Average Error: 17.8 → 0.4
Time: 43.8s
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 r77800 = J;
        double r77801 = l;
        double r77802 = exp(r77801);
        double r77803 = -r77801;
        double r77804 = exp(r77803);
        double r77805 = r77802 - r77804;
        double r77806 = r77800 * r77805;
        double r77807 = K;
        double r77808 = 2.0;
        double r77809 = r77807 / r77808;
        double r77810 = cos(r77809);
        double r77811 = r77806 * r77810;
        double r77812 = U;
        double r77813 = r77811 + r77812;
        return r77813;
}
↓
double f(double J, double l, double K, double U) {
        double r77814 = J;
        double r77815 = 0.3333333333333333;
        double r77816 = l;
        double r77817 = 3.0;
        double r77818 = pow(r77816, r77817);
        double r77819 = r77815 * r77818;
        double r77820 = 0.016666666666666666;
        double r77821 = 5.0;
        double r77822 = pow(r77816, r77821);
        double r77823 = r77820 * r77822;
        double r77824 = 2.0;
        double r77825 = r77824 * r77816;
        double r77826 = r77823 + r77825;
        double r77827 = r77819 + r77826;
        double r77828 = r77814 * r77827;
        double r77829 = K;
        double r77830 = 2.0;
        double r77831 = r77829 / r77830;
        double r77832 = cos(r77831);
        double r77833 = r77828 * r77832;
        double r77834 = U;
        double r77835 = r77833 + r77834;
        return r77835;
}

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 17.8

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

  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 2019326 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))