Average Error: 17.6 → 0.5
Time: 8.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r134761 = J;
        double r134762 = l;
        double r134763 = exp(r134762);
        double r134764 = -r134762;
        double r134765 = exp(r134764);
        double r134766 = r134763 - r134765;
        double r134767 = r134761 * r134766;
        double r134768 = K;
        double r134769 = 2.0;
        double r134770 = r134768 / r134769;
        double r134771 = cos(r134770);
        double r134772 = r134767 * r134771;
        double r134773 = U;
        double r134774 = r134772 + r134773;
        return r134774;
}
↓
double f(double J, double l, double K, double U) {
        double r134775 = J;
        double r134776 = 0.3333333333333333;
        double r134777 = l;
        double r134778 = 3.0;
        double r134779 = pow(r134777, r134778);
        double r134780 = r134776 * r134779;
        double r134781 = 0.016666666666666666;
        double r134782 = 5.0;
        double r134783 = pow(r134777, r134782);
        double r134784 = r134781 * r134783;
        double r134785 = 2.0;
        double r134786 = r134785 * r134777;
        double r134787 = r134784 + r134786;
        double r134788 = r134780 + r134787;
        double r134789 = K;
        double r134790 = 2.0;
        double r134791 = r134789 / r134790;
        double r134792 = cos(r134791);
        double r134793 = r134788 * r134792;
        double r134794 = r134775 * r134793;
        double r134795 = U;
        double r134796 = r134794 + r134795;
        return r134796;
}

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 17.6

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

  2. Taylor expanded around 0 0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))