Maksimov and Kolovsky, Equation (3)

Time bar (total: 9.9s)

analyze404.0ms (4.1%)

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: 232.0ms
ival-mult: 130.0ms (56.1% of total)
ival-pow: 28.0ms (12.1% of total)
ival-div: 27.0ms (11.7% of total)
ival-sqrt: 16.0ms (6.9% of total)
ival-cos: 13.0ms (5.6% of total)
ival-add: 12.0ms (5.2% of total)
const: 5.0ms (2.2% of total)
backward-pass: 1.0ms (0.4% of total)

sample1.6s (16.6%)

Results
1.3s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 920.0ms
ival-mult: 310.0ms (33.7% of total)
ival-cos: 213.0ms (23.2% of total)
ival-div: 136.0ms (14.8% of total)
ival-pow: 104.0ms (11.3% of total)
ival-add: 74.0ms (8% of total)
ival-sqrt: 60.0ms (6.5% of total)
const: 19.0ms (2.1% of total)
backward-pass: 3.0ms (0.3% of total)
Bogosity

preprocess109.0ms (1.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
075246
1192210
2641210
32298210
44615210
01724
13321
27821
320421
461221
5112621
6154521
7160721
8162521
9164321
10165121
11165321
12165321
0165321
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 (/ 1/2 J)) (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 (/ 1/2 J)) (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 (/ 1/2 J)) (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 (/ 1/2 J)) (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 (/ 1/2 J)) (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 (/ 1/2 J)) (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 (/ 1/2 J)) (cos (/ K 2)))))
(* (* (* -2 K) (cos (/ J 2))) (sqrt (+ 1 (pow (/ U (* (* 2 K) (cos (/ J 2)))) 2))))
(* (* (* -2 K) (cos (/ J 2))) (hypot 1 (/ U (* (cos (/ J 2)) (* K 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 (* (hypot 1 (/ K (* (* J 2) (cos (* U 1/2))))) (* J (cos (* U 1/2)))))
Symmetry

(abs K)

(abs U)

(negabs J)

explain195.0ms (2%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
420-0-(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))))
400-0-(*.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
062(3.616839315651624e+240 4.003667141002677e-123 7.073867711573596e+279)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)
0111(2.454657514217583e+112 3.5367451827084884e+113 1.5076515368982418e-26)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
116.0ms512×0valid
Compiler

Compiled 255 to 53 computations (79.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 79.0ms
ival-cos: 32.0ms (40.4% of total)
ival-mult: 26.0ms (32.8% of total)
ival-div: 7.0ms (8.8% of total)
ival-pow: 6.0ms (7.6% of total)
ival-sqrt: 4.0ms (5% of total)
ival-add: 3.0ms (3.8% of total)
const: 1.0ms (1.3% 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
▶85.2%
(*.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))))))
▶69.6%
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
Compiler

Compiled 51 to 32 computations (37.3% saved)

simplify63.0ms (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-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))))
✓cost-diff6528
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
Rules
852×*-lowering-*.f32
852×*-lowering-*.f64
802×associate-*r/
758×/-lowering-/.f32
758×/-lowering-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025179
154179
2107179
3305179
4785179
51316179
61559179
71839179
82118179
92192179
102192179
112334179
122334179
02334179
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 U (*.f64 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 U (*.f64 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 U (*.f64 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 U (*.f64 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 U (*.f64 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 U (*.f64 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 U (*.f64 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 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ U (* J 2))
(/.f64 U (*.f64 J #s(literal 2 binary64)))
U
(* J 2)
(*.f64 J #s(literal 2 binary64))

localize138.0ms (1.4%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy99.9%
(*.f64 (*.f64 #s(literal -2 binary64) J) (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))))
✓accuracy85.3%
(*.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 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy99.7%
(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%
(*.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)))))
✓accuracy84.6%
(sqrt.f64 (+.f64 #s(literal 1 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
72.0ms256×0valid
Compiler

Compiled 189 to 23 computations (87.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-mult: 16.0ms (33.6% of total)
ival-div: 7.0ms (14.7% of total)
compiled-spec: 7.0ms (14.7% of total)
ival-cos: 6.0ms (12.6% of total)
ival-add: 5.0ms (10.5% of total)
ival-sqrt: 4.0ms (8.4% of total)
ival-pow: 3.0ms (6.3% of total)
const: 1.0ms (2.1% of total)
backward-pass: 0.0ms (0% of total)

series45.0ms (0.5%)

Counts
10 → 300
Calls
Call 1
Inputs
#<alt (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))>
#<alt (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 (* (* 2 J) (cos (/ K 2))))>
#<alt (/ (/ U (* J 2)) (cos (/ K 2)))>
#<alt (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2))))))>
Outputs
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))>
#<alt (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))>
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#<alt (cos (* 1/2 K))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (pow J 2)))>
#<alt (+ (* 1/16 (/ (* (pow K 2) (pow U 2)) (pow J 2))) (* 1/4 (/ (pow U 2) (pow J 2))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))) (* 1/16 (/ (pow U 2) (pow J 2))))))>
#<alt (+ (* 1/4 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* 1/16 (/ (pow U 2) (pow J 2))) (* (pow K 2) (+ (* -1/4 (* (pow K 2) (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))) (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))))))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U J))>
#<alt (+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U J))>
#<alt (+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))>
#<alt (+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))>
#<alt (+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/128 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 4)))))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))>
#<alt (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))>
#<alt (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))>
#<alt (* -1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))>
#<alt (* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))>
#<alt (* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)>
#<alt (/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -1 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 3)) (pow U 3))) (/ (cos (* 1/2 K)) U)))) J)>
#<alt (/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))>
#<alt (+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))>
#<alt (+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))>
#<alt (+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (pow K 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
#<alt (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))>
Calls

75 calls:

TimeVariablePointExpression
4.0ms
K
@inf
(/ U (* (* 2 J) (cos (/ K 2))))
4.0ms
K
@0
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
4.0ms
K
@inf
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
3.0ms
K
@0
(* (* -2 J) (cos (/ K 2)))
2.0ms
K
@-inf
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite283.0ms (2.8%)

Algorithm
1×batch-egg-rewrite
Rules
5664×*-lowering-*.f32
5664×*-lowering-*.f64
2726×/-lowering-/.f32
2726×/-lowering-/.f64
1140×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025113
1120113
2892113
09356113
Stop Event
1×iter limit
1×node limit
Counts
10 → 564
Calls
Call 1
Inputs
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 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 (* (* 2 J) (cos (/ K 2))))
(/ (/ U (* J 2)) (cos (/ K 2)))
(sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2))))))
Outputs
(neg.f64 (*.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 J #s(literal 2 binary64)))))))
(neg.f64 (*.f64 (*.f64 J #s(literal 2 binary64)) (*.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 J #s(literal 2 binary64))))))))
(neg.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))
(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 J #s(literal 2 binary64)))))) (*.f64 J #s(literal 2 binary64))))
(*.f64 #s(literal -2 binary64) (*.f64 J (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))))))
(*.f64 J (*.f64 #s(literal -2 binary64) (*.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 J #s(literal 2 binary64))))))))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) J)) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))))
(*.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 0 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 J #s(literal 2 binary64))))))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))))
(*.f64 (*.f64 J #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 0 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 J #s(literal 2 binary64)))))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) (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 J #s(literal 2 binary64)))))))
(*.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 J #s(literal 2 binary64))))))
(*.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 J #s(literal 2 binary64)))))))
(*.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))))
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(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 2 binary64) (/.f64 U J))) #s(literal -4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 J (*.f64 J #s(literal -4 binary64)))) (+.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 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 2 binary64) (/.f64 U J))) #s(literal -4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 U U) (*.f64 J (*.f64 J #s(literal -4 binary64)))) (+.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 U (*.f64 J (*.f64 #s(literal 4 binary64) (/.f64 J U)))) (+.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 U (*.f64 J (*.f64 #s(literal 4 binary64) (/.f64 J U)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) #s(literal 1/4 binary64)))

simplify401.0ms (4%)

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
03897079
113706736
258746706
085776706
Stop Event
1×iter limit
1×node limit
Counts
300 → 300
Calls
Call 1
Inputs
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
(* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1))
(* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1))
U
(* -1 (* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1)))
(* -1 (* U (- (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4)))) 1)))
(* -1 (* U (- (+ (* -4 (/ (* (pow J 6) (pow (cos (* 1/2 K)) 6)) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) (* 2 (/ (* (pow J 4) (pow (cos (* 1/2 K)) 4)) (pow U 4))))) 1)))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (* (pow U 2) (+ (* -1/128 (/ (pow U 2) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(+ 1 (* (pow U 2) (+ (* (pow U 2) (- (* 1/1024 (/ (pow U 2) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/128 (/ 1 (* (pow J 4) (pow (cos (* 1/2 K)) 4)))))) (* 1/8 (/ 1 (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1/2 (/ U (* J (cos (* 1/2 K)))))
(* -1 (* U (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2))))))
(* -1 (* U (+ (* -1 (/ (* (pow J 3) (pow (cos (* 1/2 K)) 3)) (pow U 4))) (+ (* 2 (/ (* (pow J 5) (pow (cos (* 1/2 K)) 5)) (pow U 6))) (+ (* 1/2 (/ 1 (* J (cos (* 1/2 K))))) (/ (* J (cos (* 1/2 K))) (pow U 2)))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (/ (* (pow J 2) (cos (* 1/2 K))) U)) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* -1 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 3)) (pow U 3))) (/ (cos (* 1/2 K)) U)))) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
1
(+ 1 (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(+ 1 (+ (* -1/128 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 4)))) (+ (* 1/1024 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 6)))) (* 1/8 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2)))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* 1/32 (* (/ (* (pow K 2) (pow U 2)) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))
(+ (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))) (* (pow K 2) (+ (* 1/32 (* (/ (pow U 2) (pow J 2)) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* (pow K 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* 1/2 (* (* (pow K 2) (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
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Outputs
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(* -1 U)
(-.f64 #s(literal 0 binary64) U)
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(/ (+ (* 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 (*.f64 (*.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)
(/.f64 (+.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 (*.f64 J J) (-.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) U) (*.f64 (*.f64 J J) (pow.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) U) #s(literal 3 binary64)))))) J)
(/ (+ (* 1/2 (/ U (cos (* 1/2 K)))) (* (pow J 2) (+ (* (pow J 2) (+ (* -1 (/ (pow (cos (* 1/2 K)) 3) (pow U 3))) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 5)) (pow U 5))))) (/ (cos (* 1/2 K)) U)))) J)
(/.f64 (+.f64 (/.f64 (*.f64 U #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 J (*.f64 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 (*.f64 U U) #s(literal 1/8 binary64)) (*.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 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/8 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #s(literal -1/128 binary64)) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))))
(+ 1 (+ (* -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 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/8 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #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 (/.f64 (*.f64 (pow.f64 U #s(literal 6 binary64)) #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))))
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 (*.f64 U U) #s(literal 1/8 binary64)) (*.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 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/8 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #s(literal -1/128 binary64)) (pow.f64 J #s(literal 4 binary64))) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64))))
(+ 1 (+ (* -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 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (*.f64 U U) #s(literal 1/8 binary64)) (*.f64 J J)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) (/.f64 (/.f64 (*.f64 (pow.f64 U #s(literal 4 binary64)) #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 (/.f64 (*.f64 (pow.f64 U #s(literal 6 binary64)) #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))))
(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 U (*.f64 U (*.f64 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 #s(literal -1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (*.f64 (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)))))))))))))
(+.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 (*.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 U U)) (*.f64 J J))) (*.f64 (*.f64 (*.f64 K K) #s(literal 1/2 binary64)) (*.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 (/.f64 (*.f64 U U) (*.f64 J J)) #s(literal 1/96 binary64)) (/.f64 (*.f64 #s(literal -1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (*.f64 (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)))))) (*.f64 K (*.f64 K (+.f64 (*.f64 #s(literal -1/4 binary64) (+.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)))) (*.f64 (/.f64 (*.f64 (*.f64 U U) (+.f64 (*.f64 (/.f64 (*.f64 U U) (*.f64 J J)) #s(literal 1/96 binary64)) (/.f64 (*.f64 #s(literal -1/1024 binary64) (pow.f64 U #s(literal 4 binary64))) (*.f64 (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))))))) (*.f64 (*.f64 J J) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J))))) #s(literal -1/32 binary64)))))))))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))
(sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.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)))))

