)))
Outputs
(neg.f64 U)
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
Calls

5 calls:

16.0ms
K
15.0ms
J
15.0ms
(/.f64 K #s(literal 2 binary64))
14.0ms
U
14.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
75.0%1K
75.0%1(cos.f64 (/.f64 K #s(literal 2 binary64)))
75.0%1(/.f64 K #s(literal 2 binary64))
81.2%2J
80.1%2U
Compiler

Compiled 25 to 20 computations (20% saved)

regimes73.0ms (0.7%)

Counts
45 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
(*.f64 U (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 J J) U) U)))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (*.f64 (/.f64 J U) (/.f64 #s(literal 1 binary64) U)))) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J U)) (/.f64 (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U))) U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U)))))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U)))) (*.f64 (*.f64 U U) (*.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 U (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) (/.f64 (*.f64 U #s(literal 1/4 binary64)) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 J #s(literal -2 binary64)))
Outputs
(neg.f64 U)
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
Calls

5 calls:

15.0ms
K
14.0ms
(/.f64 K #s(literal 2 binary64))
13.0ms
U
13.0ms
J
12.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
69.2%3K
69.2%3(/.f64 K #s(literal 2 binary64))
69.0%3(cos.f64 (/.f64 K #s(literal 2 binary64)))
68.2%2U
68.3%2J
Compiler

Compiled 25 to 20 computations (20% saved)

regimes35.0ms (0.3%)

Counts
36 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
(-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U)
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (*.f64 J #s(literal -2 binary64)))
(*.f64 U (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 J (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (/.f64 U J) J)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (*.f64 K K))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 J J) U) U)))))
(-.f64 #s(literal 0 binary64) (*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U) U))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 (*.f64 #s(literal -1/192 binary64) (*.f64 K K)) #s(literal 1/4 binary64))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (*.f64 (/.f64 J U) (/.f64 #s(literal 1 binary64) U)))) (*.f64 J #s(literal -2 binary64)))
(-.f64 (*.f64 (*.f64 J J) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) U) U)) U)) U)
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 J J)) (*.f64 U (*.f64 U U))))) U)
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J U)) (/.f64 (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U))) U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64))))))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 (*.f64 K K) #s(literal 61/46080 binary64)))))))))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 J J) (*.f64 U (*.f64 U U)))))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) U) (*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal 1 binary64) U) (/.f64 (*.f64 (/.f64 J (*.f64 U U)) J) U)))) J) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 U (+.f64 (/.f64 J (*.f64 U U)) (-.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U U) (*.f64 U U)))))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 (*.f64 J J) (*.f64 #s(literal 1/2 binary64) (*.f64 U U)))) (*.f64 (*.f64 U U) (*.f64 J (*.f64 U U)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J)))) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 J (*.f64 J J))) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 U (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 J J)) (/.f64 (-.f64 (/.f64 J (*.f64 U U)) (/.f64 #s(literal 1/2 binary64) J)) (/.f64 (*.f64 U U) J))))) (*.f64 J #s(literal -2 binary64)))
Outputs
(*.f64 #s(literal -2 binary64) J)
(-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U)
Calls

3 calls:

11.0ms
J
11.0ms
U
11.0ms
K
Results
AccuracySegmentsBranch
49.5%4K
51.9%2U
51.5%2J
Compiler

Compiled 12 to 9 computations (25% saved)

regimes8.0ms (0.1%)

Counts
10 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(/.f64 (*.f64 J (*.f64 J #s(literal 2 binary64))) U)
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 J U)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (/.f64 (*.f64 U #s(literal -1/2 binary64)) J) (*.f64 J #s(literal -2 binary64)))
Outputs
(*.f64 #s(literal -2 binary64) J)
(neg.f64 U)
Calls

2 calls:

4.0ms
J
4.0ms
U
Results
AccuracySegmentsBranch
51.4%2J
51.5%2U
Compiler

Compiled 8 to 6 computations (25% saved)

regimes6.0ms (0.1%)

Counts
2 → 3
Calls
Call 1
Inputs
U
(neg.f64 U)
Outputs
(neg.f64 U)
U
(neg.f64 U)
Calls

3 calls:

3.0ms
J
2.0ms
U
2.0ms
K
Results
AccuracySegmentsBranch
43.8%3K
38.7%1J
38.7%1U
Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
U
Outputs
U
Calls

3 calls:

