Average Error: 17.4 → 0.7
Time: 58.4s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2.0}\right) + U\]
↓
\[\left(\ell \cdot J + \ell \cdot J\right) \cdot \cos \left(\frac{K}{2.0}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2.0}\right) + U
↓
\left(\ell \cdot J + \ell \cdot J\right) \cdot \cos \left(\frac{K}{2.0}\right) + U
double f(double J, double l, double K, double U) {
        double r3479610 = J;
        double r3479611 = l;
        double r3479612 = exp(r3479611);
        double r3479613 = -r3479611;
        double r3479614 = exp(r3479613);
        double r3479615 = r3479612 - r3479614;
        double r3479616 = r3479610 * r3479615;
        double r3479617 = K;
        double r3479618 = 2.0;
        double r3479619 = r3479617 / r3479618;
        double r3479620 = cos(r3479619);
        double r3479621 = r3479616 * r3479620;
        double r3479622 = U;
        double r3479623 = r3479621 + r3479622;
        return r3479623;
}
↓
double f(double J, double l, double K, double U) {
        double r3479624 = l;
        double r3479625 = J;
        double r3479626 = r3479624 * r3479625;
        double r3479627 = r3479626 + r3479626;
        double r3479628 = K;
        double r3479629 = 2.0;
        double r3479630 = r3479628 / r3479629;
        double r3479631 = cos(r3479630);
        double r3479632 = r3479627 * r3479631;
        double r3479633 = U;
        double r3479634 = r3479632 + r3479633;
        return r3479634;
}

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 17.4

    \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2.0}\right) + U\]

  2. Taylor expanded around 0 0.7

    \[\leadsto \color{blue}{\left(2 \cdot \left(J \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2.0}\right) + U\]

  3. Simplified0.7

    \[\leadsto \color{blue}{\left(\ell \cdot J + \ell \cdot J\right)} \cdot \cos \left(\frac{K}{2.0}\right) + U\]

  4. Final simplification0.7

    \[\leadsto \left(\ell \cdot J + \ell \cdot J\right) \cdot \cos \left(\frac{K}{2.0}\right) + U\]

Reproduce

herbie shell --seed 2019165 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))