Average Error: 17.9 → 0.4
Time: 25.7s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \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
double f(double J, double l, double K, double U) {
        double r156682 = J;
        double r156683 = l;
        double r156684 = exp(r156683);
        double r156685 = -r156683;
        double r156686 = exp(r156685);
        double r156687 = r156684 - r156686;
        double r156688 = r156682 * r156687;
        double r156689 = K;
        double r156690 = 2.0;
        double r156691 = r156689 / r156690;
        double r156692 = cos(r156691);
        double r156693 = r156688 * r156692;
        double r156694 = U;
        double r156695 = r156693 + r156694;
        return r156695;
}
↓
double f(double J, double l, double K, double U) {
        double r156696 = J;
        double r156697 = 0.3333333333333333;
        double r156698 = l;
        double r156699 = 3.0;
        double r156700 = pow(r156698, r156699);
        double r156701 = r156697 * r156700;
        double r156702 = 0.016666666666666666;
        double r156703 = 5.0;
        double r156704 = pow(r156698, r156703);
        double r156705 = r156702 * r156704;
        double r156706 = 2.0;
        double r156707 = r156706 * r156698;
        double r156708 = r156705 + r156707;
        double r156709 = r156701 + r156708;
        double r156710 = r156696 * r156709;
        double r156711 = K;
        double r156712 = 2.0;
        double r156713 = r156711 / r156712;
        double r156714 = cos(r156713);
        double r156715 = r156710 * r156714;
        double r156716 = U;
        double r156717 = r156715 + r156716;
        return r156717;
}

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 17.9

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020042 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))