Average Error: 17.8 → 0.4
Time: 42.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \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
double f(double J, double l, double K, double U) {
        double r77763 = J;
        double r77764 = l;
        double r77765 = exp(r77764);
        double r77766 = -r77764;
        double r77767 = exp(r77766);
        double r77768 = r77765 - r77767;
        double r77769 = r77763 * r77768;
        double r77770 = K;
        double r77771 = 2.0;
        double r77772 = r77770 / r77771;
        double r77773 = cos(r77772);
        double r77774 = r77769 * r77773;
        double r77775 = U;
        double r77776 = r77774 + r77775;
        return r77776;
}
↓
double f(double J, double l, double K, double U) {
        double r77777 = J;
        double r77778 = 0.3333333333333333;
        double r77779 = l;
        double r77780 = 3.0;
        double r77781 = pow(r77779, r77780);
        double r77782 = r77778 * r77781;
        double r77783 = 0.016666666666666666;
        double r77784 = 5.0;
        double r77785 = pow(r77779, r77784);
        double r77786 = r77783 * r77785;
        double r77787 = 2.0;
        double r77788 = r77787 * r77779;
        double r77789 = r77786 + r77788;
        double r77790 = r77782 + r77789;
        double r77791 = r77777 * r77790;
        double r77792 = K;
        double r77793 = 2.0;
        double r77794 = r77792 / r77793;
        double r77795 = cos(r77794);
        double r77796 = r77791 * r77795;
        double r77797 = U;
        double r77798 = r77796 + r77797;
        return r77798;
}

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 17.8

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

  2. Taylor expanded around 0 0.4

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

  3. Final simplification0.4

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

Reproduce

herbie shell --seed 2019326 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))