Average Error: 18.0 → 0.7
Time: 28.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(2 \cdot \left(J \cdot \ell\right)\right)\]
\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(2 \cdot \left(J \cdot \ell\right)\right)
double f(double J, double l, double K, double U) {
        double r3213782 = J;
        double r3213783 = l;
        double r3213784 = exp(r3213783);
        double r3213785 = -r3213783;
        double r3213786 = exp(r3213785);
        double r3213787 = r3213784 - r3213786;
        double r3213788 = r3213782 * r3213787;
        double r3213789 = K;
        double r3213790 = 2.0;
        double r3213791 = r3213789 / r3213790;
        double r3213792 = cos(r3213791);
        double r3213793 = r3213788 * r3213792;
        double r3213794 = U;
        double r3213795 = r3213793 + r3213794;
        return r3213795;
}
↓
double f(double J, double l, double K, double U) {
        double r3213796 = U;
        double r3213797 = K;
        double r3213798 = 2.0;
        double r3213799 = r3213797 / r3213798;
        double r3213800 = cos(r3213799);
        double r3213801 = J;
        double r3213802 = l;
        double r3213803 = r3213801 * r3213802;
        double r3213804 = r3213798 * r3213803;
        double r3213805 = r3213800 * r3213804;
        double r3213806 = r3213796 + r3213805;
        return r3213806;
}

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 18.0

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

  2. Simplified18.1

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

  3. Taylor expanded around 0 0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2019168 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))