Average Error: 17.1 → 0.4
Time: 28.6s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right) + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right) + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r86709 = J;
        double r86710 = l;
        double r86711 = exp(r86710);
        double r86712 = -r86710;
        double r86713 = exp(r86712);
        double r86714 = r86711 - r86713;
        double r86715 = r86709 * r86714;
        double r86716 = K;
        double r86717 = 2.0;
        double r86718 = r86716 / r86717;
        double r86719 = cos(r86718);
        double r86720 = r86715 * r86719;
        double r86721 = U;
        double r86722 = r86720 + r86721;
        return r86722;
}
↓
double f(double J, double l, double K, double U) {
        double r86723 = J;
        double r86724 = 0.3333333333333333;
        double r86725 = l;
        double r86726 = 3.0;
        double r86727 = pow(r86725, r86726);
        double r86728 = r86724 * r86727;
        double r86729 = 0.016666666666666666;
        double r86730 = 5.0;
        double r86731 = pow(r86725, r86730);
        double r86732 = r86729 * r86731;
        double r86733 = r86728 + r86732;
        double r86734 = 2.0;
        double r86735 = r86734 * r86725;
        double r86736 = r86733 + r86735;
        double r86737 = r86723 * r86736;
        double r86738 = K;
        double r86739 = 2.0;
        double r86740 = r86738 / r86739;
        double r86741 = cos(r86740);
        double r86742 = r86737 * r86741;
        double r86743 = U;
        double r86744 = r86742 + r86743;
        return r86744;
}

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 17.1

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

  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-+r+0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019209 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))