Maksimov and Kolovsky, Equation (3)

Time bar (total: 11.5s)

analyze417.0ms (3.6%)

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: 203.0ms
ival-mult: 73.0ms (35.9% of total)
ival-pow: 58.0ms (28.6% of total)
ival-div: 24.0ms (11.8% of total)
ival-sqrt: 15.0ms (7.4% of total)
ival-add: 13.0ms (6.4% of total)
ival-cos: 13.0ms (6.4% of total)
const: 4.0ms (2% of total)
backward-pass: 1.0ms (0.5% of total)

sample1.8s (15.6%)

Results
1.4s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.0s
ival-mult: 308.0ms (30.6% of total)
ival-cos: 244.0ms (24.2% of total)
ival-div: 194.0ms (19.3% of total)
ival-pow: 111.0ms (11% of total)
ival-add: 70.0ms (6.9% of total)
ival-sqrt: 59.0ms (5.9% of total)
const: 18.0ms (1.8% of total)
backward-pass: 3.0ms (0.3% of total)
Bogosity

preprocess119.0ms (1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
075246
1192210
2648210
32306210
44630210
01724
13321
27921
320621
461921
5113321
6156821
7163021
8164821
9166621
10167421
11167621
12167621
0167621
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 U (*.f64 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 J) 1/2) (cos (/ K 2)))))
(* (* (* -2 (neg J)) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 (neg J)) (cos (/ K 2)))) 2))))
(* (* (cos (/ K 2)) (* J 2)) (hypot 1 (/ (* (/ U J) 1/2) (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 J) 1/2) (cos (/ K 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 J) 1/2) (cos (/ K 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 J) 1/2) (cos (/ K 2)))))
(neg (* (* (* -2 J) (cos (/ (neg K) 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ (neg K) 2)))) 2)))))
(* (* (cos (/ K 2)) (* J 2)) (hypot 1 (/ (* (/ U J) 1/2) (cos (/ K 2)))))
(neg (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ (neg U) (* (* 2 J) (cos (/ K 2)))) 2)))))
(* (* (cos (/ K 2)) (* J 2)) (hypot 1 (/ (* (/ U J) 1/2) (cos (/ K 2)))))
(* (* (* -2 K) (cos (/ J 2))) (sqrt (+ 1 (pow (/ U (* (* 2 K) (cos (/ J 2)))) 2))))
(* -2 (* (hypot 1 (/ U (* (cos (/ J 2)) (* K 2)))) (* K (cos (/ J 2)))))
(* (* (* -2 U) (cos (/ K 2))) (sqrt (+ 1 (pow (/ J (* (* 2 U) (cos (/ K 2)))) 2))))
(* -2 (* (hypot 1 (/ (/ (/ J 2) U) (cos (/ K 2)))) (* (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 2) J) (cos (* U 1/2)))))
Symmetry

(abs K)

(abs U)

(negabs J)

explain205.0ms (1.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
400-0-(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))))
270-0-(*.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)))))
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
074(1.6882139770263146e+198 4.590266994213307e-170 5.523855867814707e+233)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)
0130(5.986626980333376e+44 1.9746583159946293e+241 1.7619843597668437e-214)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
127.0ms512×0valid
Compiler

Compiled 255 to 53 computations (79.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-mult: 18.0ms (34.6% of total)
ival-cos: 13.0ms (25% of total)
ival-div: 8.0ms (15.4% of total)
ival-pow: 5.0ms (9.6% of total)
ival-sqrt: 4.0ms (7.7% of total)
ival-add: 3.0ms (5.8% of total)
const: 1.0ms (1.9% 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
▶90.0%
(*.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))))))
▶75.1%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
Compiler

Compiled 51 to 32 computations (37.3% saved)

simplify69.0ms (0.6%)

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 U (*.f64 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
822×associate-*r/
758×/-lowering-/.f32
758×/-lowering-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025177
155177
2108177
3307177
4795177
51314177
61566177
71846177
82125177
92199177
102199177
112339177
122339177
02339177
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 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))))))
(* (* -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 (*.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))))))
(* (* -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 2)
(*.f64 J #s(literal 2 binary64))

localize164.0ms (1.4%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 (/.f64 U (*.f64 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))))
✓accuracy90.1%
(*.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))))))
✓accuracy99.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.6%
(pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
✓accuracy90.1%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
✓accuracy85.3%
(sqrt.f64 (+.f64 #s(literal 1 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
113.0ms256×0valid
Compiler

Compiled 189 to 23 computations (87.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 81.0ms
ival-mult: 31.0ms (38.4% of total)
compiled-spec: 25.0ms (31% of total)
ival-div: 7.0ms (8.7% of total)
ival-cos: 7.0ms (8.7% of total)
ival-sqrt: 5.0ms (6.2% of total)
ival-pow: 3.0ms (3.7% of total)
ival-add: 2.0ms (2.5% of total)
const: 1.0ms (1.2% of total)
backward-pass: 0.0ms (0% of total)

series83.0ms (0.7%)

Counts
8 → 228
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)))>
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))))))>
#<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)))))))>
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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)))>
#<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)))))>
Calls

57 calls:

TimeVariablePointExpression
38.0ms
J
@inf
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
7.0ms
U
@0
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
3.0ms
K
@0
(* (* -2 J) (cos (/ K 2)))
3.0ms
K
@0
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
3.0ms
K
@-inf
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite264.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
4472×*-lowering-*.f32
4472×*-lowering-*.f64
2962×/-lowering-/.f32
2962×/-lowering-/.f64
1158×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02590
112190
289890
0871490
Stop Event
1×iter limit
1×node limit
Counts
8 → 399
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)))
Outputs
(exp.f64 (*.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) #s(literal 1/2 binary64)))
(hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64))))) (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 6 binary64))))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)) #s(literal -1 binary64))) (sqrt.f64 (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64))))
(/.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))) #s(literal 1/2 binary64))
(*.f64 (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64)))))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (+.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 (*.f64 #s(literal -4 binary64) J) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) #s(literal 1/4 binary64)))
(neg.f64 (*.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))))
(neg.f64 (*.f64 (*.f64 #s(literal 2 binary64) J) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))))))
(neg.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.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 2 binary64) J))))
(neg.f64 (*.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))) (*.f64 #s(literal 2 binary64) J)))
(*.f64 J (*.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.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 (*.f64 J #s(literal -2 binary64)) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))))
(*.f64 #s(literal -2 binary64) (*.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.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 J #s(literal -2 binary64))))
(*.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal -2 binary64))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))))
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(*.f64 (*.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 (*.f64 (*.f64 U U) (/.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) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(exp.f64 (log.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) J) U))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal -2 binary64)))) (/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(neg.f64 (/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(neg.f64 (*.f64 (/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (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 (*.f64 #s(literal 2 binary64) J) U)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) J) U) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #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 U J)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 J #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) U) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) J) (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))
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(/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
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(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 2 binary64) J) U))
(/.f64 (/.f64 U J) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 U J) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U (*.f64 J #s(literal -2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (neg.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 U J)) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (*.f64 J #s(literal -2 binary64)) U))
(/.f64 (/.f64 (/.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 U (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) J))
(/.f64 (exp.f64 (log.f64 U)) (exp.f64 (log.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))))
(/.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 (*.f64 J #s(literal -2 binary64))))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) U))) (exp.f64 (log.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal -2 binary64))))))
(/.f64 (neg.f64 (/.f64 U #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) J)))
(/.f64 (neg.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -2 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 J #s(literal -2 binary64)))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) J))
(pow.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 1 binary64))
(pow.f64 (/.f64 (/.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal 4 binary64) J)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2 binary64) J) U)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))
(*.f64 U (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 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 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) U) #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 U (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 J U)))
(*.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) U) (neg.f64 (/.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 U (*.f64 #s(literal 2 binary64) J)))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) U)
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) U) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 U (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1/2 binary64) J) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) U) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) U)))
(*.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 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 2 binary64)))
(*.f64 (/.f64 U J) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal -2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 U 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 U J)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64)))
(*.f64 #s(literal -1/2 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) J))))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U (*.f64 J #s(literal -2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) J) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) U)))
(*.f64 (/.f64 #s(literal -1/2 binary64) J) (/.f64 U (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))) (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))))
(*.f64 (/.f64 (/.f64 U J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (/.f64 U #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 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 (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) J))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1 binary64)) (pow.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U (*.f64 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 (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) U) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) J))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) U)) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 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 (exp.f64 (log.f64 U)) (exp.f64 (log.f64 (/.f64 (/.f64 #s(literal 1/2 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 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(*.f64 (/.f64 #s(literal -1 binary64) J) (/.f64 U (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 U #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 U (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1/2 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 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64))) (/.f64 U J))
(*.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) J))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) J))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) J)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) U) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) J))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 U (*.f64 #s(literal 2 binary64) J)))
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J))))) (sqrt.f64 (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) J)))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) U) (/.f64 #s(literal 1/2 binary64) J))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) U)) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 U J)) #s(literal 1/2 binary64))

simplify368.0ms (3.2%)

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
03895504
113704713
258814506
085954506
Stop Event
1×iter limit
1×node limit
Counts
228 → 228
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))))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -1 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 3)) (pow U 3))) (/ (cos (* 1/2 K)) U)))) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
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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))))
(* 1/2 (/ 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 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 (*.f64 U 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 #s(literal -1/128 binary64) (*.f64 (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 J (*.f64 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 (*.f64 J J) (-.f64 (*.f64 #s(literal 2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)) (/.f64 (*.f64 J J) (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 (*.f64 (*.f64 U U) K) K)) (*.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)))))))))))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 (*.f64 K K) (*.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 (*.f64 #s(literal 1/32 binary64) (*.f64 U U)) (*.f64 J J)) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 K K)) (-.f64 (*.f64 (/.f64 (*.f64 U U) (*.f64 J J)) #s(literal 1/96 binary64)) (/.f64 (/.f64 (*.f64 #s(literal 1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (pow.f64 J #s(literal 4 binary64))) (+.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))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (pow K 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
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(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
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(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
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(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
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(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
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(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (pow J 2)))
(/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))
(+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))
(+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 U U) K) K) #s(literal 1/16 binary64)) (*.f64 J J)))
(+ (* 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))))))
(+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/16 binary64)) (*.f64 J J)) (*.f64 (*.f64 K K) (*.f64 (/.f64 (*.f64 U U) (*.f64 J J)) #s(literal 1/96 binary64))))))
(+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))) (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))))
(+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/16 binary64)) (*.f64 J J)) (*.f64 (*.f64 (*.f64 K K) #s(literal -1/4 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal -1/24 binary64)) (*.f64 J J)) (*.f64 K (*.f64 K (+.f64 (*.f64 (/.f64 (*.f64 U U) (*.f64 J J)) #s(literal -1/96 binary64)) (*.f64 (/.f64 (*.f64 U U) (*.f64 J J)) #s(literal 13/2880 binary64))))))))))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))
(* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))
(/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 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)))
(* 1/2 (/ 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 (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 (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))
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 U J)) (*.f64 #s(literal 1/16 binary64) (*.f64 U (/.f64 (*.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 K (*.f64 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 #s(literal 1/2 binary64) (/.f64 U J)) (*.f64 K (*.f64 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)))

eval150.0ms (1.3%)