eval136.0ms (1.4%)

Compiler

Compiled 29991 to 2727 computations (90.9% saved)

prune128.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New9918999
Fresh000
Picked112
Done000
Total99291001
Accuracy
99.9%
Counts
1001 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶41.6%
(-.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))) U)
44.6%
(-.f64 #s(literal 0 binary64) U)
▶47.0%
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #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))))))
47.2%
(*.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 J (*.f64 J #s(literal 4 binary64)))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 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))))))
▶85.2%
(*.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))))))
✓85.2%
(*.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))))))
35.3%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 U U) #s(literal 1/4 binary64)) (*.f64 J J)))) (*.f64 #s(literal -2 binary64) J))
▶51.1%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
▶9.9%
U
Compiler

Compiled 348 to 229 computations (34.2% saved)

simplify228.0ms (2.3%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))
✓cost-diff256
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64)))))
✓cost-diff640
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))
✓cost-diff640
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #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
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))
✓cost-diff0
(*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U)))
✓cost-diff0
(-.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))) U)
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓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 #s(literal -2 binary64) J))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓cost-diff256
(*.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-diff256
(*.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))))))
Rules
4894×*-lowering-*.f32
4894×*-lowering-*.f64
2098×/-lowering-/.f32
2098×/-lowering-/.f64
1124×distribute-rgt-neg-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
043338
1111333
2378325
32339316
45462316
08285316
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
(* (* -2 J) (/ 1 (/ 1 (cos (/ K 2)))))
(* -2 J)
-2
J
(/ 1 (/ 1 (cos (/ K 2))))
1
(/ 1 (cos (/ K 2)))
(cos (/ K 2))
(/ K 2)
K
2
(sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2))))))
(/ (/ U (* J 2)) (cos (/ K 2)))
(/ U (* J 2))
U
(* J 2)
U
(* (cos (* 1/2 K)) (* -2 J))
(cos (* 1/2 K))
(* 1/2 K)
1/2
K
(* -2 J)
-2
J
(- (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))) U)
(* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U)))
-2
(* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))
(pow (cos (* 1/2 K)) 2)
(cos (* 1/2 K))
(* 1/2 K)
1/2
K
2
(/ (* J J) U)
(* J J)
J
U
(* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2)))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
(/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2))))
(- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4))))
0
(* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))
(+ 1/2 (* 1/2 (cos K)))
1/2
(* 1/2 (cos K))
(cos K)
K
(* J (* J 4))
J
(* J 4)
4
(+ 0 (* (cos (/ K 2)) (* J 2)))
(* (cos (/ K 2)) (* J 2))
(cos (/ K 2))
(/ K 2)
2
(* J 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
Outputs
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
(*.f64 #s(literal -2 binary64) (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(* (* -2 J) (/ 1 (/ 1 (cos (/ K 2)))))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(/ 1 (/ 1 (cos (/ K 2))))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(/ 1 (cos (/ K 2)))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2))))))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/ (/ U (* J 2)) (cos (/ K 2)))
(/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ U (* J 2))
(/.f64 U (*.f64 J #s(literal 2 binary64)))
U
(* J 2)
(*.f64 J #s(literal 2 binary64))
U
(* (cos (* 1/2 K)) (* -2 J))
(*.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
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
-2
#s(literal -2 binary64)
J
(- (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))) U)
(-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U)) U)
(* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U)))
(*.f64 (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) U))
-2
#s(literal -2 binary64)
(* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))
(*.f64 (pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))
(pow (cos (* 1/2 K)) 2)
(pow.f64 (cos.f64 (*.f64 K #s(literal 1/2 binary64))) #s(literal 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
2
#s(literal 2 binary64)
(/ (* J J) U)
(/.f64 (*.f64 J J) U)
(* J J)
(*.f64 J J)
J
U
(* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 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 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 (*.f64 (*.f64 J (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))) #s(literal -2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2))))
(/.f64 (*.f64 (*.f64 J (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))) #s(literal -2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 #s(literal -2 binary64) (*.f64 J J)))
0
#s(literal 0 binary64)
(* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J (*.f64 J #s(literal 2 binary64))))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
1/2
#s(literal 1/2 binary64)
(* 1/2 (cos K))
(*.f64 #s(literal 1/2 binary64) (cos.f64 K))
(cos K)
(cos.f64 K)
K
(* J (* J 4))
(*.f64 J (*.f64 J #s(literal 4 binary64)))
J
(* J 4)
(*.f64 J #s(literal 4 binary64))
4
#s(literal 4 binary64)
(+ 0 (* (cos (/ K 2)) (* J 2)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))
(* (cos (/ K 2)) (* J 2))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* J 2)
(*.f64 J #s(literal 2 binary64))
(sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2))))))
(hypot.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(/ (/ U (* J 2)) (cos (/ K 2)))
(/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ U (* J 2))
(/.f64 U (*.f64 J #s(literal 2 binary64)))
U

localize235.0ms (2.4%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy99.8%
(/.f64 (/.f64 U (*.f64 J #s(literal 2 binary64))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.4%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
✓accuracy85.3%
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #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))))))
✓accuracy52.5%
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U)))
✓accuracy99.9%
(*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))
✓accuracy99.7%
(pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))
✓accuracy89.6%
(/.f64 (*.f64 J J) U)
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) K)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
✓accuracy99.9%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (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))))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy85.3%
(*.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
165.0ms256×0valid
Compiler

Compiled 365 to 41 computations (88.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 110.0ms
ival-mult: 44.0ms (39.9% of total)
ival-cos: 33.0ms (29.9% of total)
ival-div: 11.0ms (10% of total)
compiled-spec: 7.0ms (6.3% of total)
ival-pow: 5.0ms (4.5% of total)
ival-add: 4.0ms (3.6% of total)
ival-sub: 3.0ms (2.7% of total)
ival-sqrt: 2.0ms (1.8% of total)
const: 1.0ms (0.9% of total)
backward-pass: 0.0ms (0% of total)

series56.0ms (0.6%)

Counts
19 → 444
Calls
Call 1
Inputs
#<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 (/ 1 (/ 1 (cos (/ K 2))))>
#<alt (* -2 J)>
#<alt (* (cos (* 1/2 K)) (* -2 J))>
#<alt (cos (* 1/2 K))>
#<alt (* 1/2 K)>
#<alt (- (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))) U)>
#<alt (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U)))>
#<alt (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))>
#<alt (pow (cos (* 1/2 K)) 2)>
#<alt (* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2)))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))>
#<alt (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2))))>
#<alt (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4))))>
#<alt (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))>
#<alt (/ (/ U (* J 2)) (cos (/ K 2)))>
#<alt (/ 1 (cos (/ K 2)))>
#<alt (/ (* J J) U)>
#<alt (+ 1/2 (* 1/2 (cos K)))>
Outputs
#<alt (* -1 U)>
#<alt (+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))>
#<alt (+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))>
#<alt (* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))>
#<alt (* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))>
#<alt (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))>
#<alt (+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<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 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -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))))>
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#<alt (* -1 (* U (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))))))>
#<alt (* -1 (* U (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (+ (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))) (* 2 (/ (* (pow J 4) (* (pow (cos (* 1/2 K)) 2) (+ 1/2 (* 1/2 (cos K))))) (pow U 4)))))))>
#<alt (* -1 (* U (+ (* -4 (/ (* (pow J 6) (* (pow (cos (* 1/2 K)) 4) (+ 1/2 (* 1/2 (cos K))))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (+ (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))) (* 2 (/ (* (pow J 4) (* (pow (cos (* 1/2 K)) 2) (+ 1/2 (* 1/2 (cos K))))) (pow U 4))))))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* -2 (* (pow K 2) (- (* -1/4 J) (* -1/8 J)))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J))))) (* -2 (- (* -1/4 J) (* -1/8 J))))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -2 (- (* -1/4 J) (* -1/8 J))) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* -1/1440 J) (+ (* -1/8 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))) (+ (* -1/46080 J) (* 1/384 (- (* -1/4 J) (* -1/8 J)))))))) (* -2 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))))))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -4 (pow J 2))>
#<alt (- (* (pow J 2) (pow K 2)) (* 4 (pow J 2)))>
#<alt (- (* (pow K 2) (- (* -1/12 (* (pow J 2) (pow K 2))) (* -1 (pow J 2)))) (* 4 (pow J 2)))>
#<alt (- (* (pow K 2) (- (* (pow K 2) (- (* 1/360 (* (pow J 2) (pow K 2))) (* 1/12 (pow J 2)))) (* -1 (pow J 2)))) (* 4 (pow J 2)))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (pow J 2))>
#<alt (+ (* -1 (* (pow J 2) (pow K 2))) (* 4 (pow J 2)))>
#<alt (+ (* 4 (pow J 2)) (* (pow K 2) (+ (* -1 (pow J 2)) (* 1/12 (* (pow J 2) (pow K 2))))))>
#<alt (+ (* 4 (pow J 2)) (* (pow K 2) (+ (* -1 (pow J 2)) (* (pow K 2) (+ (* -1/360 (* (pow J 2) (pow K 2))) (* 1/12 (pow J 2)))))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos 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 (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U J))>
#<alt (+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))>
#<alt (+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt (* 1/2 (/ U (* J (cos (* 1/2 K)))))>
#<alt 1>
#<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 (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<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

