Average Error: 17.2 → 9.7
Time: 32.0s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le -6.414707636852215 \cdot 10^{+301}:\\ \;\;\;\;-U\\ \mathbf{elif}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le 1.3904547616940519 \cdot 10^{+307}:\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\sqrt{1 + \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}} \cdot \cos \left(\frac{K}{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array}\]
\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}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le -6.414707636852215 \cdot 10^{+301}:\\
\;\;\;\;-U\\

\mathbf{elif}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le 1.3904547616940519 \cdot 10^{+307}:\\
\;\;\;\;\left(-2 \cdot J\right) \cdot \left(\sqrt{1 + \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}} \cdot \cos \left(\frac{K}{2}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;-U\\

\end{array}
double f(double J, double K, double U) {
        double r4494104 = -2.0;
        double r4494105 = J;
        double r4494106 = r4494104 * r4494105;
        double r4494107 = K;
        double r4494108 = 2.0;
        double r4494109 = r4494107 / r4494108;
        double r4494110 = cos(r4494109);
        double r4494111 = r4494106 * r4494110;
        double r4494112 = 1.0;
        double r4494113 = U;
        double r4494114 = r4494108 * r4494105;
        double r4494115 = r4494114 * r4494110;
        double r4494116 = r4494113 / r4494115;
        double r4494117 = pow(r4494116, r4494108);
        double r4494118 = r4494112 + r4494117;
        double r4494119 = sqrt(r4494118);
        double r4494120 = r4494111 * r4494119;
        return r4494120;
}
↓
double f(double J, double K, double U) {
        double r4494121 = U;
        double r4494122 = J;
        double r4494123 = 2.0;
        double r4494124 = r4494122 * r4494123;
        double r4494125 = K;
        double r4494126 = r4494125 / r4494123;
        double r4494127 = cos(r4494126);
        double r4494128 = r4494124 * r4494127;
        double r4494129 = r4494121 / r4494128;
        double r4494130 = pow(r4494129, r4494123);
        double r4494131 = 1.0;
        double r4494132 = r4494130 + r4494131;
        double r4494133 = sqrt(r4494132);
        double r4494134 = -2.0;
        double r4494135 = r4494134 * r4494122;
        double r4494136 = r4494127 * r4494135;
        double r4494137 = r4494133 * r4494136;
        double r4494138 = -6.414707636852215e+301;
        bool r4494139 = r4494137 <= r4494138;
        double r4494140 = -r4494121;
        double r4494141 = 1.3904547616940519e+307;
        bool r4494142 = r4494137 <= r4494141;
        double r4494143 = r4494121 / r4494123;
        double r4494144 = r4494127 * r4494122;
        double r4494145 = r4494143 / r4494144;
        double r4494146 = r4494145 * r4494145;
        double r4494147 = r4494131 + r4494146;
        double r4494148 = sqrt(r4494147);
        double r4494149 = r4494148 * r4494127;
        double r4494150 = r4494135 * r4494149;
        double r4494151 = r4494142 ? r4494150 : r4494140;
        double r4494152 = r4494139 ? r4494140 : r4494151;
        return r4494152;
}

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 (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) < -6.414707636852215e+301 or 1.3904547616940519e+307 < (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

    1. Initial program 58.7

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

    3. Applied associate-*l*58.7

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

    4. Simplified58.7

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

    5. Taylor expanded around 0 32.9

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

    6. Simplified32.9

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

    if -6.414707636852215e+301 < (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))) < 1.3904547616940519e+307

    1. Initial program 0.1

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

    3. Applied associate-*l*0.2

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

    4. Simplified0.2

      \[\leadsto \left(-2 \cdot J\right) \cdot \color{blue}{\left(\sqrt{1 + \frac{\frac{U}{2}}{J \cdot \cos \left(\frac{K}{2}\right)} \cdot \frac{\frac{U}{2}}{J \cdot \cos \left(\frac{K}{2}\right)}} \cdot \cos \left(\frac{K}{2}\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le -6.414707636852215 \cdot 10^{+301}:\\ \;\;\;\;-U\\ \mathbf{elif}\;\sqrt{{\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2} + 1} \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right) \le 1.3904547616940519 \cdot 10^{+307}:\\ \;\;\;\;\left(-2 \cdot J\right) \cdot \left(\sqrt{1 + \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J} \cdot \frac{\frac{U}{2}}{\cos \left(\frac{K}{2}\right) \cdot J}} \cdot \cos \left(\frac{K}{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-U\\ \end{array}\]

Reproduce

herbie shell --seed 2019138 
(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)))))