1.0ms
U
1.0ms
J
1.0ms
K
Results
AccuracySegmentsBranch
12.4%1J
12.4%1U
12.4%1K
Compiler

Compiled 12 to 9 computations (25% saved)

bsearch1.0ms (0%)

Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
8.750402620820767e+303
+inf
0.0ms
-inf
-1.6985781499175439e+307
Compiler

Compiled 33 to 22 computations (33.3% saved)

bsearch22.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
1.1628790078485794e+253
2.8383638616378086e+254
Results
15.0ms112×0valid
Compiler

Compiled 299 to 197 computations (34.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-cos: 3.0ms (28.9% of total)
ival-mult: 3.0ms (28.9% of total)
ival-div: 1.0ms (9.6% of total)
ival-add: 1.0ms (9.6% of total)
ival-sqrt: 1.0ms (9.6% of total)
ival-pow: 1.0ms (9.6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch13.0ms (0.1%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
1.1462408318017744e-176
2.2244372810457783e-176
Results
8.0ms64×0valid
Compiler

Compiled 137 to 106 computations (22.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-mult: 2.0ms (36.1% of total)
ival-div: 1.0ms (18% of total)
ival-cos: 1.0ms (18% of total)
ival-pow: 1.0ms (18% of total)
ival-add: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch19.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
17.0ms
2.108891485349522e-97
1.5935306109484456e-96
Results
13.0ms96×0valid
Compiler

Compiled 141 to 112 computations (20.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 3.0ms (31.5% of total)
ival-add: 2.0ms (21% of total)
ival-cos: 2.0ms (21% of total)
ival-div: 1.0ms (10.5% of total)
ival-sqrt: 1.0ms (10.5% of total)
ival-pow: 1.0ms (10.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch27.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
24.0ms
9.001342565936516e-116
1.149209537195604e-111
Results
18.0ms128×0valid
Compiler

Compiled 193 to 142 computations (26.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-mult: 4.0ms (34.4% of total)
ival-cos: 3.0ms (25.8% of total)
ival-div: 2.0ms (17.2% of total)
ival-pow: 2.0ms (17.2% of total)
ival-add: 1.0ms (8.6% of total)
ival-sqrt: 1.0ms (8.6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch26.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
24.0ms
9.001342565936516e-116
1.149209537195604e-111
Results
17.0ms128×0valid
Compiler

Compiled 137 to 110 computations (19.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-mult: 4.0ms (34.1% of total)
ival-cos: 3.0ms (25.6% of total)
ival-div: 2.0ms (17.1% of total)
ival-add: 1.0ms (8.5% of total)
ival-sqrt: 1.0ms (8.5% of total)
ival-pow: 1.0ms (8.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch74.0ms (0.7%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.136787560746733e+239
6.569787119430629e+239
48.0ms
2.6071114970286533e+115
2.0593316216421794e+118
Results
38.0ms224×0valid
Compiler