111 calls:

TimeVariablePointExpression
10.0ms
J
@-inf
(* (* (* -2 J) (/ 1 (/ 1 (cos (/ K 2))))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
8.0ms
K
@inf
(* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2)))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
3.0ms
K
@-inf
(/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2))))
2.0ms
K
@0
(* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2)))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
2.0ms
K
@-inf
(* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2)))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))

rewrite373.0ms (3.8%)

Algorithm
1×batch-egg-rewrite
Rules
3936×/-lowering-/.f32
3936×/-lowering-/.f64
3650×*-lowering-*.f32
3650×*-lowering-*.f64
1780×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043206
1237193
22079192
08783192
Stop Event
1×iter limit
1×node limit
Counts
19 → 680
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)))))
(/ 1 (/ 1 (cos (/ K 2))))
(* -2 J)
(* (cos (* 1/2 K)) (* -2 J))
(cos (* 1/2 K))
(* 1/2 K)
(- (* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))) U)
(* -2 (* (pow (cos (* 1/2 K)) 2) (/ (* J J) U)))
(* (pow (cos (* 1/2 K)) 2) (/ (* J J) U))
(pow (cos (* 1/2 K)) 2)
(* (/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2)))) (sqrt (+ (* 1 1) (* (/ (/ U (* J 2)) (cos (/ K 2))) (/ (/ U (* J 2)) (cos (/ K 2)))))))
(/ (- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))) (+ 0 (* (cos (/ K 2)) (* J 2))))
(- 0 (* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4))))
(* (+ 1/2 (* 1/2 (cos K))) (* J (* J 4)))
(/ (/ U (* J 2)) (cos (/ K 2)))
(/ 1 (cos (/ K 2)))
(/ (* J J) U)
(+ 1/2 (* 1/2 (cos K)))
Outputs
(/.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 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 J #s(literal 2 binary64))))))))
(*.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 J #s(literal 2 binary64)))))))
(*.f64 J (*.f64 #s(literal -2 binary64) (*.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 J #s(literal 2 binary64))))))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -2 binary64) J) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))))
(*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(*.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 J #s(literal 2 binary64))))))
(*.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 J #s(literal 2 binary64)))))))
(*.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 J (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.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))) (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64)))))) (*.f64 #s(literal -2 binary64) J))
(*.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) #s(literal -2 binary64)) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (*.f64 (hypot.f64 #s(literal 1 binary64) (/.f64 U (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) J)
(+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))
(+.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.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 #s(literal -2 binary64) J)) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)))) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))) (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J))) (neg.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)))))
(fma.f64 #s(literal -2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 J (*.f64 #s(literal -2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J)) #s(literal 0 binary64))
(fma.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J) #s(literal 0 binary64))
(fma.f64 (*.f64 J #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 J #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 0 binary64))
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(fma.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64) #s(literal 0 binary64))
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(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) U) #s(literal -1 binary64)) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)) #s(literal -1 binary64)))
(*.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 binary64) (*.f64 #s(literal -2 binary64) J)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 U J)) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(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 1/2 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) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #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 (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 (sqrt.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 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)))
(exp.f64 (*.f64 (log.f64 (/.f64 U (*.f64 J J))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) U)) (/.f64 (*.f64 J J) (-.f64 #s(literal 0 binary64) U)))
(neg.f64 (/.f64 (*.f64 J J) (-.f64 #s(literal 0 binary64) U)))
(neg.f64 (/.f64 (*.f64 J (neg.f64 J)) U))
(/.f64 #s(literal 1 binary64) (/.f64 U (*.f64 J J)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 U (*.f64 J J)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 U (*.f64 J J)))))
(/.f64 (*.f64 J J) U)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 U (*.f64 J J))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 U (*.f64 J J)) #s(literal 1 binary64))))
(/.f64 (*.f64 J (neg.f64 J)) (-.f64 #s(literal 0 binary64) U))
(/.f64 (neg.f64 (*.f64 J (neg.f64 J))) (neg.f64 (-.f64 #s(literal 0 binary64) U)))
(/.f64 (*.f64 (*.f64 J J) #s(literal 1 binary64)) U)
(/.f64 (neg.f64 (neg.f64 (*.f64 J (neg.f64 J)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) U))))
(/.f64 (neg.f64 (*.f64 (*.f64 J J) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) U))
(pow.f64 (/.f64 U (*.f64 J J)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 U (*.f64 J J)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 J (/.f64 J U))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 J J) U))
(*.f64 (*.f64 J J) (/.f64 #s(literal 1 binary64) U))
(*.f64 (*.f64 J (neg.f64 J)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) U)))
(*.f64 (/.f64 #s(literal 1 binary64) U) (*.f64 J J))
(*.f64 (/.f64 #s(literal 1 binary64) U) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 J J)) #s(literal -1 binary64)))
(*.f64 (/.f64 J U) J)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K)))) (/.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) K))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K)))))
(-.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) K))))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 K) #s(literal 1/2 binary64))
(fma.f64 (cos.f64 K) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #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) K))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 K)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64)))) (neg.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) K))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 K))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K))))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K)))))
(/.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) K))))) #s(literal 1/4 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K))) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K))))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K))))))
(/.f64 (neg.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) K))))) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #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 K))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K))))))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 1/2 binary64))))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 K)))))
(*.f64 (+.f64 (cos.f64 K) #s(literal 1 binary64)) #s(literal 1/2 binary64))

simplify404.0ms (4.1%)

Algorithm
1×egg-herbie
Rules
8150×*-lowering-*.f32
8150×*-lowering-*.f64
3758×+-lowering-+.f64
3758×+-lowering-+.f32
1586×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05817600
121517237
084747237
Stop Event
1×iter limit
1×node limit
Counts
444 → 444
Calls
Call 1
Inputs
(* -1 U)
(+ (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) U)) (* -1 U))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 4)) (pow U 3))))))
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* (pow J 2) (+ (* -4 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 6)) (pow U 5))) (* 2 (/ (pow (cos (* 1/2 K)) 4) (pow U 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))) (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))))))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* (pow K 2) (+ (* -2 (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))))) (* (pow K 2) (+ (* -2 (* (pow K 2) (+ (* -1/16 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* -1/46080 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (+ (* 1/12288 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/1440 (/ (pow U 2) (pow J 2))) (+ (* 1/192 (/ (pow U 2) (pow J 2))) (* 1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2)))))))) (* 1/32 (/ (* (pow U 2) (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (* (pow J 2) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))) (* -2 (+ (* -1/256 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))) (+ (* 1/384 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/2 (* (* J (- (* -1/4 (+ (* -1/16 (/ (pow U 2) (pow J 2))) (* 1/48 (/ (pow U 2) (pow J 2))))) (* 1/1024 (/ (pow U 4) (* (pow J 4) (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* (* J (cos (* 1/2 K))) (sqrt (+ 1 (* 1/4 (/ (pow U 2) (* (pow J 2) (pow (cos (* 1/2 K)) 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* -1/4 (/ (pow U 2) (* J (cos (* 1/2 K))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* 1/64 (/ (pow U 2) (* (pow J 3) (pow (cos (* 1/2 K)) 3)))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(+ (* -2 (* J (cos (* 1/2 K)))) (* (pow U 2) (- (* (pow U 2) (+ (* -1/512 (/ (pow U 2) (* (pow J 5) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ 1 (* (pow J 3) (pow (cos (* 1/2 K)) 3)))))) (* 1/4 (/ 1 (* J (cos (* 1/2 K))))))))
(* -1 U)
(* U (- (* -2 (/ (* (pow J 2) (pow (cos (* 1/2 K)) 2)) (pow U 2))) 1))
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(+ (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K)))) (* (pow U 2) (+ (* -1/4 (/ (+ 1/2 (* 1/2 (cos K))) (* J (pow (cos (* 1/2 K)) 3)))) (* (pow U 2) (+ (* -1/512 (/ (* (pow U 2) (+ 1/2 (* 1/2 (cos K)))) (* (pow J 5) (pow (cos (* 1/2 K)) 7)))) (* 1/64 (/ (+ 1/2 (* 1/2 (cos K))) (* (pow J 3) (pow (cos (* 1/2 K)) 5)))))))))
(* -1 (/ (* U (+ 1/2 (* 1/2 (cos K)))) (pow (cos (* 1/2 K)) 2)))
(* U (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2)))))
(* U (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (+ (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))) (* 2 (/ (* (pow J 4) (* (pow (cos (* 1/2 K)) 2) (+ 1/2 (* 1/2 (cos K))))) (pow U 4))))))
(* U (+ (* -4 (/ (* (pow J 6) (* (pow (cos (* 1/2 K)) 4) (+ 1/2 (* 1/2 (cos K))))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (+ (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))) (* 2 (/ (* (pow J 4) (* (pow (cos (* 1/2 K)) 2) (+ 1/2 (* 1/2 (cos K))))) (pow U 4)))))))
(/ (* U (+ 1/2 (* 1/2 (cos K)))) (pow (cos (* 1/2 K)) 2))
(* -1 (* U (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))))))
(* -1 (* U (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (+ (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))) (* 2 (/ (* (pow J 4) (* (pow (cos (* 1/2 K)) 2) (+ 1/2 (* 1/2 (cos K))))) (pow U 4)))))))
(* -1 (* U (+ (* -4 (/ (* (pow J 6) (* (pow (cos (* 1/2 K)) 4) (+ 1/2 (* 1/2 (cos K))))) (pow U 6))) (+ (* -2 (/ (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))) (pow U 2))) (+ (* -1 (/ (+ 1/2 (* 1/2 (cos K))) (pow (cos (* 1/2 K)) 2))) (* 2 (/ (* (pow J 4) (* (pow (cos (* 1/2 K)) 2) (+ 1/2 (* 1/2 (cos K))))) (pow U 4))))))))
(* -2 J)
(+ (* -2 J) (* -2 (* (pow K 2) (- (* -1/4 J) (* -1/8 J)))))
(+ (* -2 J) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J))))) (* -2 (- (* -1/4 J) (* -1/8 J))))))
(+ (* -2 J) (* (pow K 2) (+ (* -2 (- (* -1/4 J) (* -1/8 J))) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* -1/1440 J) (+ (* -1/8 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))) (+ (* -1/46080 J) (* 1/384 (- (* -1/4 J) (* -1/8 J)))))))) (* -2 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))))))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -4 (pow J 2))
(- (* (pow J 2) (pow K 2)) (* 4 (pow J 2)))
(- (* (pow K 2) (- (* -1/12 (* (pow J 2) (pow K 2))) (* -1 (pow J 2)))) (* 4 (pow J 2)))
(- (* (pow K 2) (- (* (pow K 2) (- (* 1/360 (* (pow J 2) (pow K 2))) (* 1/12 (pow J 2)))) (* -1 (pow J 2)))) (* 4 (pow J 2)))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* -4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (pow J 2))
(+ (* -1 (* (pow J 2) (pow K 2))) (* 4 (pow J 2)))
(+ (* 4 (pow J 2)) (* (pow K 2) (+ (* -1 (pow J 2)) (* 1/12 (* (pow J 2) (pow K 2))))))
(+ (* 4 (pow J 2)) (* (pow K 2) (+ (* -1 (pow J 2)) (* (pow K 2) (+ (* -1/360 (* (pow J 2) (pow K 2))) (* 1/12 (pow J 2)))))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos K)))))
(* 4 (* (pow J 2) (+ 1/2 (* 1/2 (cos 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 (cos (* 1/2 K)))))
(* 1/2 (/ U J))
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/64 (/ U J)) (* 1/384 (/ U J))))) (* 1/16 (/ U J)))))
(+ (* 1/2 (/ U J)) (* (pow K 2) (+ (* 1/16 (/ U J)) (* (pow K 2) (+ (* -1/2 (* (pow K 2) (+ (* -1/46080 (/ U J)) (+ (* 1/3072 (/ U J)) (* 1/8 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))) (* -1/2 (+ (* -1/64 (/ U J)) (* 1/384 (/ U J)))))))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
(* 1/2 (/ U (* J (cos (* 1/2 K)))))
1
(+ 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)))
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
Outputs
(* -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 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)))) U) U)
(+ (* -1 U) (* (pow J 2) (+ (* -2 (/ (pow (cos (* 1/2 K)) 2) U)) (* 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 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) (*.f64 (*.f64 (*.f64 J J) #s(literal 2 binary64)) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (*.f64 U (*.f64 U U)))))) 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 J (*.f64 J (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64))) U) (*.f64 (*.f64 J J) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 J J) #s(literal -4 binary64)) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 6 binary64))) (pow.f64 U #s(literal 5 binary64))) (*.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 4 binary64)) (*.f64 U (*.f64 U U))))))))) U)
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* J (+ (* -2 (cos (* 1/2 K))) (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K)))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 (*.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))))))
(*.f64 J (+.f64 (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (+.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 (*.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))) (/.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 #s(literal 1/2 binary64) K)) #s(literal 3 binary64))))))
(* J (+ (* -2 (cos (* 1/2 K))) (+ (* -1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (+ (* -1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (* 1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3))))))))
(*.f64 J (+.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (*.f64 (*.f64 J J) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))) (/.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 #s(literal 1/2 binary64) K)) #s(literal 5 binary64)))) (+.f64 (/.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 #s(literal 1/2 binary64) K)) #s(literal 3 binary64))) (*.f64 #s(literal -2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -1 (* J (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))
(*.f64 (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 U U)) (*.f64 J J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))) (neg.f64 J))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K)))))))
(-.f64 #s(literal 0 binary64) (*.f64 J (+.f64 (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 U U)) (*.f64 J J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))) (/.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 #s(literal 1/2 binary64) K)) #s(literal 3 binary64))))))
(* -1 (* J (+ (* -1/64 (/ (pow U 4) (* (pow J 4) (pow (cos (* 1/2 K)) 3)))) (+ (* 1/512 (/ (pow U 6) (* (pow J 6) (pow (cos (* 1/2 K)) 5)))) (+ (* 1/4 (/ (pow U 2) (* (pow J 2) (cos (* 1/2 K))))) (* 2 (cos (* 1/2 K))))))))
(-.f64 #s(literal 0 binary64) (*.f64 J (+.f64 (+.f64 (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 U U)) (*.f64 J J)) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))) (/.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 #s(literal 1/2 binary64) K)) #s(literal 3 binary64)))) (/.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 #s(literal 1/2 binary64) K)) #s(literal 5 binary64))))))
(* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 U U)) (*.f64 J J)))) (*.f64 #s(literal -2 binary64) J))
(+ (* -2 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* -2 (* (pow K 2) (+ (* -1/8 (* J (sqrt (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))) (* 1/32 (* (/ (pow U 2) J) (sqrt (/ 1 (+ 1 (* 1/4 (/ (pow U 2) (pow J 2))))))))))))
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(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 K K)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 (*.f64 (*.f64 K K) #s(literal 1/48 binary64)) #s(literal -1/4 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 (*.f64 K (*.f64 K (+.f64 #s(literal 1/48 binary64) (*.f64 (*.f64 K K) #s(literal -1/1440 binary64))))) #s(literal -1/4 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)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))

