Average Error: 17.2 → 0.3
Time: 7.7s
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 r118749 = J;
        double r118750 = l;
        double r118751 = exp(r118750);
        double r118752 = -r118750;
        double r118753 = exp(r118752);
        double r118754 = r118751 - r118753;
        double r118755 = r118749 * r118754;
        double r118756 = K;
        double r118757 = 2.0;
        double r118758 = r118756 / r118757;
        double r118759 = cos(r118758);
        double r118760 = r118755 * r118759;
        double r118761 = U;
        double r118762 = r118760 + r118761;
        return r118762;
}
↓
double f(double J, double l, double K, double U) {
        double r118763 = J;
        double r118764 = 0.3333333333333333;
        double r118765 = l;
        double r118766 = 3.0;
        double r118767 = pow(r118765, r118766);
        double r118768 = r118764 * r118767;
        double r118769 = 0.016666666666666666;
        double r118770 = 5.0;
        double r118771 = pow(r118765, r118770);
        double r118772 = r118769 * r118771;
        double r118773 = 2.0;
        double r118774 = r118773 * r118765;
        double r118775 = r118772 + r118774;
        double r118776 = r118768 + r118775;
        double r118777 = K;
        double r118778 = 2.0;
        double r118779 = r118777 / r118778;
        double r118780 = cos(r118779);
        double r118781 = r118776 * r118780;
        double r118782 = r118763 * r118781;
        double r118783 = U;
        double r118784 = r118782 + r118783;
        return r118784;
}

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 17.2

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

  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 associate-*l*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))