Compiler

Compiled 22681 to 2232 computations (90.2% saved)

prune114.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New7539762
Fresh000
Picked202
Done000
Total7559764
Accuracy
99.9%
Counts
764 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
34.7%
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) U)
37.1%
(-.f64 #s(literal 0 binary64) U)
▶52.3%
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
50.5%
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 0 binary64) (*.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))))))
▶89.9%
(*.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 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
▶76.5%
(*.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))))
33.2%
(*.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)))
▶55.2%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
▶13.0%
U
Compiler

Compiled 328 to 226 computations (31.1% saved)

simplify405.0ms (3.5%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓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 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
✓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 #s(literal 1/2 binary64) (/.f64 U 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 -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 U (*.f64 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
3584×*-lowering-*.f32
3584×*-lowering-*.f64
1542×/-lowering-/.f32
1542×/-lowering-/.f64
1302×associate-/r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038228
198228
2260228
3729228
42082228
52586228
62708228
72751228
82751228
93473228
103497228
113510228
123518228
133518228
143571228
153573228
163573228
175077228
185632228
195660228
205661228
215661228
225662228
235663228
245663228
255906228
266059228
276068228
286068228
296068228
06068228
Stop Event
1×iter limit
1×saturated
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 2)
U
(* (cos (* 1/2 K)) (* J -2))
(cos (* 1/2 K))
(* 1/2 K)
1/2
K
(* J -2)
J
-2
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
(* (* -2 J) (cos (/ K 2)))
(* -2 J)
-2
J
(cos (/ K 2))
(/ K 2)
K
2
(sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J)))))
1
(* 1/2 (/ U J))
1/2
(/ U J)
U
(+ (* (cos (* 1/2 K)) (* J -2)) (/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K))))
(* (cos (* 1/2 K)) (* J -2))
(cos (* 1/2 K))
(* 1/2 K)
1/2
K
(* J -2)
J
-2
(/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K)))
(* -1/4 (/ (* U U) J))
-1/4
(/ (* U U) J)
(* U U)
U
Outputs
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 U #s(literal 2 binary64)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 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 (/.f64 U #s(literal 2 binary64)) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/ (/ U (* J 2)) (cos (/ K 2)))
(/.f64 (/.f64 (/.f64 U #s(literal 2 binary64)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ U (* J 2))
(/.f64 (/.f64 U #s(literal 2 binary64)) J)
U
(* J 2)
(*.f64 J #s(literal 2 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)
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
(*.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 #s(literal 2 binary64)) J)))
(* (* -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) (* (* 1/2 (/ U J)) (* 1/2 (/ U J)))))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U #s(literal 2 binary64)) J))
1
#s(literal 1 binary64)
(* 1/2 (/ U J))
(/.f64 (/.f64 U #s(literal 2 binary64)) J)
1/2
#s(literal 1/2 binary64)
(/ U J)
(/.f64 U J)
U
(+ (* (cos (* 1/2 K)) (* J -2)) (/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(* (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)
(/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K)))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (* U U) J))
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)
-1/4
#s(literal -1/4 binary64)
(/ (* U U) J)
(/.f64 (*.f64 U U) J)
(* U U)
(*.f64 U U)
U

localize313.0ms (2.7%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
✓accuracy99.8%
(/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (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)))
✓accuracy89.7%
(/.f64 (*.f64 U U) J)
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
✓accuracy99.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy90.1%
(*.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))))
✓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)))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓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))))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy90.1%
(*.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 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
Results
218.0ms256×0valid
Compiler

Compiled 252 to 34 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 70.0ms
ival-mult: 23.0ms (32.9% of total)
ival-div: 14.0ms (20.1% of total)
compiled-spec: 13.0ms (18.6% of total)
ival-cos: 12.0ms (17.2% of total)
ival-add: 4.0ms (5.7% of total)
ival-sqrt: 4.0ms (5.7% of total)
const: 1.0ms (1.4% of total)
backward-pass: 0.0ms (0% of total)

series38.0ms (0.3%)

Counts
16 → 348
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 (* (cos (* 1/2 K)) (* J -2))>
#<alt (cos (* 1/2 K))>
#<alt (* 1/2 K)>
#<alt (* J -2)>
#<alt (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))>
#<alt (* (* -2 J) (cos (/ K 2)))>
#<alt (cos (/ K 2))>
#<alt (+ (* (cos (* 1/2 K)) (* J -2)) (/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K))))>
#<alt (/ 1 (cos (/ K 2)))>
#<alt (* 1/2 (/ U J))>
#<alt (/ (* U U) J)>
#<alt (/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K)))>
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 (* -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 (* U (cos (* 1/2 K))))>
#<alt (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) U)) (* -1 (* U (cos (* 1/2 K)))))>
#<alt (+ (* -1 (* U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -2 (/ (cos (* 1/2 K)) U)) (* 2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 3))))))>
#<alt (+ (* -1 (* U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -2 (/ (cos (* 1/2 K)) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 5))) (* 2 (/ (cos (* 1/2 K)) (pow U 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2)))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (+ (* -1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (pow J 6))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4)))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 2 (cos (* 1/2 K))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 2 (cos (* 1/2 K)))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (pow J 6))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 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))))))) (* 1/4 (* (* J (pow K 2)) (sqrt (+ 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) (+ (* -1/192 (* (* J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/4 (* J (sqrt (+ 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) (+ (* 1/4 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -1/192 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/23040 (* (* J (pow K 2)) (sqrt (+ 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)))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 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)))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 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)))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 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)))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) J)))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) J)) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 3))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) J)) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 5))) (* 1/64 (/ (cos (* 1/2 K)) (pow J 3))))))))>
#<alt (* -1 (* U (cos (* 1/2 K))))>
#<alt (* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (* -1 (cos (* 1/2 K)))))>
#<alt (* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4))))))>
#<alt (* U (+ (* -4 (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)))))))>
#<alt (* U (cos (* 1/2 K)))>
#<alt (* -1 (* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (* -1 (cos (* 1/2 K))))))>
#<alt (* -1 (* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)))))))>
#<alt (* -1 (* U (+ (* -4 (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt 1>
#<alt (+ 1 (* -1/8 (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) (* -1/4 (/ (pow U 2) J)))>
#<alt (+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 J)))))>
#<alt (+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))>
#<alt (+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (+ (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))) (* (pow K 2) (+ (* 1/23040 J) (* 1/4 (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 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)))) (* -1/4 (/ (pow U 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)))) (* -1/4 (/ (pow U 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)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (/ (+ (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)>
#<alt (/ (+ (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)>
#<alt (/ (+ (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)>
#<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)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<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 (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (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 (* -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)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* 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 (* 1/2 (/ 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))>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (+ (* -1/4 (/ (pow U 2) J)) (* -1/32 (/ (* (pow K 2) (pow U 2)) J)))>
#<alt (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 (* (pow K 2) (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))))>
#<alt (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* (pow K 2) (+ (* 1/4 (* (pow K 2) (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
Calls

87 calls:

TimeVariablePointExpression
7.0ms
K
@inf
(+ (* (cos (* 1/2 K)) (* J -2)) (/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K))))
4.0ms
K
@-inf
(* 1/2 K)
2.0ms
J
@-inf
(/ (* U U) J)
2.0ms
J
@inf
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
1.0ms
K
@inf
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))

rewrite377.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
4204×*-lowering-*.f32
4204×*-lowering-*.f64
2688×/-lowering-/.f32
2688×/-lowering-/.f64
2592×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038125
1200125
21857125
09091125
Stop Event
1×iter limit
1×node limit
Counts
16 → 476
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)
(* (cos (* 1/2 K)) (* J -2))
(cos (* 1/2 K))
(* 1/2 K)
(* J -2)
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
(* (* -2 J) (cos (/ K 2)))
(cos (/ K 2))
(+ (* (cos (* 1/2 K)) (* J -2)) (/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K))))
(/ 1 (cos (/ K 2)))
(* 1/2 (/ U J))
(/ (* U U) J)
(/ (* -1/4 (/ (* U U) J)) (cos (* 1/2 K)))
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)))
(cos.f64 (/.f64 K #s(literal -2 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.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 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 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 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 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)))
(*.f64 (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
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(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 U J) #s(literal 1 binary64)))
(*.f64 (/.f64 U J) #s(literal 1/2 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) U) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J)))
(*.f64 (/.f64 #s(literal 1 binary64) J) (pow.f64 (/.f64 #s(literal 2 binary64) U) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) J) U)
(*.f64 (/.f64 #s(literal 1/2 binary64) J) (pow.f64 (/.f64 #s(literal 1 binary64) U) #s(literal -1 binary64)))
(*.f64 (*.f64 U #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) J))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) J) #s(literal 1 binary64)) U)
(*.f64 (pow.f64 (/.f64 U J) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 U #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 J (*.f64 U U))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 U U) (-.f64 #s(literal 0 binary64) J)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) J))
(/.f64 #s(literal 1 binary64) (/.f64 J (*.f64 U U)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 J (*.f64 U U)) #s(literal 1 binary64)))
(/.f64 U (/.f64 J U))
(/.f64 (*.f64 U U) J)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 J (*.f64 U U))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (-.f64 #s(literal 0 binary64) J))
(/.f64 (*.f64 U #s(literal 1 binary64)) (/.f64 J U))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U))) (neg.f64 (-.f64 #s(literal 0 binary64) J)))
(/.f64 (*.f64 (*.f64 U U) #s(literal 1 binary64)) J)
(pow.f64 (/.f64 J (*.f64 U U)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 J (*.f64 U U)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 U (/.f64 J U)))
(*.f64 U (/.f64 U J))
(*.f64 (/.f64 U J) U)
(*.f64 (*.f64 U U) (/.f64 #s(literal 1 binary64) J))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) J)))
(*.f64 (/.f64 #s(literal 1 binary64) J) (*.f64 U U))
(*.f64 (/.f64 #s(literal 1 binary64) J) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 U U)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(neg.f64 (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)) #s(literal 1 binary64)))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (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 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))))
(/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) J))
(/.f64 (*.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) #s(literal 1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) #s(literal 1 binary64)) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) J))
(/.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) #s(literal -1 binary64)) (*.f64 J (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (neg.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (*.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) J)
(/.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) #s(literal 1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U (/.f64 J U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 U (/.f64 J U)) (/.f64 #s(literal -1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 U (/.f64 J U)) (*.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 U (/.f64 J U)) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 U (/.f64 J U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/4 binary64))
(*.f64 (*.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 U (/.f64 J U)) #s(literal 1 binary64)) (/.f64 #s(literal -1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) 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 #s(literal -1/4 binary64) (*.f64 U U))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) J))

