Average Error: 17.4 → 0.3
Time: 19.0s
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 r94750 = J;
        double r94751 = l;
        double r94752 = exp(r94751);
        double r94753 = -r94751;
        double r94754 = exp(r94753);
        double r94755 = r94752 - r94754;
        double r94756 = r94750 * r94755;
        double r94757 = K;
        double r94758 = 2.0;
        double r94759 = r94757 / r94758;
        double r94760 = cos(r94759);
        double r94761 = r94756 * r94760;
        double r94762 = U;
        double r94763 = r94761 + r94762;
        return r94763;
}
↓
double f(double J, double l, double K, double U) {
        double r94764 = J;
        double r94765 = 0.3333333333333333;
        double r94766 = l;
        double r94767 = 3.0;
        double r94768 = pow(r94766, r94767);
        double r94769 = r94765 * r94768;
        double r94770 = 0.016666666666666666;
        double r94771 = 5.0;
        double r94772 = pow(r94766, r94771);
        double r94773 = r94770 * r94772;
        double r94774 = 2.0;
        double r94775 = r94774 * r94766;
        double r94776 = r94773 + r94775;
        double r94777 = r94769 + r94776;
        double r94778 = K;
        double r94779 = 2.0;
        double r94780 = r94778 / r94779;
        double r94781 = cos(r94780);
        double r94782 = r94777 * r94781;
        double r94783 = r94764 * r94782;
        double r94784 = U;
        double r94785 = r94783 + r94784;
        return r94785;
}

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

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  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 2019308 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))