Average Error: 17.1 → 0.4
Time: 9.6s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\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 r145747 = J;
        double r145748 = l;
        double r145749 = exp(r145748);
        double r145750 = -r145748;
        double r145751 = exp(r145750);
        double r145752 = r145749 - r145751;
        double r145753 = r145747 * r145752;
        double r145754 = K;
        double r145755 = 2.0;
        double r145756 = r145754 / r145755;
        double r145757 = cos(r145756);
        double r145758 = r145753 * r145757;
        double r145759 = U;
        double r145760 = r145758 + r145759;
        return r145760;
}
↓
double f(double J, double l, double K, double U) {
        double r145761 = J;
        double r145762 = 0.3333333333333333;
        double r145763 = l;
        double r145764 = 3.0;
        double r145765 = pow(r145763, r145764);
        double r145766 = r145762 * r145765;
        double r145767 = 0.016666666666666666;
        double r145768 = 5.0;
        double r145769 = pow(r145763, r145768);
        double r145770 = r145767 * r145769;
        double r145771 = 2.0;
        double r145772 = r145771 * r145763;
        double r145773 = r145770 + r145772;
        double r145774 = r145766 + r145773;
        double r145775 = r145761 * r145774;
        double r145776 = K;
        double r145777 = 2.0;
        double r145778 = r145776 / r145777;
        double r145779 = cos(r145778);
        double r145780 = r145775 * r145779;
        double r145781 = U;
        double r145782 = r145780 + r145781;
        return r145782;
}

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. 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 2020060 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))