simplify322.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
5272×*-lowering-*.f32
5272×*-lowering-*.f64
2154×+-lowering-+.f64
2154×+-lowering-+.f32
2100×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04345056
115324486
264334405
080544405
Stop Event
1×iter limit
1×node limit
Counts
348 → 348
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)
(* -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 (* U (cos (* 1/2 K))))
(+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) U)) (* -1 (* U (cos (* 1/2 K)))))
(+ (* -1 (* U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -2 (/ (cos (* 1/2 K)) U)) (* 2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 3))))))
(+ (* -1 (* U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -2 (/ (cos (* 1/2 K)) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 5))) (* 2 (/ (cos (* 1/2 K)) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2)))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (+ (* -1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (pow J 6))) (* 1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4)))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (* (pow U 4) (cos (* 1/2 K))) (pow J 4))) (+ (* 1/512 (/ (* (pow U 6) (cos (* 1/2 K))) (pow J 6))) (+ (* 1/4 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 2))) (* 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))))))) (* 1/4 (* (* J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -1/192 (* (* J (pow K 2)) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/4 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* 1/4 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -1/192 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/23040 (* (* J (pow K 2)) (sqrt (+ 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)))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 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)))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 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)))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 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)))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (* (pow U 2) (cos (* 1/2 K))) J)))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) J)) (* 1/64 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 3))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (cos (* 1/2 K)) J)) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (cos (* 1/2 K))) (pow J 5))) (* 1/64 (/ (cos (* 1/2 K)) (pow J 3))))))))
(* -1 (* U (cos (* 1/2 K))))
(* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (* -1 (cos (* 1/2 K)))))
(* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4))))))
(* U (+ (* -4 (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)))))))
(* U (cos (* 1/2 K)))
(* -1 (* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (* -1 (cos (* 1/2 K))))))
(* -1 (* U (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4)))))))
(* -1 (* U (+ (* -4 (/ (* (pow J 6) (cos (* 1/2 K))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (cos (* 1/2 K))) (pow U 2))) (+ (* -1 (cos (* 1/2 K))) (* 2 (/ (* (pow J 4) (cos (* 1/2 K))) (pow U 4))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
1
(+ 1 (* -1/8 (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) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 J)))))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))
(+ (* -2 J) (+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (+ (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))) (* (pow K 2) (+ (* 1/23040 J) (* 1/4 (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/ (+ (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/ (+ (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/ (+ (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(* -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)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
1
(+ 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)))
(* 1/2 (/ 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))
(/ (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) 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) 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) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) J))
(+ (* -1/4 (/ (pow U 2) J)) (* -1/32 (/ (* (pow K 2) (pow U 2)) J)))
(+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 (* (pow K 2) (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))))
(+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* (pow K 2) (+ (* 1/4 (* (pow K 2) (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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 K (*.f64 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 #s(literal -4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 6 binary64)) (/.f64 (*.f64 J J) (pow.f64 U #s(literal 5 binary64))))) (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 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 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 J J)))))
(* 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 (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 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 J J))) (/.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 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal -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 -1/4 binary64) (*.f64 U U)) (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 J J))) (/.f64 (*.f64 #s(literal -1/512 binary64) (/.f64 (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 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (*.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 (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) (/.f64 (*.f64 #s(literal -1/64 binary64) (/.f64 (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)))) (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))))))))
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U
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(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (-.f64 (/.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) (/.f64 (/.f64 #s(literal 1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (-.f64 (/.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) (/.f64 (/.f64 #s(literal 1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (-.f64 (/.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) (/.f64 (/.f64 #s(literal 1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (-.f64 (/.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) (/.f64 (/.f64 #s(literal 1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (-.f64 (/.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) (/.f64 (/.f64 #s(literal 1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (-.f64 (/.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 U U)) (/.f64 (/.f64 #s(literal 1/4 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 K (*.f64 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 (*.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 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))))
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) J))
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)
(+ (* -1/4 (/ (pow U 2) J)) (* -1/32 (/ (* (pow K 2) (pow U 2)) J)))
(+.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 (*.f64 K K) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/32 binary64)) J)))
(+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* 1/4 (* (pow K 2) (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))))
(+.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal -1/32 binary64)) J) (*.f64 K (*.f64 K (*.f64 (/.f64 (*.f64 U U) J) #s(literal -5/1536 binary64)))))))
(+ (* -1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/32 (/ (pow U 2) J)) (* (pow K 2) (+ (* 1/4 (* (pow K 2) (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))) (* 1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))
(+.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 (*.f64 K K) (+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal -1/32 binary64)) J) (*.f64 (*.f64 (*.f64 K K) #s(literal 1/4 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal -5/384 binary64)) J) (*.f64 K (*.f64 K (+.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -5/3072 binary64)) (*.f64 (/.f64 (*.f64 U U) J) #s(literal 7/23040 binary64))))))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))

eval163.0ms (1.4%)

Compiler

Compiled 27372 to 2107 computations (92.3% saved)

prune179.0ms (1.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1080121092
Fresh224
Picked325
Done000
Total1085161101
Accuracy
100.0%
Counts
1101 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
52.1%
(/.f64 (+.f64 (*.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 (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))))
56.1%
(/.f64 (+.f64 (*.f64 (neg.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 (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))))
31.9%
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
55.2%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
▶55.1%
(/.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)))
34.7%
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) U)
▶56.3%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
37.1%
(-.f64 #s(literal 0 binary64) U)
51.5%
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
▶28.0%
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
27.4%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
▶41.2%
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64)) (*.f64 J #s(literal -2 binary64)))
55.7%
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
✓55.2%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
▶29.7%
(*.f64 #s(literal -2 binary64) J)
✓13.0%
U
Compiler

Compiled 567 to 370 computations (34.7% saved)

simplify158.0ms (1.4%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64)) (*.f64 J #s(literal -2 binary64)))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))))
✓cost-diff256
(*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))
✓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)))
✓cost-diff0
(*.f64 #s(literal -1/4 binary64) (*.f64 U U))
✓cost-diff0
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(/.f64 K #s(literal 2 binary64))
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
✓cost-diff0
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Rules
2710×fma-define
2344×fma-lowering-fma.f32
2344×fma-lowering-fma.f64
1700×fnmadd-define
1552×*-lowering-*.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
034218
177210
2159198
3425186
41207186
52866186
64267186
76384186
08182186
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (* (cos (/ K 2)) (* -2 J)) (/ (* (/ U (/ J U)) 1/4) (cos (/ K 2))))
(* (cos (/ K 2)) (* -2 J))
(cos (/ K 2))
(/ K 2)
K
2
(* -2 J)
-2
J
(/ (* (/ U (/ J U)) 1/4) (cos (/ K 2)))
(* (/ U (/ J U)) 1/4)
(/ U (/ J U))
U
(/ J U)
1/4
(* -2 J)
-2
J
(+ (* -2 J) (/ (* -1/4 (* U U)) J))
(* -2 J)
-2
J
(/ (* -1/4 (* U U)) J)
(* -1/4 (* U U))
-1/4
(* U U)
U
(/ 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
(* (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2) (* J -2))
(pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2)
(/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2))))))
1
(+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))
1/2
(* 1/2 (cos (* 2 (/ K 2))))
(cos (* 2 (/ K 2)))
(* 2 (/ K 2))
2
(/ K 2)
K
-1/2
(* J -2)
J
-2
Outputs
(- (* (cos (/ K 2)) (* -2 J)) (/ (* (/ U (/ J U)) 1/4) (cos (/ K 2))))
(+.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(* (cos (/ K 2)) (* -2 J))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 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)
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(/ (* (/ U (/ J U)) 1/4) (cos (/ K 2)))
(/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(* (/ U (/ J U)) 1/4)
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 U U)) J)
(/ U (/ J U))
(/.f64 U (/.f64 J U))
U
(/ J U)
(/.f64 J U)
1/4
#s(literal 1/4 binary64)
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(+ (* -2 J) (/ (* -1/4 (* U U)) J))
(+.f64 (/.f64 J #s(literal -1/2 binary64)) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(/ (* -1/4 (* U U)) J)
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)
(* -1/4 (* U U))
(*.f64 #s(literal -1/4 binary64) (*.f64 U U))
-1/4
#s(literal -1/4 binary64)
(* U U)
(*.f64 U U)
U
(/ 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
(* (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2) (* J -2))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K))) #s(literal -1/2 binary64)) (/.f64 #s(literal -1/2 binary64) J))
(pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2)
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K))) #s(literal -1/2 binary64))
(/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2))))))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
1
#s(literal 1 binary64)
(+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
1/2
#s(literal 1/2 binary64)
(* 1/2 (cos (* 2 (/ K 2))))
(*.f64 #s(literal 1/2 binary64) (cos.f64 K))
(cos (* 2 (/ K 2)))
(cos.f64 K)
(* 2 (/ K 2))
K
2
#s(literal 2 binary64)
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
-1/2
#s(literal -1/2 binary64)
(* J -2)
(/.f64 J #s(literal -1/2 binary64))
J
-2
#s(literal -2 binary64)

localize228.0ms (2%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))))
✓accuracy99.8%
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64)) (*.f64 J #s(literal -2 binary64)))
✓accuracy99.5%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.7%
(/.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)))
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
✓accuracy100.0%
(*.f64 #s(literal -1/4 binary64) (*.f64 U U))
✓accuracy89.7%
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy99.8%
(/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.8%
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
✓accuracy99.7%
(/.f64 U (/.f64 J U))
Results
170.0ms256×0valid
Compiler

Compiled 243 to 35 computations (85.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-div: 15.0ms (28.6% of total)
ival-mult: 14.0ms (26.7% of total)
ival-cos: 12.0ms (22.9% of total)
ival-pow: 7.0ms (13.3% of total)
ival-add: 2.0ms (3.8% of total)
ival-sub: 1.0ms (1.9% of total)
const: 1.0ms (1.9% of total)
backward-pass: 0.0ms (0% of total)

series24.0ms (0.2%)