eval467.0ms (4.7%)

Compiler

Compiled 40685 to 3160 computations (92.2% saved)

prune206.0ms (2.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New1321101331
Fresh213
Picked325
Done011
Total1326141340
Accuracy
100.0%
Counts
1340 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶50.8%
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
▶51.1%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
▶51.0%
(/.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)))
41.6%
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U)
▶41.5%
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
44.6%
(-.f64 #s(literal 0 binary64) U)
29.8%
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 #s(literal 1/4 binary64) (*.f64 J (*.f64 K K))))
39.2%
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
✓85.2%
(*.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))))))
39.1%
(*.f64 (exp.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J))
✓51.1%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
46.8%
(*.f64 J (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (/.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (*.f64 (*.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 binary64))))))
▶31.4%
(*.f64 #s(literal -2 binary64) J)
✓9.9%
U
Compiler

Compiled 401 to 283 computations (29.4% saved)

simplify169.0ms (1.7%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
✓cost-diff0
(*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))
✓cost-diff256
(*.f64 #s(literal -2 binary64) (*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))))
✓cost-diff256
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
✓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-diff256
(/.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 J J)
✓cost-diff0
(/.f64 (*.f64 J J) U)
✓cost-diff0
(*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U))
✓cost-diff0
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff0
(*.f64 #s(literal -2 binary64) J)
✓cost-diff128
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Rules
2872×*-lowering-*.f32
2872×*-lowering-*.f64
1766×/-lowering-/.f32
1766×/-lowering-/.f64
1330×fnmadd-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
026154
164148
2160145
3358143
4729141
51435139
62824139
75185139
08179139
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (* -2 J) (/ 1 (cos (/ K 2))))
(* -2 J)
-2
J
(/ 1 (cos (/ K 2)))
1
(cos (/ K 2))
(/ K 2)
K
2
(* -2 J)
-2
J
(- (* -2 (/ (* J J) U)) U)
(* -2 (/ (* J J) U))
-2
(/ (* J J) U)
(* J J)
J
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
(/ (* -2 (* J (+ 1/2 (* 1/2 (cos K))))) (cos (* 1/2 K)))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
-2
(* J (+ 1/2 (* 1/2 (cos K))))
J
(+ 1/2 (* 1/2 (cos K)))
1/2
(* 1/2 (cos K))
(cos K)
K
(cos (* 1/2 K))
(* 1/2 K)
Outputs
(/ (* -2 J) (/ 1 (cos (/ K 2))))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(/ 1 (cos (/ K 2)))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
K
2
#s(literal 2 binary64)
(* -2 J)
(/.f64 J #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
J
(- (* -2 (/ (* J J) U)) U)
(-.f64 (/.f64 J (/.f64 U (/.f64 J #s(literal -1/2 binary64)))) U)
(* -2 (/ (* J J) U))
(/.f64 J (/.f64 U (/.f64 J #s(literal -1/2 binary64))))
-2
#s(literal -2 binary64)
(/ (* J J) U)
(/.f64 (*.f64 J J) U)
(* J J)
(*.f64 J J)
J
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
(/ (* -2 (* J (+ 1/2 (* 1/2 (cos K))))) (cos (* 1/2 K)))
(/.f64 (*.f64 J (-.f64 #s(literal -1 binary64) (cos.f64 K))) (cos.f64 (*.f64 K #s(literal 1/2 binary64))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(*.f64 J (-.f64 #s(literal -1 binary64) (cos.f64 K)))
-2
#s(literal -2 binary64)
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))
J
(+ 1/2 (* 1/2 (cos K)))
(+.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 K))
(*.f64 #s(literal 1/2 binary64) (cos.f64 K))
(cos K)
(cos.f64 K)
K
(cos (* 1/2 K))
(cos.f64 (*.f64 K #s(literal 1/2 binary64)))
(* 1/2 K)
(*.f64 K #s(literal 1/2 binary64))

localize129.0ms (1.3%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(cos.f64 K)
✓accuracy99.8%
(*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))
✓accuracy99.7%
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
✓accuracy99.4%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.8%
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) J))
✓accuracy99.6%
(/.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 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
✓accuracy100.0%
(*.f64 J J)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U))
✓accuracy89.6%
(/.f64 (*.f64 J J) U)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(*.f64 #s(literal -2 binary64) J)
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
Results
85.0ms256×0valid
Compiler

Compiled 166 to 27 computations (83.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 44.0ms
ival-cos: 15.0ms (33.8% of total)
ival-div: 13.0ms (29.3% of total)
ival-mult: 13.0ms (29.3% of total)
ival-sub: 1.0ms (2.3% of total)
ival-add: 1.0ms (2.3% of total)
const: 1.0ms (2.3% of total)
backward-pass: 0.0ms (0% of total)

series13.0ms (0.1%)

Counts
15 → 288
Calls
Call 1
Inputs
#<alt (/ (* -2 J) (/ 1 (cos (/ K 2))))>
#<alt (* -2 J)>
#<alt (/ 1 (cos (/ K 2)))>
#<alt (cos (/ K 2))>
#<alt (- (* -2 (/ (* J J) U)) U)>
#<alt (* -2 (/ (* J J) U))>
#<alt (/ (* J J) U)>
#<alt (* J J)>
#<alt (/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))>
#<alt (/ (/ 1 (cos (/ K 2))) (* -2 J))>
#<alt (/ (* -2 (* J (+ 1/2 (* 1/2 (cos K))))) (cos (* 1/2 K)))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (+ 1/2 (* 1/2 (cos K)))>
#<alt (cos K)>
Outputs
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt (* -2 J)>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))>
#<alt (+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt (/ 1 (cos (* 1/2 K)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (cos (* 1/2 K))>
#<alt (* -1 U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (- (* -2 (/ (pow J 2) U)) U)>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)>
#<alt (/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)>
#<alt (/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)>
#<alt (* -1 U)>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))>
#<alt (* -1 U)>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (* -2 (/ (pow J 2) U))>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (/ (pow J 2) U)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (pow J 2)>
#<alt (* -2 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 (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* -2 (* (pow K 2) (- (* -1/4 J) (* -1/8 J)))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J))))) (* -2 (- (* -1/4 J) (* -1/8 J))))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -2 (- (* -1/4 J) (* -1/8 J))) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* -1/1440 J) (+ (* -1/8 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))) (+ (* -1/46080 J) (* 1/384 (- (* -1/4 J) (* -1/8 J)))))))) (* -2 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))))))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/2 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/24 (* J (pow K 2))) (* 1/2 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/2 J) (* (pow K 2) (+ (* -1/24 J) (* 1/720 (* J (pow K 2))))))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* -2 (* J (+ 1/2 (* 1/2 (cos K)))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt J>
#<alt (+ J (* -1/4 (* J (pow K 2))))>
#<alt (+ J (* (pow K 2) (+ (* -1/4 J) (* 1/48 (* J (pow K 2))))))>
#<alt (+ J (* (pow K 2) (+ (* -1/4 J) (* (pow K 2) (+ (* -1/1440 (* J (pow K 2))) (* 1/48 J))))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos K))))>
#<alt (* J (+ 1/2 (* 1/2 (cos 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)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
Calls

