Average Error: 17.9 → 17.9
Time: 23.8s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\left(\sqrt{1 + \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot -2\right)\right) \cdot J\]
\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 + \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot -2\right)\right) \cdot J
double f(double J, double K, double U) {
        double r4202021 = -2.0;
        double r4202022 = J;
        double r4202023 = r4202021 * r4202022;
        double r4202024 = K;
        double r4202025 = 2.0;
        double r4202026 = r4202024 / r4202025;
        double r4202027 = cos(r4202026);
        double r4202028 = r4202023 * r4202027;
        double r4202029 = 1.0;
        double r4202030 = U;
        double r4202031 = r4202025 * r4202022;
        double r4202032 = r4202031 * r4202027;
        double r4202033 = r4202030 / r4202032;
        double r4202034 = pow(r4202033, r4202025);
        double r4202035 = r4202029 + r4202034;
        double r4202036 = sqrt(r4202035);
        double r4202037 = r4202028 * r4202036;
        return r4202037;
}
↓
double f(double J, double K, double U) {
        double r4202038 = 1.0;
        double r4202039 = U;
        double r4202040 = 2.0;
        double r4202041 = J;
        double r4202042 = r4202040 * r4202041;
        double r4202043 = K;
        double r4202044 = r4202043 / r4202040;
        double r4202045 = cos(r4202044);
        double r4202046 = r4202042 * r4202045;
        double r4202047 = r4202039 / r4202046;
        double r4202048 = r4202047 * r4202047;
        double r4202049 = r4202038 + r4202048;
        double r4202050 = sqrt(r4202049);
        double r4202051 = -2.0;
        double r4202052 = r4202045 * r4202051;
        double r4202053 = r4202050 * r4202052;
        double r4202054 = r4202053 * r4202041;
        return r4202054;
}

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 17.9

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

  2. Simplified17.9

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

  4. Applied associate-*l*17.9

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

  5. Final simplification17.9

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

Reproduce

herbie shell --seed 2019153 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))