Counts
18 → 348
Calls
Call 1
Inputs
#<alt (- (* (cos (/ K 2)) (* -2 J)) (/ (* (/ U (/ J U)) 1/4) (cos (/ K 2))))>
#<alt (* (cos (/ K 2)) (* -2 J))>
#<alt (cos (/ K 2))>
#<alt (/ K 2)>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (/ (* -1/4 (* U U)) J))>
#<alt (/ (* -1/4 (* U U)) J)>
#<alt (* -1/4 (* U U))>
#<alt (/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))>
#<alt (/ (/ 1 (cos (/ K 2))) (* -2 J))>
#<alt (/ 1 (cos (/ K 2)))>
#<alt (* 2 (/ K 2))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2))))))>
#<alt (* (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2) (* J -2))>
#<alt (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2)>
#<alt (/ U (/ J U))>
#<alt (/ (* (/ U (/ J U)) 1/4) (cos (/ K 2)))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))>
Outputs
#<alt (- (* -2 J) (* 1/4 (/ (pow U 2) J)))>
#<alt (- (+ (* -2 J) (* (pow K 2) (- (* 1/4 J) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))>
#<alt (- (+ (* -2 J) (* (pow K 2) (- (+ (* 1/4 J) (* (pow K 2) (- (* -1/192 J) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))>
#<alt (- (+ (* -2 J) (* (pow K 2) (- (+ (* 1/4 J) (* (pow K 2) (- (+ (* -1/192 J) (* (pow K 2) (- (* 1/23040 J) (* -1/4 (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))>
#<alt (- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 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)))) (* 1/4 (/ (pow U 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)))) (* 1/4 (/ (pow U 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)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)>
#<alt (/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)>
#<alt (/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)>
#<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)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<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 (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (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 (* -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)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))>
#<alt (* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* 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 (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 (* -1/4 (/ (pow U 2) J))>
#<alt (/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)>
#<alt (/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)>
#<alt (/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)>
#<alt (* -2 J)>
#<alt (* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))>
#<alt (* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))>
#<alt (* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))>
#<alt (* -2 J)>
#<alt (* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))>
#<alt (* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))>
#<alt (* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* -1/4 (/ (pow U 2) J)))>
#<alt (+ (* -2 J) (* -1/4 (/ (pow U 2) J)))>
#<alt (+ (* -2 J) (* -1/4 (/ (pow U 2) J)))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))>
#<alt (* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))>
#<alt (* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))>
#<alt (* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))>
#<alt (* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<alt (* -1/4 (pow U 2))>
#<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 K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt K>
#<alt 1>
#<alt (+ 1 (* 1/4 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (+ 1/4 (* 1/24 (pow K 2)))))>
#<alt (+ 1 (* (pow K 2) (+ 1/4 (* (pow K 2) (+ 1/24 (* 17/2880 (pow K 2)))))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ 1 (+ 1/2 (* 1/2 (cos 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 (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))>
#<alt (* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos 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 (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (sqrt (+ 1/2 (* 1/2 (cos K))))>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) J))>
#<alt (+ (* 1/32 (/ (* (pow K 2) (pow U 2)) J)) (* 1/4 (/ (pow U 2) J)))>
#<alt (+ (* 1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))) (* 1/32 (/ (pow U 2) J)))))>
#<alt (+ (* 1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* 1/32 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
Calls

87 calls:

TimeVariablePointExpression
4.0ms
U
@inf
(/ (* (/ U (/ J U)) 1/4) (cos (/ K 2)))
1.0ms
J
@0
(* (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2) (* J -2))
1.0ms
K
@-inf
(/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2))))))
1.0ms
K
@inf
(* (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2) (* J -2))
1.0ms
K
@inf
(/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2))))))

rewrite393.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
3758×*-lowering-*.f32
3758×*-lowering-*.f64
2738×/-lowering-/.f32
2738×/-lowering-/.f64
2456×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
034132
1183117
21432116
08415116
Stop Event
1×iter limit
1×node limit
Counts
18 → 858
Calls
Call 1
Inputs
(- (* (cos (/ K 2)) (* -2 J)) (/ (* (/ U (/ J U)) 1/4) (cos (/ K 2))))
(* (cos (/ K 2)) (* -2 J))
(cos (/ K 2))
(/ K 2)
(* -2 J)
(+ (* -2 J) (/ (* -1/4 (* U U)) J))
(/ (* -1/4 (* U U)) J)
(* -1/4 (* U U))
(/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))
(/ (/ 1 (cos (/ K 2))) (* -2 J))
(/ 1 (cos (/ K 2)))
(* 2 (/ K 2))
(/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2))))))
(* (pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2) (* J -2))
(pow (/ 1 (+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))) -1/2)
(/ U (/ J U))
(/ (* (/ U (/ J U)) 1/4) (cos (/ K 2)))
(+ 1/2 (* 1/2 (cos (* 2 (/ K 2)))))
Outputs
(+.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(+.f64 (+.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (+.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 U (/.f64 J U))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 J (*.f64 U U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(+.f64 (+.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 J (*.f64 U U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(+.f64 (+.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (fma.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 J (*.f64 U U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(+.f64 (+.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (fma.f64 (neg.f64 (/.f64 U (/.f64 J U))) (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 J (*.f64 U U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(+.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) 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 (fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) (neg.f64 (*.f64 (*.f64 (/.f64 U J) (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) U))) (fma.f64 (neg.f64 (*.f64 (/.f64 U J) (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) U (*.f64 (*.f64 (/.f64 U J) (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) U)))
(+.f64 (fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) (neg.f64 (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1/4 binary64)))) (fma.f64 (neg.f64 (*.f64 (/.f64 U (/.f64 J U)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal 1/4 binary64) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1/4 binary64))))
(+.f64 (fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) (neg.f64 (*.f64 (/.f64 (/.f64 U (/.f64 J U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1/4 binary64)))) (fma.f64 (neg.f64 (/.f64 (/.f64 U (/.f64 J U)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1/4 binary64) (*.f64 (/.f64 (/.f64 U (/.f64 J U)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1/4 binary64))))
(+.f64 (fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)))) (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))))
(+.f64 (fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) (neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 J (*.f64 U U)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))) (fma.f64 (/.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 J (*.f64 U U)) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) (neg.f64 (*.f64 (*.f64 U (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 U J)))) (fma.f64 (neg.f64 (*.f64 U (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (/.f64 U J) (*.f64 (*.f64 U (/.f64 #s(literal 1/4 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 U J))))
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(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 3 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64))))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 3 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64)))))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64)))))))) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64))))))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64))))))) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(/.f64 (+.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64))))))))) (pow.f64 (sin.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 4 binary64)))
(pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64))))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))) #s(literal -1 binary64))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64))))) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))) #s(literal 1/2 binary64))))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (*.f64 K #s(literal 1 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 K #s(literal 1 binary64)))))))
(*.f64 (+.f64 (cos.f64 (*.f64 K #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64))

simplify460.0ms (4%)

Algorithm
1×egg-herbie
Rules
4242×*-lowering-*.f32
4242×*-lowering-*.f64
3252×+-lowering-+.f64
3252×+-lowering-+.f32
1542×fnmadd-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02273291
17232934
225172893
360902893
081362893
Stop Event
1×iter limit
1×node limit
Counts
348 → 348
Calls
Call 1
Inputs
(- (* -2 J) (* 1/4 (/ (pow U 2) J)))
(- (+ (* -2 J) (* (pow K 2) (- (* 1/4 J) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))
(- (+ (* -2 J) (* (pow K 2) (- (+ (* 1/4 J) (* (pow K 2) (- (* -1/192 J) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))
(- (+ (* -2 J) (* (pow K 2) (- (+ (* 1/4 J) (* (pow K 2) (- (+ (* -1/192 J) (* (pow K 2) (- (* 1/23040 J) (* -1/4 (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(* -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)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(* -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)
(* -1/4 (/ (pow U 2) J))
(/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)
(/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)
(/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)
(* -2 J)
(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
(* -2 J)
(* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))
(* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))
(* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))
(* -2 J)
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(* -1/4 (/ (pow U 2) J))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* -1/4 (/ (pow U 2) J))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
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(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
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(* -1/4 (pow U 2))
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(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
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(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
(* -1/4 (pow U 2))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -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)))
(+ 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)))
K
K
K
K
K
K
K
K
K
K
K
K
1
(+ 1 (* 1/4 (pow K 2)))
(+ 1 (* (pow K 2) (+ 1/4 (* 1/24 (pow K 2)))))
(+ 1 (* (pow K 2) (+ 1/4 (* (pow K 2) (+ 1/24 (* 17/2880 (pow K 2)))))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos K))))
(/ 1 (+ 1/2 (* 1/2 (cos 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 (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
(* -2 (* J (sqrt (+ 1/2 (* 1/2 (cos K))))))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(sqrt (+ 1/2 (* 1/2 (cos K))))
(/ (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) 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) 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) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) J))
(+ (* 1/32 (/ (* (pow K 2) (pow U 2)) J)) (* 1/4 (/ (pow U 2) J)))
(+ (* 1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))) (* 1/32 (/ (pow U 2) J)))))
(+ (* 1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* 1/32 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
Outputs
(- (* -2 J) (* 1/4 (/ (pow U 2) J)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)))
(- (+ (* -2 J) (* (pow K 2) (- (* 1/4 J) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))
(+.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))) (*.f64 (*.f64 K K) (+.f64 (*.f64 J #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/32 binary64)) J))))
(- (+ (* -2 J) (* (pow K 2) (- (+ (* 1/4 J) (* (pow K 2) (- (* -1/192 J) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 (*.f64 (*.f64 K K) (+.f64 (+.f64 (*.f64 J #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/32 binary64)) J)) (*.f64 (*.f64 K K) (+.f64 (*.f64 J #s(literal -1/192 binary64)) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -5/1536 binary64)))))) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))
(- (+ (* -2 J) (* (pow K 2) (- (+ (* 1/4 J) (* (pow K 2) (- (+ (* -1/192 J) (* (pow K 2) (- (* 1/23040 J) (* -1/4 (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))))) (* 1/32 (/ (pow U 2) J))))) (* 1/4 (/ (pow U 2) J)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (+.f64 (*.f64 (*.f64 K K) (+.f64 (*.f64 J #s(literal 1/4 binary64)) (+.f64 (*.f64 (*.f64 K K) (+.f64 (+.f64 (*.f64 J #s(literal -1/192 binary64)) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -5/1536 binary64))) (*.f64 (*.f64 K K) (+.f64 (*.f64 J #s(literal 1/23040 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -61/46080 binary64))))))) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/32 binary64)) J)))) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) (cos (* 1/2 K))))) J)
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 (*.f64 U U) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) 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)))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) J)))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U)) (/.f64 (/.f64 #s(literal -1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U)) (/.f64 (/.f64 #s(literal -1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U)) (/.f64 (/.f64 #s(literal -1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/4 binary64)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U)) (/.f64 (/.f64 #s(literal -1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U)) (/.f64 (/.f64 #s(literal -1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 (* J (cos (* 1/2 K)))))))
(*.f64 (*.f64 U U) (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U)) (/.f64 (/.f64 #s(literal -1/4 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))))
(* -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 #s(literal -1/192 binary64) (*.f64 K K))))))
(+ (* -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 (*.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
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
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1
#s(literal 1 binary64)
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(sqrt (+ 1/2 (* 1/2 (cos K))))
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(/ (pow U 2) J)
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(/ (pow U 2) J)
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* 1/4 (/ (pow U 2) J))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J))
(+ (* 1/32 (/ (* (pow K 2) (pow U 2)) J)) (* 1/4 (/ (pow U 2) J)))
(*.f64 (/.f64 (*.f64 U U) J) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/32 binary64) (*.f64 K K))))
(+ (* 1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J))))) (* 1/32 (/ (pow U 2) J)))))
(+.f64 (*.f64 (*.f64 K K) (*.f64 (*.f64 K K) (*.f64 (/.f64 (*.f64 U U) J) #s(literal 5/1536 binary64)))) (*.f64 (/.f64 (*.f64 U U) J) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/32 binary64) (*.f64 K K)))))
(+ (* 1/4 (/ (pow U 2) J)) (* (pow K 2) (+ (* 1/32 (/ (pow U 2) J)) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/46080 (/ (pow U 2) J)) (+ (* 1/3072 (/ (pow U 2) J)) (* 1/8 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))) (* -1/4 (+ (* -1/64 (/ (pow U 2) J)) (* 1/384 (/ (pow U 2) J)))))))))
(+.f64 (*.f64 (+.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal 5/1536 binary64)) (*.f64 (*.f64 (/.f64 (*.f64 U U) J) #s(literal -61/46080 binary64)) (*.f64 (*.f64 K K) #s(literal -1/4 binary64)))) (*.f64 (*.f64 K K) (*.f64 K K))) (*.f64 (/.f64 (*.f64 U U) J) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/32 binary64) (*.f64 K K)))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
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(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* 1/4 (/ (pow U 2) (* J (cos (* 1/2 K)))))
(/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/4 binary64)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/4 binary64) (*.f64 K (*.f64 K #s(literal 1/48 binary64)))))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 K K) #s(literal -1/1440 binary64)))))))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
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eval233.0ms (2%)

