Average Error: 17.4 → 0.7
Time: 57.0s
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 r3140714 = J;
        double r3140715 = l;
        double r3140716 = exp(r3140715);
        double r3140717 = -r3140715;
        double r3140718 = exp(r3140717);
        double r3140719 = r3140716 - r3140718;
        double r3140720 = r3140714 * r3140719;
        double r3140721 = K;
        double r3140722 = 2.0;
        double r3140723 = r3140721 / r3140722;
        double r3140724 = cos(r3140723);
        double r3140725 = r3140720 * r3140724;
        double r3140726 = U;
        double r3140727 = r3140725 + r3140726;
        return r3140727;
}
↓
double f(double J, double l, double K, double U) {
        double r3140728 = l;
        double r3140729 = J;
        double r3140730 = r3140728 * r3140729;
        double r3140731 = r3140730 + r3140730;
        double r3140732 = K;
        double r3140733 = 2.0;
        double r3140734 = r3140732 / r3140733;
        double r3140735 = cos(r3140734);
        double r3140736 = r3140731 * r3140735;
        double r3140737 = U;
        double r3140738 = r3140736 + r3140737;
        return r3140738;
}

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 +o rules:numerics
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))