Average Error: 17.4 → 0.3
Time: 41.7s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left(\frac{1}{60} \cdot {\ell}^{5} + \left(2 + \left(\ell \cdot \ell\right) \cdot \frac{1}{3}\right) \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left(\frac{1}{60} \cdot {\ell}^{5} + \left(2 + \left(\ell \cdot \ell\right) \cdot \frac{1}{3}\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 r4434753 = J;
        double r4434754 = l;
        double r4434755 = exp(r4434754);
        double r4434756 = -r4434754;
        double r4434757 = exp(r4434756);
        double r4434758 = r4434755 - r4434757;
        double r4434759 = r4434753 * r4434758;
        double r4434760 = K;
        double r4434761 = 2.0;
        double r4434762 = r4434760 / r4434761;
        double r4434763 = cos(r4434762);
        double r4434764 = r4434759 * r4434763;
        double r4434765 = U;
        double r4434766 = r4434764 + r4434765;
        return r4434766;
}
↓
double f(double J, double l, double K, double U) {
        double r4434767 = 0.016666666666666666;
        double r4434768 = l;
        double r4434769 = 5.0;
        double r4434770 = pow(r4434768, r4434769);
        double r4434771 = r4434767 * r4434770;
        double r4434772 = 2.0;
        double r4434773 = r4434768 * r4434768;
        double r4434774 = 0.3333333333333333;
        double r4434775 = r4434773 * r4434774;
        double r4434776 = r4434772 + r4434775;
        double r4434777 = r4434776 * r4434768;
        double r4434778 = r4434771 + r4434777;
        double r4434779 = J;
        double r4434780 = r4434778 * r4434779;
        double r4434781 = K;
        double r4434782 = r4434781 / r4434772;
        double r4434783 = cos(r4434782);
        double r4434784 = r4434780 * r4434783;
        double r4434785 = U;
        double r4434786 = r4434784 + r4434785;
        return r4434786;
}

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 17.4

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

  2. Taylor expanded around 0 0.3

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

  3. Simplified0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019142 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))