Compiler

Compiled 37158 to 2996 computations (91.9% saved)

prune232.0ms (2%)

Pruning

21 alts after pruning (16 fresh and 5 done)

PrunedKeptTotal
New1425121437
Fresh549
Picked235
Done022
Total1432211453
Accuracy
100.0%
Counts
1453 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
9.6%
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
55.2%
(/.f64 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
55.1%
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
✓55.1%
(/.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)))
55.1%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
15.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
40.9%
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))) (*.f64 #s(literal -2 binary64) J)))
29.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
34.7%
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) U)
✓56.3%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
▶51.5%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
▶37.1%
(-.f64 #s(literal 0 binary64) U)
▶30.4%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
27.4%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
▶9.6%
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
14.5%
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
▶55.7%
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
✓55.2%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
27.4%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
✓29.7%
(*.f64 #s(literal -2 binary64) J)
✓13.0%
U
Compiler

Compiled 716 to 474 computations (33.8% saved)

simplify206.0ms (1.8%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 K #s(literal 2 binary64))
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
✓cost-diff0
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
✓cost-diff0
(*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J)))
✓cost-diff0
(+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64)))
✓cost-diff128
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
✓cost-diff256
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))
✓cost-diff0
(/.f64 U (/.f64 J U))
✓cost-diff0
(*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
✓cost-diff0
(-.f64 #s(literal 0 binary64) U)
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
✓cost-diff0
(hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J)))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
Rules
4116×*-lowering-*.f32
4116×*-lowering-*.f64
2012×/-lowering-/.f32
2012×/-lowering-/.f64
1246×fma-lowering-fma.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
049316
1136299
2372299
31193283
44333279
08275279
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (* -2 J) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
(* -2 J)
-2
J
(sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J)))))
1
(* 1/2 (/ U J))
1/2
(/ U J)
U
(- 0 U)
0
U
(+ (* -2 J) (* (/ U (/ J U)) -1/4))
(* -2 J)
-2
J
(* (/ U (/ J U)) -1/4)
(/ U (/ J U))
U
(/ J U)
-1/4
(* (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)) (/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))))
(+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64))
(* -8 (* J (* J J)))
-8
(* J (* J J))
J
(* J J)
(* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)
(* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U))))
(/ U (/ J U))
U
(/ J U)
(* (/ U (/ J U)) (/ U (/ J U)))
-1/64
(/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))))
1
(+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))
(* (* J J) 4)
4
(/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))
(- (/ (* -1/4 (* U U)) J) (* -2 J))
(/ (* -1/4 (* U U)) J)
(* -1/4 (* U U))
-1/4
(* U U)
(* -2 J)
-2
(/ J (* -1/4 (* U U)))
(- (* (cos (/ K 2)) (* -2 J)) (* 1/4 (/ (* U U) J)))
(* (cos (/ K 2)) (* -2 J))
(cos (/ K 2))
(/ K 2)
K
2
(* -2 J)
-2
J
(* 1/4 (/ (* U U) J))
1/4
(/ (* U U) J)
(* U U)
U
Outputs
(* (* -2 J) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
(*.f64 #s(literal -2 binary64) (*.f64 J (hypot.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) U) J))))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J)))))
(hypot.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) U) J))
1
#s(literal 1 binary64)
(* 1/2 (/ U J))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
1/2
#s(literal 1/2 binary64)
(/ U J)
(/.f64 U J)
U
(- 0 U)
(-.f64 #s(literal 0 binary64) U)
0
#s(literal 0 binary64)
U
(+ (* -2 J) (* (/ U (/ J U)) -1/4))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(* (/ U (/ J U)) -1/4)
(/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) J)
(/ U (/ J U))
(/.f64 (*.f64 U U) J)
U
(/ J U)
(/.f64 J U)
-1/4
#s(literal -1/4 binary64)
(* (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)) (/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))))
(/.f64 (+.f64 (*.f64 J (*.f64 #s(literal -8 binary64) (*.f64 J J))) (/.f64 (*.f64 (*.f64 U U) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/64 binary64))) (/.f64 (/.f64 (*.f64 J J) U) U))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 U (*.f64 U (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 U U) J) J) #s(literal 1/16 binary64)) #s(literal -1/2 binary64))))))
(+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64))
(+.f64 (*.f64 J (*.f64 #s(literal -8 binary64) (*.f64 J J))) (/.f64 (*.f64 (*.f64 U U) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/64 binary64))) (/.f64 (/.f64 (*.f64 J J) U) U)))
(* -8 (* J (* J J)))
(*.f64 J (*.f64 #s(literal -8 binary64) (*.f64 J J)))
-8
#s(literal -8 binary64)
(* J (* J J))
(*.f64 J (*.f64 J J))
J
(* J J)
(*.f64 J J)
(* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)
(/.f64 (*.f64 (*.f64 U U) (*.f64 (/.f64 (*.f64 U U) J) #s(literal -1/64 binary64))) (/.f64 (/.f64 (*.f64 J J) U) U))
(* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U))))
(/.f64 (*.f64 U (*.f64 U (/.f64 (*.f64 U U) J))) (/.f64 (/.f64 (*.f64 J J) U) U))
(/ U (/ J U))
(/.f64 (*.f64 U U) J)
U
(/ J U)
(/.f64 J U)
(* (/ U (/ J U)) (/ U (/ J U)))
(/.f64 (/.f64 (*.f64 U U) J) (/.f64 J (*.f64 U U)))
-1/64
#s(literal -1/64 binary64)
(/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 U (*.f64 U (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 U U) J) J) #s(literal 1/16 binary64)) #s(literal -1/2 binary64))))))
1
#s(literal 1 binary64)
(+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))
(+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 U (*.f64 U (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 U U) J) J) #s(literal 1/16 binary64)) #s(literal -1/2 binary64)))))
(* (* J J) 4)
(*.f64 (*.f64 J J) #s(literal 4 binary64))
4
#s(literal 4 binary64)
(/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))
(*.f64 U (*.f64 U (+.f64 (*.f64 (/.f64 (/.f64 (*.f64 U U) J) J) #s(literal 1/16 binary64)) #s(literal -1/2 binary64))))
(- (/ (* -1/4 (* U U)) J) (* -2 J))
(+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) J) (*.f64 J #s(literal 2 binary64)))
(/ (* -1/4 (* U U)) J)
(/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) J)
(* -1/4 (* U U))
(*.f64 U (*.f64 U #s(literal -1/4 binary64)))
-1/4
#s(literal -1/4 binary64)
(* U U)
(*.f64 U U)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
(/ J (* -1/4 (* U U)))
(/.f64 (/.f64 J (*.f64 U U)) #s(literal -1/4 binary64))
(- (* (cos (/ K 2)) (* -2 J)) (* 1/4 (/ (* U U) J)))
(+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) J) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(* (cos (/ K 2)) (* -2 J))
(*.f64 (*.f64 #s(literal -2 binary64) J) (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 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(* 1/4 (/ (* U U) J))
(/.f64 (*.f64 U (*.f64 U #s(literal 1/4 binary64))) J)
1/4
#s(literal 1/4 binary64)
(/ (* U U) J)
(/.f64 (*.f64 U U) J)
(* U U)
(*.f64 U U)
U

localize297.0ms (2.6%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy100.0%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
✓accuracy99.8%
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
✓accuracy89.7%
(/.f64 (*.f64 U U) J)
✓accuracy93.1%
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))
✓accuracy89.7%
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J)
✓accuracy89.1%
(/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))
✓accuracy25.9%
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
✓accuracy100.0%
(*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64))
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
✓accuracy99.7%
(/.f64 U (/.f64 J U))
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) U)
✓accuracy100.0%
(/.f64 U J)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
✓accuracy90.1%
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
Results
199.0ms256×0valid
Compiler

Compiled 403 to 47 computations (88.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 74.0ms
ival-mult: 31.0ms (41.9% of total)
ival-div: 15.0ms (20.3% of total)
compiled-spec: 7.0ms (9.5% of total)
ival-add: 6.0ms (8.1% of total)
ival-cos: 6.0ms (8.1% of total)
ival-sub: 5.0ms (6.8% of total)
ival-sqrt: 2.0ms (2.7% of total)
const: 1.0ms (1.4% of total)
backward-pass: 0.0ms (0% of total)

series80.0ms (0.7%)

Counts
20 → 432
Calls
Call 1
Inputs
#<alt (* (* -2 J) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))>
#<alt (* -2 J)>
#<alt (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J)))))>
#<alt (* 1/2 (/ U J))>
#<alt (- 0 U)>
#<alt (+ (* -2 J) (* (/ U (/ J U)) -1/4))>
#<alt (* (/ U (/ J U)) -1/4)>
#<alt (/ U (/ J U))>
#<alt (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))>
#<alt (* (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)) (/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))))>
#<alt (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64))>
#<alt (* -8 (* J (* J J)))>
#<alt (- (* (cos (/ K 2)) (* -2 J)) (* 1/4 (/ (* U U) J)))>
#<alt (* (cos (/ K 2)) (* -2 J))>
#<alt (cos (/ K 2))>
#<alt (/ K 2)>
#<alt (/ U J)>
#<alt (/ J (* -1/4 (* U U)))>
#<alt (/ (* -1/4 (* U U)) J)>
#<alt (/ (* U U) J)>
Outputs
#<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 (* -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)))>
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#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (* -1/4 (/ (pow U 2) J))>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
#<alt (/ (pow U 2) J)>
Calls

