Average Error: 17.3 → 0.6
Time: 25.8s
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 r1415667 = J;
        double r1415668 = l;
        double r1415669 = exp(r1415668);
        double r1415670 = -r1415668;
        double r1415671 = exp(r1415670);
        double r1415672 = r1415669 - r1415671;
        double r1415673 = r1415667 * r1415672;
        double r1415674 = K;
        double r1415675 = 2.0;
        double r1415676 = r1415674 / r1415675;
        double r1415677 = cos(r1415676);
        double r1415678 = r1415673 * r1415677;
        double r1415679 = U;
        double r1415680 = r1415678 + r1415679;
        return r1415680;
}
↓
double f(double J, double l, double K, double U) {
        double r1415681 = U;
        double r1415682 = K;
        double r1415683 = 2.0;
        double r1415684 = r1415682 / r1415683;
        double r1415685 = cos(r1415684);
        double r1415686 = J;
        double r1415687 = l;
        double r1415688 = r1415686 * r1415687;
        double r1415689 = r1415688 * r1415683;
        double r1415690 = r1415685 * r1415689;
        double r1415691 = r1415681 + r1415690;
        return r1415691;
}

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 2019153 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))