Compiled 187 to 148 computations (20.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-cos: 13.0ms (44.9% of total)
ival-mult: 7.0ms (24.2% of total)
ival-div: 3.0ms (10.4% of total)
ival-pow: 3.0ms (10.4% of total)
ival-sqrt: 2.0ms (6.9% of total)
ival-add: 1.0ms (3.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify14.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
24×*-commutative_binary64
6×+-commutative_binary64
4×sub-neg_binary64
2×1-exp_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061189
183189
286189
387189
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)) (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 9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856118056162172578717193742636030530235798840866882774987301441682011041067710253162440905843719802548551599076639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744 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))))) U))
(if (<=.f64 U #s(literal 49000000000000000788616346716151610627149124530830350982220089026432403494640578570068165307244835039196252592962430125215732742749829568907453805016723504020294363455929799117712820189772496903593709823664779553437375337760674458228645729709704276344832 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U))
(if (<=.f64 J #s(literal 2423796578111791/142576269300693600582536612678134103902913390851517497830599766184352348975271168328309775353667856243082572174174825228459022022542982437445395666241319193382874833573758279690089818507706368 binary64)) (neg.f64 U) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J)))))
(if (<=.f64 J #s(literal 931901696844657/601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856 binary64)) (neg.f64 U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))))
(if (<=.f64 U #s(literal 93076680405667/84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768 binary64)) (*.f64 #s(literal -2 binary64) J) (-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U))
(if (<=.f64 U #s(literal 7971425370597343/86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432 binary64)) (*.f64 #s(literal -2 binary64) J) (neg.f64 U))
(if (<=.f64 K #s(literal 1450000000000000136298191076443542452559007835651850076750977748071755676828967303051784773744366806753184312457166848 binary64)) (neg.f64 U) (if (<=.f64 K #s(literal 175000000000000007067434385668530323646898952040723999259474729086818702090858568662159061452543623982497984003496804043400523315275013652906810167632171437322005435871687595192180132511538414053096014797538897218980817577744336868077469696 binary64)) U (neg.f64 U)))
U
Outputs
(if (<=.f64 (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -inf.0 binary64)) (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 9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856118056162172578717193742636030530235798840866882774987301441682011041067710253162440905843719802548551599076639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744 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))))) U))
(if (<=.f64 (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal -inf.0 binary64)) (-.f64 #s(literal 0 binary64) U) (if (<=.f64 (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))) #s(literal 2 binary64))))) #s(literal 9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856118056162172578717193742636030530235798840866882774987301441682011041067710253162440905843719802548551599076639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744 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))))) U))
(if (<=.f64 U #s(literal 49000000000000000788616346716151610627149124530830350982220089026432403494640578570068165307244835039196252592962430125215732742749829568907453805016723504020294363455929799117712820189772496903593709823664779553437375337760674458228645729709704276344832 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U J) #s(literal 2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U))
(if (<=.f64 J #s(literal 2423796578111791/142576269300693600582536612678134103902913390851517497830599766184352348975271168328309775353667856243082572174174825228459022022542982437445395666241319193382874833573758279690089818507706368 binary64)) (neg.f64 U) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J)))))
(if (<=.f64 J #s(literal 2423796578111791/142576269300693600582536612678134103902913390851517497830599766184352348975271168328309775353667856243082572174174825228459022022542982437445395666241319193382874833573758279690089818507706368 binary64)) (-.f64 #s(literal 0 binary64) U) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 (/.f64 U J) #s(literal 1/2 binary64)))))
(if (<=.f64 J #s(literal 931901696844657/601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856 binary64)) (neg.f64 U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))))
(if (<=.f64 J #s(literal 931901696844657/601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856 binary64)) (-.f64 #s(literal 0 binary64) U) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(if (<=.f64 U #s(literal 93076680405667/84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768 binary64)) (*.f64 #s(literal -2 binary64) J) (-.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 J U)) U))
(if (<=.f64 U #s(literal 7971425370597343/86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432 binary64)) (*.f64 #s(literal -2 binary64) J) (neg.f64 U))
(if (<=.f64 U #s(literal 7971425370597343/86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543475342543861619655442432 binary64)) (*.f64 #s(literal -2 binary64) J) (-.f64 #s(literal 0 binary64) U))
(if (<=.f64 K #s(literal 1450000000000000136298191076443542452559007835651850076750977748071755676828967303051784773744366806753184312457166848 binary64)) (neg.f64 U) (if (<=.f64 K #s(literal 175000000000000007067434385668530323646898952040723999259474729086818702090858568662159061452543623982497984003496804043400523315275013652906810167632171437322005435871687595192180132511538414053096014797538897218980817577744336868077469696 binary64)) U (neg.f64 U)))
(if (<=.f64 K #s(literal 1450000000000000136298191076443542452559007835651850076750977748071755676828967303051784773744366806753184312457166848 binary64)) (-.f64 #s(literal 0 binary64) U) (if (<=.f64 K #s(literal 175000000000000007067434385668530323646898952040723999259474729086818702090858568662159061452543623982497984003496804043400523315275013652906810167632171437322005435871687595192180132511538414053096014797538897218980817577744336868077469696 binary64)) U (-.f64 #s(literal 0 binary64) U)))
U

soundness1.5s (14.1%)

Rules
6680×*-lowering-*.f32
6680×*-lowering-*.f64
6122×*-lowering-*.f32
6122×*-lowering-*.f64
4358×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038164
1242151
22472151
08836151
035106
1178103
21486103
08385103
03895624
113764833
258944626
086104626
04293810
114663356
256713233
083423233
01724
13421
28021
320521
461621
5114521
6158921
7165221
8167021
9168821
10169621
11169821
12169821
0169821
Stop Event
1×fuel
1×iter limit
1×saturated
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 464 to 257 computations (44.6% saved)

preprocess156.0ms (1.5%)

Remove

(abs K)

Compiler

Compiled 1302 to 406 computations (68.8% saved)

end0.0ms (0%)

Profiling

Loading profile data...