108 calls:

TimeVariablePointExpression
38.0ms
U
@inf
(+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64))
16.0ms
U
@0
(/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))
2.0ms
J
@0
(/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))
2.0ms
J
@0
(* (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)) (/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))))
1.0ms
U
@0
(* (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)) (/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))))

rewrite456.0ms (3.9%)

Algorithm
1×batch-egg-rewrite
Rules
6132×*-lowering-*.f32
6132×*-lowering-*.f64
3646×/-lowering-/.f32
3646×/-lowering-/.f64
2312×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
049139
1287138
22877138
010785138
Stop Event
1×iter limit
1×node limit
Counts
20 → 643
Calls
Call 1
Inputs
(* (* -2 J) (sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J))))))
(* -2 J)
(sqrt (+ (* 1 1) (* (* 1/2 (/ U J)) (* 1/2 (/ U J)))))
(* 1/2 (/ U J))
(- 0 U)
(+ (* -2 J) (* (/ U (/ J U)) -1/4))
(* (/ U (/ J U)) -1/4)
(/ U (/ J U))
(/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U))))
(* (+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64)) (/ 1 (+ (* (* J J) 4) (/ (- (/ (* -1/4 (* U U)) J) (* -2 J)) (/ J (* -1/4 (* U U)))))))
(+ (* -8 (* J (* J J))) (* (* (/ U (/ J U)) (* (/ U (/ J U)) (/ U (/ J U)))) -1/64))
(* -8 (* J (* J J)))
(- (* (cos (/ K 2)) (* -2 J)) (* 1/4 (/ (* U U) J)))
(* (cos (/ K 2)) (* -2 J))
(cos (/ K 2))
(/ K 2)
(/ U J)
(/ J (* -1/4 (* U U)))
(/ (* -1/4 (* U U)) J)
(/ (* U U) J)
Outputs
(*.f64 #s(literal -2 binary64) (*.f64 J (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U)))))
(*.f64 J (*.f64 #s(literal -2 binary64) (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U))) (*.f64 #s(literal -2 binary64) J))
(*.f64 (*.f64 J (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U)))) #s(literal -2 binary64))
(*.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U))) #s(literal -2 binary64)) J)
(*.f64 #s(literal -2 binary64) J)
(*.f64 J #s(literal -2 binary64))
(exp.f64 (*.f64 (log1p.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))) #s(literal 1/2 binary64)))
(hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 J U)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) (-.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (*.f64 U (*.f64 U U)) (*.f64 J (*.f64 J J))) #s(literal 1/64 binary64)) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 U (*.f64 U U))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U J) (/.f64 J U)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U))))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 U (*.f64 U U))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) (-.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) #s(literal 1 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 U (*.f64 U U))))) (sqrt.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U J) (/.f64 J U)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U J) (/.f64 J U))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (*.f64 U (*.f64 U U)) (*.f64 J (*.f64 J J))) #s(literal 1/64 binary64)) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 U (*.f64 U U))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) (-.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U))))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U J) (/.f64 J U)))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U)))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) #s(literal 1 binary64))))
(pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)))) #s(literal 1/2 binary64))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 U (*.f64 U U))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) (-.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 U (*.f64 U U))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) (-.f64 (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U)) #s(literal 1 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U J) (/.f64 J U))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (/.f64 U J) (/.f64 J U)) (/.f64 (/.f64 U J) (/.f64 J U)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 (/.f64 U J) (/.f64 J U)))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 U J) #s(literal 1/4 binary64)) (/.f64 J U))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 J U))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 J (*.f64 #s(literal 1/2 binary64) U)))
(/.f64 #s(literal 1/2 binary64) (/.f64 J U))
(/.f64 (*.f64 #s(literal 1/2 binary64) U) J)
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) U)) (-.f64 #s(literal 0 binary64) J))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) U)) (-.f64 #s(literal 0 binary64) J))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) J))
(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 J U)) #s(literal 1 binary64))
(pow.f64 (/.f64 J (*.f64 #s(literal 1/2 binary64) U)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 U J))
(*.f64 U (*.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 1/2 binary64)))
(*.f64 U (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 U J) #s(literal 1/2 binary64))
(*.f64 (*.f64 #s(literal 1/2 binary64) U) (/.f64 #s(literal 1 binary64) J))
(*.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) U) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal 1 binary64)))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) U))
(+.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) U)
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 U U)) U)
(-.f64 (/.f64 #s(literal 0 binary64) U) (/.f64 (*.f64 U U) U))
(neg.f64 U)
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 U U) (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U)))))
(/.f64 #s(literal 1 binary64) (/.f64 U (-.f64 #s(literal 0 binary64) (*.f64 U U))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) U)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) U)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (*.f64 U U))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 U U) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) U)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U))) (-.f64 #s(literal 0 binary64) U))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U)))) (-.f64 #s(literal 0 binary64) (*.f64 U U)))
(pow.f64 (/.f64 (*.f64 U U) (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U)))) #s(literal -1 binary64))
(pow.f64 (/.f64 U (-.f64 #s(literal 0 binary64) (*.f64 U U))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) U)
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (/.f64 #s(literal 1 binary64) U))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U (*.f64 U U))) (/.f64 #s(literal 1 binary64) (*.f64 U U)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))))
(+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 #s(literal -2 binary64) J))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (/.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (/.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U)))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J)))))
(+.f64 (*.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64)))))) (*.f64 (/.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64)))))))
(+.f64 (*.f64 (/.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 J (*.f64 J J)) (*.f64 (*.f64 U (*.f64 U U)) (*.f64 U (*.f64 U U))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64)))))) (*.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))) (*.f64 J #s(literal 2 binary64))) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))) (*.f64 J (*.f64 J #s(literal 4 binary64)))))))
(-.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U))))
(-.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (-.f64 #s(literal 0 binary64) J)))
(-.f64 (/.f64 (*.f64 J (*.f64 J #s(literal 4 binary64))) (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U))))) (/.f64 (*.f64 (/.f64 (/.f64 U (/.f64 J U)) (/.f64 J (*.f64 U U))) #s(literal 1/16 binary64)) (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U))))))
(fma.f64 #s(literal -2 binary64) J (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))))
(fma.f64 J #s(literal -2 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 J (*.f64 U U))))
(fma.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64) (*.f64 #s(literal -2 binary64) J))
(fma.f64 #s(literal -1/4 binary64) (/.f64 U (/.f64 J U)) (*.f64 #s(literal -2 binary64) J))
(fma.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (/.f64 #s(literal 1 binary64) J) (*.f64 #s(literal -2 binary64) J))
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(*.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 U J)) U)
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(*.f64 (/.f64 (*.f64 U #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) J)) (-.f64 #s(literal 0 binary64) U))
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(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 U #s(literal -1/4 binary64))) #s(literal -1 binary64)) (/.f64 U J))
(exp.f64 (*.f64 (log.f64 (/.f64 J (*.f64 U U))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 U (/.f64 J U))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 J U))) (/.f64 U (-.f64 #s(literal 0 binary64) (/.f64 J U))))
(neg.f64 (/.f64 U (-.f64 #s(literal 0 binary64) (/.f64 J U))))
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(/.f64 (/.f64 U J) (/.f64 #s(literal 1 binary64) U))
(/.f64 (*.f64 U U) J)
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(*.f64 (/.f64 U J) U)
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(*.f64 (-.f64 #s(literal 0 binary64) U) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 J U))))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) J)))
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(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (*.f64 U U)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) J)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U (-.f64 #s(literal 0 binary64) J)) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) U) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 U #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 U J))

