Average Error: 17.4 → 17.2
Time: 38.7s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;J \le -7.065412618436453 \cdot 10^{-178}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\ \mathbf{elif}\;J \le -3.5882868254156677 \cdot 10^{-244}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \le 5.818795322276243 \cdot 10^{-280}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\ \mathbf{elif}\;J \le 2.7142743861140305 \cdot 10^{-203}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\ \end{array}\]
\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}}
↓
\begin{array}{l}
\mathbf{if}\;J \le -7.065412618436453 \cdot 10^{-178}:\\
\;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\

\mathbf{elif}\;J \le -3.5882868254156677 \cdot 10^{-244}:\\
\;\;\;\;-U\\

\mathbf{elif}\;J \le 5.818795322276243 \cdot 10^{-280}:\\
\;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\

\mathbf{elif}\;J \le 2.7142743861140305 \cdot 10^{-203}:\\
\;\;\;\;-U\\

\mathbf{else}:\\
\;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\

\end{array}
double f(double J, double K, double U) {
        double r6146133 = -2.0;
        double r6146134 = J;
        double r6146135 = r6146133 * r6146134;
        double r6146136 = K;
        double r6146137 = 2.0;
        double r6146138 = r6146136 / r6146137;
        double r6146139 = cos(r6146138);
        double r6146140 = r6146135 * r6146139;
        double r6146141 = 1.0;
        double r6146142 = U;
        double r6146143 = r6146137 * r6146134;
        double r6146144 = r6146143 * r6146139;
        double r6146145 = r6146142 / r6146144;
        double r6146146 = pow(r6146145, r6146137);
        double r6146147 = r6146141 + r6146146;
        double r6146148 = sqrt(r6146147);
        double r6146149 = r6146140 * r6146148;
        return r6146149;
}
↓
double f(double J, double K, double U) {
        double r6146150 = J;
        double r6146151 = -7.065412618436453e-178;
        bool r6146152 = r6146150 <= r6146151;
        double r6146153 = -2.0;
        double r6146154 = r6146153 * r6146150;
        double r6146155 = U;
        double r6146156 = r6146155 / r6146150;
        double r6146157 = 2.0;
        double r6146158 = r6146155 / r6146157;
        double r6146159 = K;
        double r6146160 = r6146159 / r6146157;
        double r6146161 = cos(r6146160);
        double r6146162 = r6146161 * r6146150;
        double r6146163 = r6146158 / r6146162;
        double r6146164 = r6146156 * r6146163;
        double r6146165 = 0.5;
        double r6146166 = r6146165 / r6146161;
        double r6146167 = r6146164 * r6146166;
        double r6146168 = 1.0;
        double r6146169 = r6146167 + r6146168;
        double r6146170 = sqrt(r6146169);
        double r6146171 = r6146154 * r6146170;
        double r6146172 = r6146171 * r6146161;
        double r6146173 = -3.5882868254156677e-244;
        bool r6146174 = r6146150 <= r6146173;
        double r6146175 = -r6146155;
        double r6146176 = 5.818795322276243e-280;
        bool r6146177 = r6146150 <= r6146176;
        double r6146178 = 2.7142743861140305e-203;
        bool r6146179 = r6146150 <= r6146178;
        double r6146180 = r6146179 ? r6146175 : r6146172;
        double r6146181 = r6146177 ? r6146172 : r6146180;
        double r6146182 = r6146174 ? r6146175 : r6146181;
        double r6146183 = r6146152 ? r6146172 : r6146182;
        return r6146183;
}

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. Split input into 2 regimes

  2. if J < -7.065412618436453e-178 or -3.5882868254156677e-244 < J < 5.818795322276243e-280 or 2.7142743861140305e-203 < J

    1. Initial program 14.9

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

    3. Applied associate-*l*14.9

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

    4. Simplified14.9

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

    6. Applied associate-*r*14.9

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

    8. Applied div-inv14.9

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

    9. Applied times-frac14.9

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

    10. Applied associate-*r*14.9

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

    if -7.065412618436453e-178 < J < -3.5882868254156677e-244 or 5.818795322276243e-280 < J < 2.7142743861140305e-203

    1. Initial program 36.7

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

    3. Applied associate-*l*36.7

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

    4. Simplified36.7

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

    6. Applied associate-*r*36.7

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

    8. Applied div-inv36.7

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

    9. Applied times-frac36.7

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

    10. Applied associate-*r*36.7

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

    11. Taylor expanded around 0 34.8

      \[\leadsto \color{blue}{-1 \cdot U}\]

    12. Simplified34.8

      \[\leadsto \color{blue}{-U}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification17.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;J \le -7.065412618436453 \cdot 10^{-178}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\ \mathbf{elif}\;J \le -3.5882868254156677 \cdot 10^{-244}:\\ \;\;\;\;-U\\ \mathbf{elif}\;J \le 5.818795322276243 \cdot 10^{-280}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\ \mathbf{elif}\;J \le 2.7142743861140305 \cdot 10^{-203}:\\ \;\;\;\;-U\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \sqrt{\left(\frac{U}{J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}\right) \cdot \frac{\frac{1}{2}}{\cos \left(\frac{K}{2}\right)} + 1}\right) \cdot \cos \left(\frac{K}{2}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(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)))))