Average Error: 17.3 → 0.4
Time: 8.0s
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 r150680 = J;
        double r150681 = l;
        double r150682 = exp(r150681);
        double r150683 = -r150681;
        double r150684 = exp(r150683);
        double r150685 = r150682 - r150684;
        double r150686 = r150680 * r150685;
        double r150687 = K;
        double r150688 = 2.0;
        double r150689 = r150687 / r150688;
        double r150690 = cos(r150689);
        double r150691 = r150686 * r150690;
        double r150692 = U;
        double r150693 = r150691 + r150692;
        return r150693;
}
↓
double f(double J, double l, double K, double U) {
        double r150694 = J;
        double r150695 = 0.3333333333333333;
        double r150696 = l;
        double r150697 = 3.0;
        double r150698 = pow(r150696, r150697);
        double r150699 = r150695 * r150698;
        double r150700 = 0.016666666666666666;
        double r150701 = 5.0;
        double r150702 = pow(r150696, r150701);
        double r150703 = r150700 * r150702;
        double r150704 = 2.0;
        double r150705 = r150704 * r150696;
        double r150706 = r150703 + r150705;
        double r150707 = r150699 + r150706;
        double r150708 = K;
        double r150709 = 2.0;
        double r150710 = r150708 / r150709;
        double r150711 = cos(r150710);
        double r150712 = r150707 * r150711;
        double r150713 = r150694 * r150712;
        double r150714 = U;
        double r150715 = r150713 + r150714;
        return r150715;
}

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

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020020 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))