simplify280.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
4176×+-lowering-+.f64
4176×+-lowering-+.f32
3830×*-lowering-*.f32
3830×*-lowering-*.f64
1132×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03373915
110543500
237493432
086513432
Stop Event
1×iter limit
1×node limit
Counts
432 → 432
Calls
Call 1
Inputs
(* -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))))))))
(* -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)))
(* -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))
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(/ (+ (* 1/2 U) (* (pow J 2) (+ (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 5))) (/ 1 (pow U 3)))) (/ 1 U)))) J)
1
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1
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(* 1/2 (/ U J))
(* 1/2 (/ U J))
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(* 1/2 (/ U J))
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(* -1/4 (/ (pow U 2) J))
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(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
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(* -1/2 (pow U 2))
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(* (pow U 4) (- (* 1/16 (/ 1 (pow J 2))) (* 1/2 (/ 1 (pow U 2)))))
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(/ (+ (* -1/2 (* (pow J 2) (pow U 2))) (* 1/16 (pow U 4))) (pow J 2))
(/ (+ (* -1/2 (* (pow J 2) (pow U 2))) (* 1/16 (pow U 4))) (pow J 2))
(/ (+ (* -1/2 (* (pow J 2) (pow U 2))) (* 1/16 (pow U 4))) (pow J 2))
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(+ (* -1/2 (pow U 2)) (* 1/16 (/ (pow U 4) (pow J 2))))
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(* -1/2 (pow U 2))
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(+ (* -1/2 (pow U 2)) (* 1/16 (/ (pow U 4) (pow J 2))))
(+ (* -1/2 (pow U 2)) (* 1/16 (/ (pow U 4) (pow J 2))))
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(/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)
(/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)
(/ (+ (* -2 (pow J 2)) (* -1/4 (pow U 2))) J)
(* -2 J)
(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
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(* J (- (* -1/8 (/ (* (pow U 2) (+ (* -1/32 (pow U 4)) (* 1/32 (pow U 4)))) (pow J 6))) (+ 2 (+ (* -1/32 (/ (pow U 4) (pow J 4))) (+ (* 1/32 (/ (pow U 4) (pow J 4))) (* 1/4 (/ (pow U 2) (pow J 2))))))))
(* -2 J)
(* -1 (* J (+ 2 (* 1/4 (/ (pow U 2) (pow J 2))))))
(* -1 (* J (- (+ 2 (* -1 (/ (+ (* -1/32 (pow U 4)) (* 1/32 (pow U 4))) (pow J 4)))) (* -1/4 (/ (pow U 2) (pow J 2))))))
(* -1 (* J (- (+ 2 (* -1/8 (/ (* (pow U 2) (+ (* -1/32 (pow U 4)) (* 1/32 (pow U 4)))) (pow J 6)))) (+ (* -1/4 (/ (pow U 2) (pow J 2))) (+ (* -1/32 (/ (pow U 4) (pow J 4))) (* 1/32 (/ (pow U 4) (pow J 4))))))))
(* -2 J)
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 J) (* -1/4 (/ (pow U 2) J)))
(* -1/4 (/ (pow U 2) J))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -1 (/ (+ (* -16 (pow J 3)) (* 16 (pow J 3))) (pow U 4))) (+ (* 2 (/ J (pow U 2))) (* 1/4 (/ 1 J)))))
(* (pow U 2) (- (* -8 (/ (* (pow J 2) (+ (* -16 (pow J 3)) (* 16 (pow J 3)))) (pow U 6))) (+ (* -16 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ J (pow U 2))) (+ (* 16 (/ (pow J 3) (pow U 4))) (* 1/4 (/ 1 J)))))))
(* -1/4 (/ (pow U 2) J))
(* (pow U 2) (- (* -2 (/ J (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -1 (/ (+ (* -16 (pow J 3)) (* 16 (pow J 3))) (pow U 4))) (+ (* 2 (/ J (pow U 2))) (* 1/4 (/ 1 J)))))
(* (pow U 2) (- (* -8 (/ (* (pow J 2) (+ (* -16 (pow J 3)) (* 16 (pow J 3)))) (pow U 6))) (+ (* -16 (/ (pow J 3) (pow U 4))) (+ (* 2 (/ J (pow U 2))) (+ (* 16 (/ (pow J 3) (pow U 4))) (* 1/4 (/ 1 J)))))))
(* -1/64 (/ (pow U 6) (pow J 3)))
(/ (+ (* -8 (pow J 6)) (* -1/64 (pow U 6))) (pow J 3))
(/ (+ (* -8 (pow J 6)) (* -1/64 (pow U 6))) (pow J 3))
(/ (+ (* -8 (pow J 6)) (* -1/64 (pow U 6))) (pow J 3))
(* -8 (pow J 3))
(* (pow J 3) (- (* -1/64 (/ (pow U 6) (pow J 6))) 8))
(* (pow J 3) (- (* -1/64 (/ (pow U 6) (pow J 6))) 8))
(* (pow J 3) (- (* -1/64 (/ (pow U 6) (pow J 6))) 8))
(* -8 (pow J 3))
(* -1 (* (pow J 3) (+ 8 (* 1/64 (/ (pow U 6) (pow J 6))))))
(* -1 (* (pow J 3) (+ 8 (* 1/64 (/ (pow U 6) (pow J 6))))))
(* -1 (* (pow J 3) (+ 8 (* 1/64 (/ (pow U 6) (pow J 6))))))
(* -8 (pow J 3))
(+ (* -8 (pow J 3)) (* -1/64 (/ (pow U 6) (pow J 3))))
(+ (* -8 (pow J 3)) (* -1/64 (/ (pow U 6) (pow J 3))))
(+ (* -8 (pow J 3)) (* -1/64 (/ (pow U 6) (pow J 3))))
(* -1/64 (/ (pow U 6) (pow J 3)))
(* (pow U 6) (- (* -8 (/ (pow J 3) (pow U 6))) (* 1/64 (/ 1 (pow J 3)))))
(* (pow U 6) (- (* -8 (/ (pow J 3) (pow U 6))) (* 1/64 (/ 1 (pow J 3)))))
(* (pow U 6) (- (* -8 (/ (pow J 3) (pow U 6))) (* 1/64 (/ 1 (pow J 3)))))
(* -1/64 (/ (pow U 6) (pow J 3)))
(* (pow U 6) (- (* -8 (/ (pow J 3) (pow U 6))) (* 1/64 (/ 1 (pow J 3)))))
(* (pow U 6) (- (* -8 (/ (pow J 3) (pow U 6))) (* 1/64 (/ 1 (pow J 3)))))
(* (pow U 6) (- (* -8 (/ (pow J 3) (pow U 6))) (* 1/64 (/ 1 (pow J 3)))))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(* -8 (pow J 3))
(- (* -2 J) (* 1/4 (/ (pow U 2) J)))
(- (+ (* -2 J) (* 1/4 (* J (pow K 2)))) (* 1/4 (/ (pow U 2) J)))
(- (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J)))) (* 1/4 (/ (pow U 2) J)))
(- (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2)))))))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(- (* -2 (* J (cos (* 1/2 K)))) (* 1/4 (/ (pow U 2) J)))
(* -1/4 (/ (pow U 2) J))
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (pow U 2))) J)
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (pow U 2))) J)
(/ (- (* -2 (* (pow J 2) (cos (* 1/2 K)))) (* 1/4 (pow U 2))) J)
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (pow J 2)))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (pow J 2)))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (pow J 2)))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* 2 (cos (* 1/2 K))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) J)))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) J)))
(* -1/4 (/ (pow U 2) J))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 J))))
(* -1/4 (/ (pow U 2) J))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 J))))
(* (pow U 2) (- (* -2 (/ (* J (cos (* 1/2 K))) (pow U 2))) (* 1/4 (/ 1 J))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
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(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -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)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(/ U J)
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -4 (/ J (pow U 2)))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (pow U 2) J))
(* -1/4 (/ (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) 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) 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) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
(/ (pow U 2) J)
Outputs
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(+ (* -2 (/ (pow J 2) U)) (* -1 U))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+ (* -1 U) (* (pow J 2) (- (* 2 (/ (pow J 2) (pow U 3))) (* 2 (/ 1 U)))))
(-.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)
(+ (* -1 U) (* (pow J 2) (- (* (pow J 2) (+ (* -4 (/ (pow J 2) (pow U 5))) (* 2 (/ 1 (pow U 3))))) (* 2 (/ 1 U)))))
(-.f64 (*.f64 (*.f64 J J) (+.f64 (*.f64 (*.f64 J J) (+.f64 (/.f64 (*.f64 (*.f64 J J) #s(literal -4 binary64)) (pow.f64 U #s(literal 5 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 U (*.f64 U U))))) (/.f64 #s(literal -2 binary64) U))) U)
(* -2 J)
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(* J (- (* -1/4 (/ (pow U 2) (pow J 2))) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J))))
(* J (- (+ (* -1/4 (/ (pow U 2) (pow J 2))) (* 1/64 (/ (pow U 4) (pow J 4)))) 2))
(*.f64 J (+.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 U U) (*.f64 U U))) (*.f64 (*.f64 J J) (*.f64 J J))) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)))))
(* 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))
(*.f64 J (+.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 U U) (*.f64 U U))) (*.f64 (*.f64 J J) (*.f64 J J))) (+.f64 (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 U #s(literal 6 binary64))) (pow.f64 J #s(literal 6 binary64))) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J))))))
(* -2 J)
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(*.f64 J (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J))))
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(/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)
(/ (pow U 2) J)
(/.f64 (*.f64 U U) J)

eval202.0ms (1.8%)

Compiler

Compiled 52702 to 3141 computations (94% saved)

prune145.0ms (1.3%)

Pruning

29 alts after pruning (21 fresh and 8 done)

PrunedKeptTotal
New1301111312
Fresh11011
Picked235
Done055
Total1304291333
Accuracy
100.0%
Counts
1333 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
55.2%
(/.f64 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
55.1%
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
✓55.1%
(/.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)))
55.1%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
15.7%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
40.9%
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))) (*.f64 #s(literal -2 binary64) J)))
29.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
34.7%
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) U)
29.8%
(-.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)
✓56.3%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓51.5%
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
34.6%
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
✓30.4%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
27.4%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
11.8%
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
9.3%
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
14.5%
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
10.0%
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
✓55.7%
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
10.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
9.8%
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
✓55.2%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
34.6%
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
14.8%
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
49.6%
(*.f64 J (+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
27.4%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
✓29.7%
(*.f64 #s(literal -2 binary64) J)
37.1%
(neg.f64 U)
✓13.0%
U
Compiler

Compiled 1330 to 535 computations (59.8% saved)

regimes119.0ms (1%)

Counts
46 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.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 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
(*.f64 J (+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 2 binary64))) U) U)
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64)) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))) (*.f64 #s(literal -2 binary64) J)))
(*.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))))))
(*.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 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 0 binary64) (*.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))))))
(*.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 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 (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 (*.f64 (neg.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 (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))))
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:

40.0ms
K
21.0ms
J
13.0ms
(/.f64 K #s(literal 2 binary64))
13.0ms
U
13.0ms
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
92.2%2J
90.0%1K
91.5%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)))))
90.0%1(cos.f64 (/.f64 K #s(literal 2 binary64)))
90.0%1(/.f64 K #s(literal 2 binary64))
Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes19.0ms (0.2%)

Counts
43 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.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 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
(*.f64 J (+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 2 binary64))) U) U)
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64)) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))) (*.f64 #s(literal -2 binary64) J)))
(*.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))))))
(*.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 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 4 binary64) (*.f64 J J))) (+.f64 #s(literal 0 binary64) (*.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))))))
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 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
Calls

1 calls:

13.0ms
J
Results
AccuracySegmentsBranch
92.2%2J
Compiler

Compiled 4 to 3 computations (25% saved)

regimes67.0ms (0.6%)

Counts
40 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.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 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
(*.f64 J (+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 2 binary64))) U) U)
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64))))))) #s(literal -1/2 binary64)) (*.f64 J #s(literal -2 binary64)))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 U U) J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (/.f64 (*.f64 (/.f64 U (/.f64 J U)) #s(literal 1/4 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (+.f64 (*.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (*.f64 J J))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))) J)
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))) (*.f64 #s(literal -2 binary64) J)))
Outputs
(-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) 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:

13.0ms
U
13.0ms
(/.f64 K #s(literal 2 binary64))
13.0ms
J
12.0ms
K
12.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
76.5%1K
76.5%1(cos.f64 (/.f64 K #s(literal 2 binary64)))
76.5%1(/.f64 K #s(literal 2 binary64))
80.1%2U
81.6%2J
Compiler

Compiled 25 to 20 computations (20% saved)

regimes17.0ms (0.1%)

Counts
34 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.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 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
(*.f64 J (+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
Outputs
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) 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

1 calls:

12.0ms
J
Results
AccuracySegmentsBranch
81.6%2J
Compiler

Compiled 4 to 3 computations (25% saved)

regimes56.0ms (0.5%)

Counts
33 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.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 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U 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 (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(-.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 U U) J)))
(*.f64 J (+.f64 (/.f64 (*.f64 U (*.f64 U #s(literal -1/4 binary64))) (*.f64 J J)) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))))
Outputs
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J))))
Calls

5 calls:

11.0ms
(/.f64 K #s(literal 2 binary64))
11.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
10.0ms
J
10.0ms
U
9.0ms
K
Results
AccuracySegmentsBranch
73.5%2K
74.5%2(cos.f64 (/.f64 K #s(literal 2 binary64)))
73.5%2(/.f64 K #s(literal 2 binary64))
70.3%3U
75.2%3J
Compiler

Compiled 25 to 20 computations (20% saved)

regimes66.0ms (0.6%)

Counts
27 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.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 (*.f64 #s(literal 2 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Outputs
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64)))
Calls

4 calls:

9.0ms
J
9.0ms
(/.f64 K #s(literal 2 binary64))
8.0ms
K
8.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
64.6%5K
64.6%5(/.f64 K #s(literal 2 binary64))
72.6%2J
55.2%1(cos.f64 (/.f64 K #s(literal 2 binary64)))
Compiler