72 calls:

TimeVariablePointExpression
1.0ms
J
@inf
(/ (/ 1 (cos (/ K 2))) (* -2 J))
0.0ms
K
@-inf
(/ (/ 1 (cos (/ K 2))) (* -2 J))
0.0ms
K
@inf
(/ (/ 1 (cos (/ K 2))) (* -2 J))
0.0ms
J
@0
(/ (/ 1 (cos (/ K 2))) (* -2 J))
0.0ms
J
@inf
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))

rewrite284.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
5126×*-lowering-*.f32
5126×*-lowering-*.f64
3336×/-lowering-/.f32
3336×/-lowering-/.f64
992×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
026103
113896
285292
0816392
Stop Event
1×iter limit
1×node limit
Counts
15 → 742
Calls
Call 1
Inputs
(/ (* -2 J) (/ 1 (cos (/ K 2))))
(* -2 J)
(/ 1 (cos (/ K 2)))
(cos (/ K 2))
(- (* -2 (/ (* J J) U)) U)
(* -2 (/ (* J J) U))
(/ (* J J) U)
(* J J)
(/ 1 (/ (/ 1 (cos (/ K 2))) (* -2 J)))
(/ (/ 1 (cos (/ K 2))) (* -2 J))
(/ (* -2 (* J (+ 1/2 (* 1/2 (cos K))))) (cos (* 1/2 K)))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* J (+ 1/2 (* 1/2 (cos K))))
(+ 1/2 (* 1/2 (cos K)))
(cos K)
Outputs
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)))
(neg.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)))
(/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 J (/.f64 #s(literal -1/2 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 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) J))
(/.f64 (*.f64 J #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) J) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) J))
(/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)) #s(literal -1 binary64))
(/.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) (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)))
(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 J (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)))
(*.f64 #s(literal 2 binary64) (*.f64 J (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 J (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) J))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)))
(*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (*.f64 J #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1/2 binary64) J) #s(literal -1 binary64)))
(*.f64 (*.f64 J #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) J)
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) J)) #s(literal -1 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) J))
(*.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) J) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) J) #s(literal -1 binary64)) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J) #s(literal 2 binary64))
(*.f64 (/.f64 J (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 J (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 J (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) (/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) J))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) J))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) J)) #s(literal -2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal -1/2 binary64) J)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 binary64)))
(neg.f64 (*.f64 J #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) J))
(/.f64 (*.f64 J #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) J) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -1/2 binary64) J) #s(literal -1 binary64))
(*.f64 #s(literal -2 binary64) J)
(*.f64 #s(literal -2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) J)))
(*.f64 J #s(literal -2 binary64))
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(*.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) J))
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(/.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 4 binary64))) #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) K)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 binary64))))) (neg.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))))
(/.f64 (neg.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) K))))) #s(literal -1/4 binary64))) (neg.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) (+.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))))) (*.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))))))
(/.f64 (*.f64 (+.f64 #s(literal 1/512 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))))) (+.f64 #s(literal 1/64 binary64) (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 6 binary64)) (*.f64 #s(literal 1/64 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))))) (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) (+.f64 #s(literal 1/16 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) K))))) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))))))))
(/.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(*.f64 (*.f64 (+.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))))))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))))))
(*.f64 (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 (cos.f64 K) #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))))) (*.f64 (+.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 K) #s(literal -1/2 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 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) K))))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 K)) #s(literal -1/2 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal 1/2 binary64))
(*.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (cos.f64 K) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1/8 binary64)) (-.f64 #s(literal 1/16 binary64) (pow.f64 (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 K) (-.f64 (*.f64 (cos.f64 K) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) K)))) #s(literal -1/4 binary64))) (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 (cos.f64 K) #s(literal 1/4 binary64)))))
(cos.f64 K)

simplify233.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
4706×*-lowering-*.f32
4706×*-lowering-*.f64
1976×fnmadd-define
1924×+-lowering-+.f64
1924×+-lowering-+.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02082394
16352290
221172177
365032177
083352177
Stop Event
1×iter limit
1×node limit
Counts
288 → 288
Calls
Call 1
Inputs
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
(* -2 J)
1
(+ 1 (* 1/8 (pow K 2)))
(+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))
(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
(/ 1 (cos (* 1/2 K)))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(* -1 U)
(- (* -2 (/ (pow J 2) U)) U)
(- (* -2 (/ (pow J 2) U)) U)
(- (* -2 (/ (pow J 2) U)) U)
(* -2 (/ (pow J 2) U))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* -2 (/ (pow J 2) U))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(* -2 (/ (pow J 2) U))
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(* -1 U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(* -1 U)
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(* -2 (/ (pow J 2) U))
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(/ (pow J 2) U)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(pow J 2)
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(/ -1/2 J)
(- (* -1/16 (/ (pow K 2) J)) (* 1/2 (/ 1 J)))
(- (* (pow K 2) (- (* -5/768 (/ (pow K 2) J)) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))
(- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (/ (pow K 2) J)) (* 5/768 (/ 1 J)))) (* 1/16 (/ 1 J)))) (* 1/2 (/ 1 J)))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(/ -1/2 (* J (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* -2 (* (pow K 2) (- (* -1/4 J) (* -1/8 J)))))
(+ (* -2 J) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J))))) (* -2 (- (* -1/4 J) (* -1/8 J))))))
(+ (* -2 J) (* (pow K 2) (+ (* -2 (- (* -1/4 J) (* -1/8 J))) (* (pow K 2) (+ (* -2 (* (pow K 2) (- (* -1/1440 J) (+ (* -1/8 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))) (+ (* -1/46080 J) (* 1/384 (- (* -1/4 J) (* -1/8 J)))))))) (* -2 (- (* 1/48 J) (+ (* -1/8 (- (* -1/4 J) (* -1/8 J))) (* 1/384 J)))))))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (/ (* J (+ 1/2 (* 1/2 (cos K)))) (cos (* 1/2 K))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 J)
(+ (* -2 J) (* 1/2 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/24 (* J (pow K 2))) (* 1/2 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/2 J) (* (pow K 2) (+ (* -1/24 J) (* 1/720 (* J (pow K 2))))))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* -2 (* J (+ 1/2 (* 1/2 (cos K)))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
J
(+ J (* -1/4 (* J (pow K 2))))
(+ J (* (pow K 2) (+ (* -1/4 J) (* 1/48 (* J (pow K 2))))))
(+ J (* (pow K 2) (+ (* -1/4 J) (* (pow K 2) (+ (* -1/1440 (* J (pow K 2))) (* 1/48 J))))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
(* J (+ 1/2 (* 1/2 (cos K))))
1
(+ 1 (* -1/4 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/48 (pow K 2)) 1/4)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/48 (* -1/1440 (pow K 2)))) 1/4)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
(+ 1/2 (* 1/2 (cos K)))
1
(+ 1 (* -1/2 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
Outputs
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 K K) #s(literal -1/192 binary64)))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 K (*.f64 K (+.f64 (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal -1/192 binary64) (*.f64 (*.f64 K K) #s(literal 1/23040 binary64))))) (*.f64 J #s(literal 1/4 binary64))))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal 1/8 binary64)))
(+ 1 (* (pow K 2) (+ 1/8 (* 5/384 (pow K 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) #s(literal 5/384 binary64))))))
(+ 1 (* (pow K 2) (+ 1/8 (* (pow K 2) (+ 5/384 (* 61/46080 (pow K 2)))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 5/384 binary64) (*.f64 K (*.f64 K #s(literal 61/46080 binary64))))))))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ 1 (cos (* 1/2 K)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K #s(literal -1/8 binary64))))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 K (*.f64 K #s(literal 1/384 binary64)))))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64)))))))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(- (* -2 (/ (pow J 2) U)) U)
(-.f64 (*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U)) U)
(- (* -2 (/ (pow J 2) U)) U)
(-.f64 (*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U)) U)
(- (* -2 (/ (pow J 2) U)) U)
(-.f64 (*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U)) U)
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 U (*.f64 J J))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 U (*.f64 J J))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 U (*.f64 J J))))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 U (*.f64 J J))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 U (*.f64 J J))))
(* (pow J 2) (- (* -1 (/ U (pow J 2))) (* 2 (/ 1 U))))
(*.f64 (*.f64 J J) (-.f64 (/.f64 #s(literal -2 binary64) U) (/.f64 U (*.f64 J J))))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U)) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U)) U)
(/ (+ (* -2 (pow J 2)) (* -1 (pow U 2))) U)
(/.f64 (-.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U)) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U))))
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U))))
(* U (- (* -2 (/ (pow J 2) (pow U 2))) 1))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U))))
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U))))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U))))
(* -1 (* U (+ 1 (* 2 (/ (pow J 2) (pow U 2))))))
(*.f64 U (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J J)) (*.f64 U U))))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(* -2 (/ (pow J 2) U))
(*.f64 J (/.f64 (*.f64 #s(literal -2 binary64) J) U))
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(/ (pow J 2) U)
(/.f64 (*.f64 J J) U)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(pow J 2)
(*.f64 J J)
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
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(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #s(literal 1/2 binary64)))
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #s(literal 1/2 binary64)))
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #s(literal 1/2 binary64)))
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #s(literal 1/2 binary64)))
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #s(literal 1/2 binary64)))
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #s(literal 1/2 binary64)))
(* J (+ 1/2 (* 1/2 (cos K))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) (*.f64 J #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 (*.f64 K 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 K (*.f64 K (+.f64 #s(literal 1/48 binary64) (*.f64 K (*.f64 K #s(literal -1/1440 binary64)))))))))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(+ 1/2 (* 1/2 (cos K)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K #s(literal -1/2 binary64))))
(+ 1 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 K K) #s(literal 1/24 binary64)))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/24 binary64) (*.f64 K (*.f64 K #s(literal -1/720 binary64))))))))
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)

eval216.0ms (2.2%)

