Average Error: 17.3 → 0.4
Time: 31.3s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3} + 2\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3} + 2\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r4071757 = J;
        double r4071758 = l;
        double r4071759 = exp(r4071758);
        double r4071760 = -r4071758;
        double r4071761 = exp(r4071760);
        double r4071762 = r4071759 - r4071761;
        double r4071763 = r4071757 * r4071762;
        double r4071764 = K;
        double r4071765 = 2.0;
        double r4071766 = r4071764 / r4071765;
        double r4071767 = cos(r4071766);
        double r4071768 = r4071763 * r4071767;
        double r4071769 = U;
        double r4071770 = r4071768 + r4071769;
        return r4071770;
}
↓
double f(double J, double l, double K, double U) {
        double r4071771 = l;
        double r4071772 = 5.0;
        double r4071773 = pow(r4071771, r4071772);
        double r4071774 = 0.016666666666666666;
        double r4071775 = r4071773 * r4071774;
        double r4071776 = r4071771 * r4071771;
        double r4071777 = 0.3333333333333333;
        double r4071778 = r4071776 * r4071777;
        double r4071779 = 2.0;
        double r4071780 = r4071778 + r4071779;
        double r4071781 = r4071780 * r4071771;
        double r4071782 = r4071775 + r4071781;
        double r4071783 = J;
        double r4071784 = r4071782 * r4071783;
        double r4071785 = K;
        double r4071786 = r4071785 / r4071779;
        double r4071787 = cos(r4071786);
        double r4071788 = r4071784 * r4071787;
        double r4071789 = U;
        double r4071790 = r4071788 + r4071789;
        return r4071790;
}

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 0.4

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

  3. Simplified0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019134 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))