Compiled 21 to 17 computations (19% saved)

regimes23.0ms (0.2%)

Counts
22 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 U (*.f64 U (+.f64 (/.f64 #s(literal -1/4 binary64) J) (*.f64 #s(literal -2 binary64) (/.f64 J (*.f64 U U))))))
(*.f64 (*.f64 U U) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) U) U) (/.f64 #s(literal -1/4 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) U) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 U (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) J) (/.f64 J (*.f64 U U))))))
(-.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 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1/4 binary64) (/.f64 J (*.f64 U U)))) (-.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))))))
(*.f64 (*.f64 J (*.f64 (*.f64 J J) #s(literal -8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (*.f64 (*.f64 U U) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U))))))
(*.f64 (+.f64 (*.f64 #s(literal -8 binary64) (*.f64 J (*.f64 J J))) (*.f64 (*.f64 (/.f64 U (/.f64 J U)) (*.f64 (/.f64 U (/.f64 J U)) (/.f64 U (/.f64 J U)))) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 J J) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) J) (*.f64 #s(literal -2 binary64) J)) (/.f64 J (*.f64 #s(literal -1/4 binary64) (*.f64 U U)))))))
Outputs
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64)))
Calls

3 calls:

8.0ms
J
7.0ms
K
7.0ms
U
Results
AccuracySegmentsBranch
49.3%5K
47.1%2U
51.7%2J
Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0%)

Counts
9 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J #s(literal 1/4 binary64)))))
Outputs
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(*.f64 #s(literal -2 binary64) J)
Calls

1 calls:

3.0ms
J
Results
AccuracySegmentsBranch
51.4%2J
Compiler

Compiled 4 to 3 computations (25% saved)

regimes4.0ms (0%)

Counts
7 → 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 -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 (*.f64 U #s(literal -1/2 binary64)) J))
Outputs
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
Calls

1 calls:

3.0ms
J
Results
AccuracySegmentsBranch
51.2%2J
Compiler

Compiled 4 to 3 computations (25% saved)

regimes6.0ms (0.1%)

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

3 calls:

3.0ms
J
2.0ms
U
2.0ms
K
Results
AccuracySegmentsBranch
39.5%2K
37.1%1U
37.1%1J
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
K
1.0ms
U
1.0ms
J
Results
AccuracySegmentsBranch
13.0%1U
13.0%1J
13.0%1K
Compiler

Compiled 12 to 9 computations (25% saved)

bsearch1.0ms (0%)

Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
1.4709797921365286e+303
+inf
0.0ms
-inf
-8.712890464022937e+307
Compiler

Compiled 33 to 22 computations (33.3% saved)

bsearch29.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
27.0ms
2.252384950953793e-207
2.2235416458077643e-202
Results
21.0ms144×0valid
Compiler

Compiled 312 to 211 computations (32.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 6.0ms (39.7% of total)
ival-cos: 3.0ms (19.8% of total)
ival-div: 2.0ms (13.2% of total)
ival-add: 1.0ms (6.6% of total)
ival-sqrt: 1.0ms (6.6% of total)
ival-pow: 1.0ms (6.6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch25.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
23.0ms
1.431114457449991e-112
3.978685403368095e-110
Results
18.0ms128×0valid
Compiler

Compiled 353 to 270 computations (23.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-mult: 5.0ms (38.3% of total)
ival-cos: 3.0ms (23% of total)
ival-div: 2.0ms (15.3% of total)
ival-add: 1.0ms (7.7% of total)
ival-sqrt: 1.0ms (7.7% of total)
ival-pow: 1.0ms (7.7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch26.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.431114457449991e-112
3.978685403368095e-110
Results
18.0ms128×0valid
Compiler

Compiled 297 to 222 computations (25.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-mult: 4.0ms (31.4% of total)
ival-div: 3.0ms (23.5% of total)
ival-cos: 3.0ms (23.5% of total)
ival-add: 1.0ms (7.8% of total)
ival-sqrt: 1.0ms (7.8% of total)
ival-pow: 1.0ms (7.8% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.9161321275194972
0.9264512543026792
Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch24.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.431114457449991e-112
3.978685403368095e-110
Results
16.0ms128×0valid
Compiler

Compiled 233 to 174 computations (25.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 4.0ms (35.3% of total)
ival-cos: 3.0ms (26.5% of total)
ival-div: 2.0ms (17.6% of total)
ival-add: 1.0ms (8.8% of total)
ival-sqrt: 1.0ms (8.8% of total)
ival-pow: 1.0ms (8.8% of total)
const: 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
618448763.7025292
7682017233.914637
Results
14.0ms96×0valid
Compiler

Compiled 201 to 142 computations (29.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 3.0ms (34.2% of total)
ival-cos: 2.0ms (22.8% of total)
ival-div: 1.0ms (11.4% of total)
ival-sqrt: 1.0ms (11.4% of total)
ival-pow: 1.0ms (11.4% of total)
ival-add: 0.0ms (0% of total)
const: 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
618448763.7025292
7682017233.914637
Results
14.0ms96×0valid
Compiler

Compiled 153 to 112 computations (26.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 3.0ms (30.8% of total)
ival-cos: 2.0ms (20.6% of total)
ival-sqrt: 2.0ms (20.6% of total)
ival-div: 1.0ms (10.3% of total)
ival-pow: 1.0ms (10.3% of total)
ival-add: 0.0ms (0% of total)
const: 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
18.0ms
618448763.7025292
7682017233.914637
Results
12.0ms96×0valid
Compiler

Compiled 111 to 88 computations (20.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 3.0ms (35.6% of total)
ival-cos: 2.0ms (23.7% of total)
ival-div: 1.0ms (11.9% of total)
ival-sqrt: 1.0ms (11.9% of total)
ival-pow: 1.0ms (11.9% of total)
ival-add: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch21.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
19.0ms
1.5558883152616945e+177
1.2734073985950112e+178
Results
16.0ms96×0valid
Compiler

Compiled 99 to 76 computations (23.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-mult: 5.0ms (41.1% of total)
ival-cos: 3.0ms (24.6% of total)
ival-div: 1.0ms (8.2% of total)
ival-add: 1.0ms (8.2% of total)
ival-sqrt: 1.0ms (8.2% of total)
ival-pow: 1.0ms (8.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify16.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
080277
1105277
2109277
3110277
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 2000000000000000000323530153572912876425337292463318876590990034202234998451477495730520486068427830507559547136360674832054891641135558399286783083212052137222301492244569952354513300088401054553614654135380924225322855000394102452979796521357526782898752177094584641628255914972661310937838244526555136 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 J #s(literal 2089770329444081/1412006979354108748474554421102313931675676955925788762341700965431346915180599249952936960497614998485448932749141998289061648432939195473813276544243473053215398045741358060286316036246351763861878679739417265182867456 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 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(if (<=.f64 J #s(literal 7473211284935009/21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885868835635965404913860608 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) 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 279230041217001/169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) 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 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 8286623314361713/9007199254740992 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J)))))
(if (<=.f64 J #s(literal 3299991396200921/84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))))
(if (<=.f64 J #s(literal 720000000 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64))))
(if (<=.f64 J #s(literal 2100000000 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 #s(literal -2 binary64) J))
(if (<=.f64 J #s(literal 1020000000 binary64)) (neg.f64 U) (*.f64 #s(literal -2 binary64) J))
(if (<=.f64 K #s(literal 3200000000000000023836737606637823652614383803466092391550856132200447527897011712843903604396502586907089928328910868107921388264991274185889821571571964278708924471553405485056 binary64)) (neg.f64 U) 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 2000000000000000000323530153572912876425337292463318876590990034202234998451477495730520486068427830507559547136360674832054891641135558399286783083212052137222301492244569952354513300088401054553614654135380924225322855000394102452979796521357526782898752177094584641628255914972661310937838244526555136 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 2000000000000000000323530153572912876425337292463318876590990034202234998451477495730520486068427830507559547136360674832054891641135558399286783083212052137222301492244569952354513300088401054553614654135380924225322855000394102452979796521357526782898752177094584641628255914972661310937838244526555136 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 J #s(literal 2089770329444081/1412006979354108748474554421102313931675676955925788762341700965431346915180599249952936960497614998485448932749141998289061648432939195473813276544243473053215398045741358060286316036246351763861878679739417265182867456 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 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(if (<=.f64 J #s(literal 2089770329444081/1412006979354108748474554421102313931675676955925788762341700965431346915180599249952936960497614998485448932749141998289061648432939195473813276544243473053215398045741358060286316036246351763861878679739417265182867456 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 (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(if (<=.f64 J #s(literal 7473211284935009/21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885868835635965404913860608 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) 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 7473211284935009/21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885868835635965404913860608 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64))) U) 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 279230041217001/169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) 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 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 8286623314361713/9007199254740992 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))) (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J)))))
(if (<=.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 8286623314361713/9007199254740992 binary64)) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))) (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 U J)))))
(if (<=.f64 J #s(literal 3299991396200921/84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 J #s(literal -2 binary64))))
(if (<=.f64 J #s(literal 3299991396200921/84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (*.f64 K #s(literal 1/2 binary64)))))
(if (<=.f64 J #s(literal 720000000 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (/.f64 U (/.f64 J U)) #s(literal -1/4 binary64))))
(if (<=.f64 J #s(literal 2100000000 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 #s(literal -2 binary64) J))
(if (<=.f64 J #s(literal 1020000000 binary64)) (neg.f64 U) (*.f64 #s(literal -2 binary64) J))
(if (<=.f64 J #s(literal 1020000000 binary64)) (-.f64 #s(literal 0 binary64) U) (*.f64 #s(literal -2 binary64) J))
(if (<=.f64 K #s(literal 3200000000000000023836737606637823652614383803466092391550856132200447527897011712843903604396502586907089928328910868107921388264991274185889821571571964278708924471553405485056 binary64)) (neg.f64 U) U)
(if (<=.f64 K #s(literal 3200000000000000023836737606637823652614383803466092391550856132200447527897011712843903604396502586907089928328910868107921388264991274185889821571571964278708924471553405485056 binary64)) (-.f64 #s(literal 0 binary64) U) U)
U

soundness1.9s (16.1%)

Rules
6680×*-lowering-*.f32
6680×*-lowering-*.f64
6132×*-lowering-*.f32
6132×*-lowering-*.f64
5272×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03373915
110543500
237493432
086513432
03895504
113704713
258814506
085954506
01724
13321
27921
320621
461921
5113321
6156821
7163021
8164821
9166621
10167421
11167621
12167621
0167621
04345056
115324486
264334405
080544405
049139
1287138
22877138
010785138
034132
1183117
21432116
08415116
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×saturated
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 894 to 520 computations (41.8% saved)

preprocess143.0ms (1.2%)

Remove

(abs K)

Compiler

Compiled 1472 to 442 computations (70% saved)

end0.0ms (0%)

Profiling

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