Compiler

Compiled 22053 to 2378 computations (89.2% saved)

prune132.0ms (1.3%)

Pruning

15 alts after pruning (10 fresh and 5 done)

PrunedKeptTotal
New115381161
Fresh426
Picked325
Done033
Total1160151175
Accuracy
100.0%
Counts
1175 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.8%
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 (cos.f64 K) (-.f64 #s(literal 0 binary64) J))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
39.0%
(/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
51.0%
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
▶51.1%
(/.f64 J (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
▶51.0%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
31.3%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
41.6%
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U)
✓41.5%
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
▶44.6%
(-.f64 #s(literal 0 binary64) U)
▶50.8%
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
✓85.2%
(*.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))))))
✓51.1%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
▶29.8%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
✓31.4%
(*.f64 #s(literal -2 binary64) J)
✓9.9%
U
Compiler

Compiled 323 to 246 computations (23.8% saved)

simplify149.0ms (1.5%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 #s(literal 1 binary64) (cos.f64 K))
✓cost-diff128
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64))
✓cost-diff128
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff128
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff0
(/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
✓cost-diff0
(*.f64 K #s(literal 1/4 binary64))
✓cost-diff0
(*.f64 K (*.f64 K #s(literal 1/4 binary64)))
✓cost-diff0
(+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))
✓cost-diff0
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
✓cost-diff0
(-.f64 #s(literal 0 binary64) U)
✓cost-diff0
(/.f64 K #s(literal 2 binary64))
✓cost-diff0
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓cost-diff0
(/.f64 J (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
Rules
2638×fma-define
2318×fnmadd-define
1830×sum3-define
1552×fma-lowering-fma.f32
1552×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
026139
155134
2115134
3228131
4475130
5740130
61170130
71887130
83039130
96680130
08081130
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ J (/ -1/2 (cos (/ K 2))))
J
(/ -1/2 (cos (/ K 2)))
-1/2
(cos (/ K 2))
(/ K 2)
K
2
(- 0 U)
0
U
(* J (+ -2 (* K (* K 1/4))))
J
(+ -2 (* K (* K 1/4)))
-2
(* K (* K 1/4))
K
(* K 1/4)
1/4
(/ 1 (/ (/ -1/2 (cos (/ K 2))) J))
1
(/ (/ -1/2 (cos (/ K 2))) J)
(/ -1/2 (cos (/ K 2)))
-1/2
(cos (/ K 2))
(/ K 2)
K
2
J
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)
(/ (* (+ 1 (cos K)) -1) (cos (/ K 2)))
(* (+ 1 (cos K)) -1)
(+ 1 (cos K))
1
(cos K)
K
-1
(cos (/ K 2))
(/ K 2)
2
J
Outputs
(/ J (/ -1/2 (cos (/ K 2))))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
J
(/ -1/2 (cos (/ K 2)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
-1/2
#s(literal -1/2 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)
(- 0 U)
(-.f64 #s(literal 0 binary64) U)
0
#s(literal 0 binary64)
U
(* J (+ -2 (* K (* K 1/4))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
J
(+ -2 (* K (* K 1/4)))
(+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))
-2
#s(literal -2 binary64)
(* K (* K 1/4))
(*.f64 K (*.f64 K #s(literal 1/4 binary64)))
K
(* K 1/4)
(*.f64 K #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(/ 1 (/ (/ -1/2 (cos (/ K 2))) J))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
1
#s(literal 1 binary64)
(/ (/ -1/2 (cos (/ K 2))) J)
(/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ -1/2 (cos (/ K 2)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
-1/2
#s(literal -1/2 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)
J
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)
(/.f64 (*.f64 J (-.f64 #s(literal -1 binary64) (cos.f64 K))) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/ (* (+ 1 (cos K)) -1) (cos (/ K 2)))
(/.f64 (-.f64 #s(literal -1 binary64) (cos.f64 K)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(* (+ 1 (cos K)) -1)
(-.f64 #s(literal -1 binary64) (cos.f64 K))
(+ 1 (cos K))
(+.f64 #s(literal 1 binary64) (cos.f64 K))
1
#s(literal 1 binary64)
(cos K)
(cos.f64 K)
K
-1
#s(literal -1 binary64)
(cos (/ K 2))
(cos.f64 (/.f64 K #s(literal 2 binary64)))
(/ K 2)
(/.f64 K #s(literal 2 binary64))
2
#s(literal 2 binary64)
J

localize167.0ms (1.7%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(cos.f64 K)
✓accuracy99.9%
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
✓accuracy99.7%
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.4%
(+.f64 #s(literal 1 binary64) (cos.f64 K))
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
✓accuracy99.8%
(/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
✓accuracy100.0%
(+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))
✓accuracy100.0%
(*.f64 K (*.f64 K #s(literal 1/4 binary64)))
✓accuracy100.0%
(*.f64 K #s(literal 1/4 binary64))
✓accuracy97.0%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) U)
✓accuracy100.0%
(/.f64 K #s(literal 2 binary64))
✓accuracy100.0%
(cos.f64 (/.f64 K #s(literal 2 binary64)))
✓accuracy99.8%
(/.f64 J (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓accuracy99.8%
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
Results
110.0ms256×0valid
Compiler

Compiled 146 to 27 computations (81.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-div: 12.0ms (30.3% of total)
ival-cos: 11.0ms (27.8% of total)
ival-mult: 11.0ms (27.8% of total)
ival-add: 3.0ms (7.6% of total)
ival-sub: 2.0ms (5.1% of total)
const: 1.0ms (2.5% of total)
backward-pass: 0.0ms (0% of total)

series17.0ms (0.2%)

Counts
16 → 252
Calls
Call 1
Inputs
#<alt (/ J (/ -1/2 (cos (/ K 2))))>
#<alt (/ -1/2 (cos (/ K 2)))>
#<alt (cos (/ K 2))>
#<alt (/ K 2)>
#<alt (- 0 U)>
#<alt (* J (+ -2 (* K (* K 1/4))))>
#<alt (+ -2 (* K (* K 1/4)))>
#<alt (* K (* K 1/4))>
#<alt (* K 1/4)>
#<alt (/ 1 (/ (/ -1/2 (cos (/ K 2))) J))>
#<alt (/ (/ -1/2 (cos (/ K 2))) J)>
#<alt (* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)>
#<alt (/ (* (+ 1 (cos K)) -1) (cos (/ K 2)))>
#<alt (* (+ 1 (cos K)) -1)>
#<alt (+ 1 (cos K))>
#<alt (cos K)>
Outputs
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt (* -2 (* J (cos (* 1/2 K))))>
#<alt -1/2>
#<alt (- (* -1/16 (pow K 2)) 1/2)>
#<alt (- (* (pow K 2) (- (* -5/768 (pow K 2)) 1/16)) 1/2)>
#<alt (- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (pow K 2)) 5/768)) 1/16)) 1/2)>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (cos (* 1/2 K)))>
#<alt (/ -1/2 (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 (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* -1 U)>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* J (- (* 1/4 (pow K 2)) 2))>
#<alt (* -2 J)>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (+ (* -2 J) (* 1/4 (* J (pow K 2))))>
#<alt (* 1/4 (* J (pow K 2)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* 1/4 (* J (pow K 2)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt (* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))>
#<alt -2>
#<alt (- (* 1/4 (pow K 2)) 2)>
#<alt (- (* 1/4 (pow K 2)) 2)>
#<alt (- (* 1/4 (pow K 2)) 2)>
#<alt (* 1/4 (pow K 2))>
#<alt (* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))>
#<alt (* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))>
#<alt (* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))>
#<alt (* 1/4 (pow K 2))>
#<alt (* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))>
#<alt (* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))>
#<alt (* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 (pow K 2))>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 K)>
#<alt (* 1/4 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 (/ -1/2 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 (* -2 J)>
#<alt (+ (* -2 J) (* -1 (* (pow K 2) (- (* -1/2 J) (* -1/4 J)))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1 (* (pow K 2) (- (* 1/24 J) (+ (* -1/8 (- (* -1/2 J) (* -1/4 J))) (* 1/192 J))))) (* -1 (- (* -1/2 J) (* -1/4 J))))))>
#<alt (+ (* -2 J) (* (pow K 2) (+ (* -1 (- (* -1/2 J) (* -1/4 J))) (* (pow K 2) (+ (* -1 (* (pow K 2) (- (* -1/720 J) (+ (* -1/8 (- (* 1/24 J) (+ (* -1/8 (- (* -1/2 J) (* -1/4 J))) (* 1/192 J)))) (+ (* -1/23040 J) (* 1/384 (- (* -1/2 J) (* -1/4 J)))))))) (* -1 (- (* 1/24 J) (+ (* -1/8 (- (* -1/2 J) (* -1/4 J))) (* 1/192 J)))))))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt (* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))>
#<alt -2>
#<alt (- (* 1/4 (pow K 2)) 2)>
#<alt (- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)>
#<alt (- (* (pow K 2) (+ 1/4 (* (pow K 2) (- (* 1/23040 (pow K 2)) 1/192)))) 2)>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt (* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))>
#<alt -2>
#<alt (- (* 1/2 (pow K 2)) 2)>
#<alt (- (* (pow K 2) (+ 1/2 (* -1/24 (pow K 2)))) 2)>
#<alt (- (* (pow K 2) (+ 1/2 (* (pow K 2) (- (* 1/720 (pow K 2)) 1/24)))) 2)>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt (* -1 (+ 1 (cos K)))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow K 2)))>
#<alt (+ 2 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))>
#<alt (+ 2 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt (+ 1 (cos K))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow K 2)))>
#<alt (+ 1 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))>
#<alt (+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
#<alt (cos K)>
Calls

63 calls:

