Average Error: 17.3 → 0.5
Time: 31.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\log \left(\sqrt[3]{e^{{\ell}^{3}}}\right) + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\log \left(\sqrt[3]{e^{{\ell}^{3}}}\right) + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r79157 = J;
        double r79158 = l;
        double r79159 = exp(r79158);
        double r79160 = -r79158;
        double r79161 = exp(r79160);
        double r79162 = r79159 - r79161;
        double r79163 = r79157 * r79162;
        double r79164 = K;
        double r79165 = 2.0;
        double r79166 = r79164 / r79165;
        double r79167 = cos(r79166);
        double r79168 = r79163 * r79167;
        double r79169 = U;
        double r79170 = r79168 + r79169;
        return r79170;
}
↓
double f(double J, double l, double K, double U) {
        double r79171 = J;
        double r79172 = l;
        double r79173 = 3.0;
        double r79174 = pow(r79172, r79173);
        double r79175 = exp(r79174);
        double r79176 = cbrt(r79175);
        double r79177 = log(r79176);
        double r79178 = 0.016666666666666666;
        double r79179 = 5.0;
        double r79180 = pow(r79172, r79179);
        double r79181 = r79178 * r79180;
        double r79182 = 2.0;
        double r79183 = r79182 * r79172;
        double r79184 = r79181 + r79183;
        double r79185 = r79177 + r79184;
        double r79186 = r79171 * r79185;
        double r79187 = K;
        double r79188 = 2.0;
        double r79189 = r79187 / r79188;
        double r79190 = cos(r79189);
        double r79191 = r79186 * r79190;
        double r79192 = U;
        double r79193 = r79191 + r79192;
        return r79193;
}

Error

Bits error versus J

Bits error versus l

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 17.3

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

  2. Taylor expanded around 0 0.3

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  3. Using strategy rm

  4. Applied add-log-exp0.5

    \[\leadsto \left(J \cdot \left(\color{blue}{\log \left(e^{\frac{1}{3} \cdot {\ell}^{3}}\right)} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  5. Simplified0.5

    \[\leadsto \left(J \cdot \left(\log \color{blue}{\left(\sqrt[3]{e^{{\ell}^{3}}}\right)} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  6. Final simplification0.5

    \[\leadsto \left(J \cdot \left(\log \left(\sqrt[3]{e^{{\ell}^{3}}}\right) + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Reproduce

herbie shell --seed 2019199 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))