Average Error: 17.3 → 0.6
Time: 22.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)
double f(double J, double l, double K, double U) {
        double r1388012 = J;
        double r1388013 = l;
        double r1388014 = exp(r1388013);
        double r1388015 = -r1388013;
        double r1388016 = exp(r1388015);
        double r1388017 = r1388014 - r1388016;
        double r1388018 = r1388012 * r1388017;
        double r1388019 = K;
        double r1388020 = 2.0;
        double r1388021 = r1388019 / r1388020;
        double r1388022 = cos(r1388021);
        double r1388023 = r1388018 * r1388022;
        double r1388024 = U;
        double r1388025 = r1388023 + r1388024;
        return r1388025;
}
↓
double f(double J, double l, double K, double U) {
        double r1388026 = U;
        double r1388027 = K;
        double r1388028 = 2.0;
        double r1388029 = r1388027 / r1388028;
        double r1388030 = cos(r1388029);
        double r1388031 = J;
        double r1388032 = l;
        double r1388033 = r1388031 * r1388032;
        double r1388034 = r1388033 * r1388028;
        double r1388035 = r1388030 * r1388034;
        double r1388036 = r1388026 + r1388035;
        return r1388036;
}

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. Simplified17.3

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

  3. Taylor expanded around 0 0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019154 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))