TimeVariablePointExpression
3.0ms
K
@-inf
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)
1.0ms
K
@inf
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)
1.0ms
J
@0
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)
1.0ms
J
@0
(* J (+ -2 (* K (* K 1/4))))
1.0ms
K
@0
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)

rewrite289.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
3648×*-lowering-*.f32
3648×*-lowering-*.f64
2754×/-lowering-/.f32
2754×/-lowering-/.f64
1220×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02699
112994
287494
3747894
0808894
Stop Event
1×iter limit
1×node limit
Counts
16 → 724
Calls
Call 1
Inputs
(/ J (/ -1/2 (cos (/ K 2))))
(/ -1/2 (cos (/ K 2)))
(cos (/ K 2))
(/ K 2)
(- 0 U)
(* J (+ -2 (* K (* K 1/4))))
(+ -2 (* K (* K 1/4)))
(* K (* K 1/4))
(* K 1/4)
(/ 1 (/ (/ -1/2 (cos (/ K 2))) J))
(/ (/ -1/2 (cos (/ K 2))) J)
(* (/ (* (+ 1 (cos K)) -1) (cos (/ K 2))) J)
(/ (* (+ 1 (cos K)) -1) (cos (/ K 2)))
(* (+ 1 (cos K)) -1)
(+ 1 (cos K))
(cos K)
Outputs
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 J #s(literal 1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 (/.f64 J #s(literal 1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(neg.f64 (*.f64 (/.f64 J #s(literal 1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 J (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
(/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) J))
(/.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) J))
(/.f64 (/.f64 J #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(/.f64 (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) J)) #s(literal 1/2 binary64))
(/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) J))
(/.f64 (*.f64 (/.f64 J #s(literal 1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 (/.f64 J #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 J #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 J (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(/.f64 (/.f64 (/.f64 J #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) J)) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))))) #s(literal -1 binary64))
(*.f64 J (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) J)))
(*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) J)))
(*.f64 #s(literal 2 binary64) (/.f64 J (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 J #s(literal -1/2 binary64)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) J)))
(*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 (/.f64 J #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1 binary64))
(*.f64 #s(literal -2 binary64) (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 J (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal -2 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) J)))
(*.f64 #s(literal -2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))))
(*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)))
(*.f64 #s(literal -1 binary64) (*.f64 (/.f64 J #s(literal 1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (/.f64 J #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) J) (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) J)
(*.f64 (/.f64 J #s(literal -1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (*.f64 J (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) J))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) J) #s(literal -1 binary64)))
(*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) J) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (/.f64 J #s(literal 1/2 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (/.f64 J #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (/.f64 J #s(literal 1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) J) #s(literal -1 binary64)) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 J #s(literal -1 binary64)) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 J (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal -2 binary64))
(*.f64 (/.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) J))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) J) #s(literal 1 binary64)) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (/.f64 J #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 J #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(*.f64 (*.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) J)
(*.f64 (*.f64 (/.f64 J #s(literal 1/2 binary64)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(*.f64 (/.f64 (/.f64 J #s(literal -1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal -1/2 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))) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
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(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.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 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 9 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 K)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))))))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))) (+.f64 (cos.f64 K) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 4 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 K)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 K)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 K)) (-.f64 #s(literal 1 binary64) (cos.f64 K))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))))) (-.f64 #s(literal 1 binary64) (cos.f64 K))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 K)))
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (cos.f64 K) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 K)))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))) (+.f64 (cos.f64 K) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64)))) (neg.f64 (+.f64 (cos.f64 K) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))) (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) #s(literal 3 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K)))) (+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K))) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K)))) (*.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K)))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K)))) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K))))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 K)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K))) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K))))) (+.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K)))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K)))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K)))) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K))))
(*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 K))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) #s(literal 1 binary64)))
(*.f64 (sin.f64 K) (*.f64 (sin.f64 K) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K)))))
(*.f64 (sin.f64 K) (/.f64 (sin.f64 K) (-.f64 #s(literal 1 binary64) (cos.f64 K))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 K) #s(literal -1 binary64))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))))))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 K))))
(*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (cos.f64 K)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))) (-.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))) #s(literal 1 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 (cos.f64 K) #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 K #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 K) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 K) (+.f64 #s(literal 1 binary64) (cos.f64 K)))))
(cos.f64 K)
(*.f64 #s(literal 1 binary64) (cos.f64 K))
(*.f64 (cos.f64 K) #s(literal 1 binary64))

simplify369.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
3968×*-lowering-*.f32
3968×*-lowering-*.f64
2052×+-lowering-+.f64
2052×+-lowering-+.f32
1626×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01831951
15571884
217311814
368441814
080531814
Stop Event
1×iter limit
1×node limit
Counts
252 → 252
Calls
Call 1
Inputs
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
(* -2 (* J (cos (* 1/2 K))))
-1/2
(- (* -1/16 (pow K 2)) 1/2)
(- (* (pow K 2) (- (* -5/768 (pow K 2)) 1/16)) 1/2)
(- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (pow K 2)) 5/768)) 1/16)) 1/2)
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
(/ -1/2 (cos (* 1/2 K)))
1
(+ 1 (* -1/8 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(cos (* 1/2 K))
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* -1 U)
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* J (- (* 1/4 (pow K 2)) 2))
(* -2 J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(* 1/4 (* J (pow K 2)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* 1/4 (* J (pow K 2)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
-2
(- (* 1/4 (pow K 2)) 2)
(- (* 1/4 (pow K 2)) 2)
(- (* 1/4 (pow K 2)) 2)
(* 1/4 (pow K 2))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(* 1/4 (pow K 2))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 (pow K 2))
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 K)
(* 1/4 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))))
(/ -1/2 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))))
(* -2 J)
(+ (* -2 J) (* -1 (* (pow K 2) (- (* -1/2 J) (* -1/4 J)))))
(+ (* -2 J) (* (pow K 2) (+ (* -1 (* (pow K 2) (- (* 1/24 J) (+ (* -1/8 (- (* -1/2 J) (* -1/4 J))) (* 1/192 J))))) (* -1 (- (* -1/2 J) (* -1/4 J))))))
(+ (* -2 J) (* (pow K 2) (+ (* -1 (- (* -1/2 J) (* -1/4 J))) (* (pow K 2) (+ (* -1 (* (pow K 2) (- (* -1/720 J) (+ (* -1/8 (- (* 1/24 J) (+ (* -1/8 (- (* -1/2 J) (* -1/4 J))) (* 1/192 J)))) (+ (* -1/23040 J) (* 1/384 (- (* -1/2 J) (* -1/4 J)))))))) (* -1 (- (* 1/24 J) (+ (* -1/8 (- (* -1/2 J) (* -1/4 J))) (* 1/192 J)))))))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
(* -1 (/ (* J (+ 1 (cos K))) (cos (* 1/2 K))))
-2
(- (* 1/4 (pow K 2)) 2)
(- (* (pow K 2) (+ 1/4 (* -1/192 (pow K 2)))) 2)
(- (* (pow K 2) (+ 1/4 (* (pow K 2) (- (* 1/23040 (pow K 2)) 1/192)))) 2)
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
(* -1 (/ (+ 1 (cos K)) (cos (* 1/2 K))))
-2
(- (* 1/2 (pow K 2)) 2)
(- (* (pow K 2) (+ 1/2 (* -1/24 (pow K 2)))) 2)
(- (* (pow K 2) (+ 1/2 (* (pow K 2) (- (* 1/720 (pow K 2)) 1/24)))) 2)
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
(* -1 (+ 1 (cos K)))
2
(+ 2 (* -1/2 (pow K 2)))
(+ 2 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))
(+ 2 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))
(+ 1 (cos K))
(+ 1 (cos K))
(+ 1 (cos K))
(+ 1 (cos K))
(+ 1 (cos K))
(+ 1 (cos K))
(+ 1 (cos K))
(+ 1 (cos K))
1
(+ 1 (* -1/2 (pow K 2)))
(+ 1 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
(cos K)
Outputs
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* (pow K 2) (+ (* -1/192 (* J (pow K 2))) (* 1/4 J))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (*.f64 K (*.f64 K #s(literal -1/192 binary64)))))))
(+ (* -2 J) (* (pow K 2) (+ (* 1/4 J) (* (pow K 2) (+ (* -1/192 J) (* 1/23040 (* J (pow K 2))))))))
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 (*.f64 K K) (+.f64 (*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal -1/192 binary64) (*.f64 (*.f64 K K) #s(literal 1/23040 binary64))))) (*.f64 J #s(literal 1/4 binary64)))))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(* -2 (* J (cos (* 1/2 K))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
-1/2
#s(literal -1/2 binary64)
(- (* -1/16 (pow K 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 K (*.f64 K #s(literal -1/16 binary64))))
(- (* (pow K 2) (- (* -5/768 (pow K 2)) 1/16)) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/16 binary64) (*.f64 K (*.f64 K #s(literal -5/768 binary64))))))
(- (* (pow K 2) (- (* (pow K 2) (- (* -61/92160 (pow K 2)) 5/768)) 1/16)) 1/2)
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/16 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -5/768 binary64) (*.f64 (*.f64 K K) #s(literal -61/92160 binary64)))))))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/ -1/2 (cos (* 1/2 K)))
(/.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/8 binary64)))
(+ 1 (* (pow K 2) (- (* 1/384 (pow K 2)) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) #s(literal 1/384 binary64))))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/384 (* -1/46080 (pow K 2)))) 1/8)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/384 binary64) (*.f64 (*.f64 K K) #s(literal -1/46080 binary64)))))))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(cos (* 1/2 K))
(cos.f64 (*.f64 #s(literal 1/2 binary64) K))
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* 1/2 K)
(*.f64 #s(literal 1/2 binary64) K)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* -1 U)
(-.f64 #s(literal 0 binary64) U)
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* J (- (* 1/4 (pow K 2)) 2))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* -2 J)
(*.f64 #s(literal -2 binary64) J)
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(+ (* -2 J) (* 1/4 (* J (pow K 2))))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K))))
(* 1/4 (* J (pow K 2)))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* 1/4 (* J (pow K 2)))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
(* (pow K 2) (+ (* -2 (/ J (pow K 2))) (* 1/4 J)))
(*.f64 (*.f64 K K) (*.f64 J (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K)))))
-2
#s(literal -2 binary64)
(- (* 1/4 (pow K 2)) 2)
(+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(- (* 1/4 (pow K 2)) 2)
(+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(- (* 1/4 (pow K 2)) 2)
(+.f64 #s(literal -2 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(* 1/4 (pow K 2))
(*.f64 #s(literal 1/4 binary64) (*.f64 K K))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K K) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K))))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
(*.f64 (*.f64 K K) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -2 binary64) (*.f64 K K))))
(* (pow K 2) (- 1/4 (* 2 (/ 1 (pow K 2)))))
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#s(literal 1 binary64)
(+ 1 (* -1/2 (pow K 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) #s(literal -1/2 binary64)))
(+ 1 (* (pow K 2) (- (* 1/24 (pow K 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 K (*.f64 K (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 K K) #s(literal 1/24 binary64))))))
(+ 1 (* (pow K 2) (- (* (pow K 2) (+ 1/24 (* -1/720 (pow K 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 K K) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 K K) #s(literal -1/720 binary64)))))))
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)
(cos K)
(cos.f64 K)

eval206.0ms (2.1%)

Compiler

Compiled 18397 to 2297 computations (87.5% saved)

prune133.0ms (1.3%)

Pruning

21 alts after pruning (13 fresh and 8 done)

