Average Error: 18.4 → 18.5
Time: 25.9s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(\sqrt{1 + {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)\]
\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}
↓
\left(\sqrt{1 + {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)
double f(double J, double K, double U) {
        double r6856289 = -2.0;
        double r6856290 = J;
        double r6856291 = r6856289 * r6856290;
        double r6856292 = K;
        double r6856293 = 2.0;
        double r6856294 = r6856292 / r6856293;
        double r6856295 = cos(r6856294);
        double r6856296 = r6856291 * r6856295;
        double r6856297 = 1.0;
        double r6856298 = U;
        double r6856299 = r6856293 * r6856290;
        double r6856300 = r6856299 * r6856295;
        double r6856301 = r6856298 / r6856300;
        double r6856302 = pow(r6856301, r6856293);
        double r6856303 = r6856297 + r6856302;
        double r6856304 = sqrt(r6856303);
        double r6856305 = r6856296 * r6856304;
        return r6856305;
}
↓
double f(double J, double K, double U) {
        double r6856306 = 1.0;
        double r6856307 = U;
        double r6856308 = J;
        double r6856309 = 2.0;
        double r6856310 = r6856308 * r6856309;
        double r6856311 = K;
        double r6856312 = r6856311 / r6856309;
        double r6856313 = cos(r6856312);
        double r6856314 = r6856310 * r6856313;
        double r6856315 = r6856307 / r6856314;
        double r6856316 = pow(r6856315, r6856309);
        double r6856317 = r6856306 + r6856316;
        double r6856318 = sqrt(r6856317);
        double r6856319 = r6856318 * r6856313;
        double r6856320 = -2.0;
        double r6856321 = r6856320 * r6856308;
        double r6856322 = r6856319 * r6856321;
        return r6856322;
}

Error

Bits error versus J

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.4

    \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
  2. Using strategy rm

  3. Applied associate-*l*18.5

    \[\leadsto \color{blue}{\left(-2 \cdot J\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right)}\]

  4. Final simplification18.5

    \[\leadsto \left(\sqrt{1 + {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \left(-2 \cdot J\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))