PrunedKeptTotal
New111881126
Fresh055
Picked235
Done055
Total1120211141
Accuracy
100.0%
Counts
1141 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.8%
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 (cos.f64 K) (-.f64 #s(literal 0 binary64) J))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
29.2%
(/.f64 (*.f64 (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)) J) (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))
39.0%
(/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
51.0%
(/.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) J))
✓51.1%
(/.f64 J (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
✓51.0%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
31.3%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
41.6%
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U)
✓41.5%
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
50.8%
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) (cos.f64 K)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
28.9%
(*.f64 (/.f64 (*.f64 J (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64)))) (-.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64))))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))))
29.1%
(*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))) J))
✓85.2%
(*.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))))))
✓51.1%
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
28.9%
(*.f64 J (/.f64 (+.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K #s(literal 1/4 binary64)) (*.f64 K (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))))))
29.2%
(*.f64 J (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)) (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)))))
✓29.8%
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
2.5%
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
✓31.4%
(*.f64 #s(literal -2 binary64) J)
44.6%
(neg.f64 U)
✓9.9%
U
Compiler

Compiled 933 to 412 computations (55.8% saved)

regimes70.0ms (0.7%)

Counts
36 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 #s(literal 1/4 binary64) (*.f64 J (*.f64 K K))))
(/.f64 (*.f64 (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)) J) (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(*.f64 J (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)) (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)))))
(*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))) J))
(*.f64 J (/.f64 (+.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K #s(literal 1/4 binary64)) (*.f64 K (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))))))
(*.f64 (/.f64 (*.f64 J (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64)))) (-.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64))))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(/.f64 J (/.f64 #s(literal -1/2 binary64) (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 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal -2 binary64) J))
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U)
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) (cos.f64 K)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 (cos.f64 K) (-.f64 #s(literal 0 binary64) J))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
(-.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))) U)
(*.f64 (exp.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J))
(/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (hypot.f64 #s(literal 1 binary64) (/.f64 (/.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 J (*.f64 J #s(literal 4 binary64)))) (+.f64 #s(literal 0 binary64) (*.f64 J #s(literal 2 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 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))) (*.f64 J (*.f64 J #s(literal 4 binary64))))) (+.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) (*.f64 J #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 J (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K))) (/.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 U U)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K)))) (*.f64 (*.f64 J J) (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 3 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

6 calls:

13.0ms
J
12.0ms
(/.f64 K #s(literal 2 binary64))
11.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
11.0ms
U
10.0ms
K
Results
AccuracySegmentsBranch
92.5%2J
85.2%1K
92.3%2U
98.8%2(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64)))))
85.2%1(cos.f64 (/.f64 K #s(literal 2 binary64)))
85.2%1(/.f64 K #s(literal 2 binary64))
Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes59.0ms (0.6%)

Counts
30 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 #s(literal 1/4 binary64) (*.f64 J (*.f64 K K))))
(/.f64 (*.f64 (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)) J) (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(*.f64 J (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)) (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)))))
(*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))) J))
(*.f64 J (/.f64 (+.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K #s(literal 1/4 binary64)) (*.f64 K (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))))))
(*.f64 (/.f64 (*.f64 J (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64)))) (-.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64))))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(/.f64 J (/.f64 #s(literal -1/2 binary64) (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 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal -2 binary64) J))
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U)
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) (cos.f64 K)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 K)) #s(literal -1 binary64)) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J)
(/.f64 (*.f64 #s(literal -2 binary64) (*.f64 J (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 K))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) J) (*.f64 (cos.f64 K) (-.f64 #s(literal 0 binary64) J))) (cos.f64 (*.f64 #s(literal 1/2 binary64) K)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) J))
(-.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) #s(literal 2 binary64)) (/.f64 (*.f64 J J) U))) U)
(*.f64 (exp.f64 (log.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) J))
(/.f64 (*.f64 #s(literal -2 binary64) J) (pow.f64 (pow.f64 (cos.f64 (/.f64 K #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
Outputs
(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U)
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
Calls

5 calls:

9.0ms
(/.f64 K #s(literal 2 binary64))
9.0ms
U
8.0ms
J
8.0ms
K
8.0ms
(cos.f64 (/.f64 K #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
60.1%4K
60.1%4(/.f64 K #s(literal 2 binary64))
59.4%3(cos.f64 (/.f64 K #s(literal 2 binary64)))
75.4%2U
75.9%2J
Compiler

Compiled 25 to 20 computations (20% saved)

regimes8.0ms (0.1%)

Counts
21 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 #s(literal 1/4 binary64) (*.f64 J (*.f64 K K))))
(/.f64 (*.f64 (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)) J) (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(*.f64 J (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)) (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)))))
(*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))) J))
(*.f64 J (/.f64 (+.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K #s(literal 1/4 binary64)) (*.f64 K (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))))))
(*.f64 (/.f64 (*.f64 J (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64)))) (-.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64))))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
(/.f64 J (/.f64 #s(literal -1/2 binary64) (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 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))) J))
(/.f64 (*.f64 #s(literal -2 binary64) J) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 K #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal -2 binary64) J))
Outputs
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J))
Calls

1 calls:

6.0ms
J
Results
AccuracySegmentsBranch
75.9%2J
Compiler

Compiled 4 to 3 computations (25% saved)

regimes13.0ms (0.1%)

Counts
14 → 2
Calls
Call 1
Inputs
U
(neg.f64 U)
(*.f64 #s(literal -2 binary64) J)
(-.f64 #s(literal 0 binary64) U)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) J))
(*.f64 J (*.f64 #s(literal 1/4 binary64) (*.f64 K K)))
(*.f64 J (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))
(-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U)
(+.f64 (*.f64 #s(literal -2 binary64) J) (*.f64 #s(literal 1/4 binary64) (*.f64 J (*.f64 K K))))
(/.f64 (*.f64 (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)) J) (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(*.f64 J (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)) (+.f64 (*.f64 K (*.f64 K (*.f64 (*.f64 K K) #s(literal 1/16 binary64)))) #s(literal -4 binary64)))))
(*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64))))) J))
(*.f64 J (/.f64 (+.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K #s(literal 1/4 binary64)) (*.f64 K (+.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) #s(literal 2 binary64)))))))
(*.f64 (/.f64 (*.f64 J (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 K K) (*.f64 K K)) #s(literal -1/16 binary64)))) (-.f64 #s(literal -8 binary64) (*.f64 (*.f64 K (*.f64 K K)) (*.f64 (*.f64 K (*.f64 K K)) #s(literal 1/64 binary64))))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 K (*.f64 K #s(literal 1/4 binary64))) (+.f64 #s(literal -2 binary64) (*.f64 K (*.f64 K #s(literal 1/4 binary64)))))))
Outputs
(*.f64 #s(literal -2 binary64) J)
(neg.f64 U)
Calls

2 calls:

8.0ms
U
5.0ms
J
Results
AccuracySegmentsBranch
59.8%2U
59.2%2J
Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

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

3 calls:

2.0ms
J
2.0ms
K
2.0ms
U
Results
AccuracySegmentsBranch
44.6%1K
44.6%1J
44.6%1U
Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

3 calls:

1.0ms
U
1.0ms
K
1.0ms
J
Results
AccuracySegmentsBranch
9.9%1J
9.9%1U
9.9%1K
Compiler

Compiled 12 to 9 computations (25% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-inf
-9.855443488397135e+304
Compiler

Compiled 33 to 22 computations (33.3% saved)

bsearch24.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
2.229930727420267e-87
2.7979581363930476e-85
Results
18.0ms112×0valid
Compiler

Compiled 285 to 211 computations (26% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-mult: 7.0ms (48.9% of total)
ival-cos: 3.0ms (21% of total)
ival-div: 2.0ms (14% of total)
ival-add: 1.0ms (7% of total)
ival-sqrt: 1.0ms (7% of total)
ival-pow: 1.0ms (7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch60.0ms (0.6%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
31.0ms
2.229930727420267e-87
2.7979581363930476e-85
Results
27.0ms112×0valid
Compiler

Compiled 208 to 155 computations (25.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 4.0ms (38% of total)
ival-cos: 2.0ms (19% of total)
ival-div: 1.0ms (9.5% of total)
ival-add: 1.0ms (9.5% of total)
ival-sqrt: 1.0ms (9.5% of total)
ival-pow: 1.0ms (9.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
17.0ms
3.521967176344865e-38
8.054781661966985e-37
Results
14.0ms112×0valid
Compiler

Compiled 124 to 99 computations (20.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 4.0ms (40.1% of total)
ival-cos: 2.0ms (20% of total)
ival-div: 1.0ms (10% of total)
ival-add: 1.0ms (10% of total)
ival-sqrt: 1.0ms (10% of total)
ival-pow: 1.0ms (10% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify33.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
051115
174115
278115
379115
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) (*.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 4899441623513947/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(if (<=.f64 J #s(literal 3849561275618101/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(if (<=.f64 U #s(literal 221493496140773/5986310706507378352962293074805895248510699696029696 binary64)) (*.f64 #s(literal -2 binary64) J) (neg.f64 U))
(neg.f64 U)
U
Outputs
(if (<=.f64 (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 U (*.f64 (*.f64 #s(literal 2 binary64) J) (cos.f64 (/.f64 K #s(literal 2 binary64))))) #s(literal 2 binary64))))) #s(literal -inf.0 binary64)) (neg.f64 U) (*.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 (*.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) (*.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 4899441623513947/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 binary64)) (-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.f64 J J)) #s(literal -2 binary64)) U) U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(if (<=.f64 J #s(literal 4899441623513947/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 binary64)) (-.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 K #s(literal 2 binary64)))))) (*.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 3849561275618101/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 binary64)) (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 J J) U)) U) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) K)) (*.f64 #s(literal -2 binary64) J)))
(if (<=.f64 J #s(literal 3849561275618101/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 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 U #s(literal 221493496140773/5986310706507378352962293074805895248510699696029696 binary64)) (*.f64 #s(literal -2 binary64) J) (neg.f64 U))
(if (<=.f64 U #s(literal 221493496140773/5986310706507378352962293074805895248510699696029696 binary64)) (*.f64 #s(literal -2 binary64) J) (-.f64 #s(literal 0 binary64) U))
(neg.f64 U)
(-.f64 #s(literal 0 binary64) U)
U

soundness1.5s (14.9%)

Rules
8150×*-lowering-*.f32
8150×*-lowering-*.f64
6680×*-lowering-*.f32
6680×*-lowering-*.f64
3936×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05817600
121517237
084747237
02699
112994
287494
3747894
0808894
01724
13321
27821
320421
461221
5112621
6154521
7160721
8162521
9164321
10165121
11165321
12165321
0165321
043206
1237193
22079192
08783192
03897079
113706736
258746706
085776706
Stop Event
1×fuel
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 242 to 145 computations (40.1% saved)

preprocess129.0ms (1.3%)

Remove

(abs K)

Compiler

Compiled 1376 to 656 computations (52.3% saved)

end0.0ms (0%)

Profiling

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