Average Error: 15.1 → 1.3
Time: 7.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
↓
e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r162739 = K;
        double r162740 = m;
        double r162741 = n;
        double r162742 = r162740 + r162741;
        double r162743 = r162739 * r162742;
        double r162744 = 2.0;
        double r162745 = r162743 / r162744;
        double r162746 = M;
        double r162747 = r162745 - r162746;
        double r162748 = cos(r162747);
        double r162749 = r162742 / r162744;
        double r162750 = r162749 - r162746;
        double r162751 = pow(r162750, r162744);
        double r162752 = -r162751;
        double r162753 = l;
        double r162754 = r162740 - r162741;
        double r162755 = fabs(r162754);
        double r162756 = r162753 - r162755;
        double r162757 = r162752 - r162756;
        double r162758 = exp(r162757);
        double r162759 = r162748 * r162758;
        return r162759;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r162760 = m;
        double r162761 = n;
        double r162762 = r162760 + r162761;
        double r162763 = 2.0;
        double r162764 = r162762 / r162763;
        double r162765 = M;
        double r162766 = r162764 - r162765;
        double r162767 = pow(r162766, r162763);
        double r162768 = -r162767;
        double r162769 = l;
        double r162770 = r162760 - r162761;
        double r162771 = fabs(r162770);
        double r162772 = r162769 - r162771;
        double r162773 = r162768 - r162772;
        double r162774 = exp(r162773);
        return r162774;
}

Error

Bits error versus K

Bits error versus m

Bits error versus n

Bits error versus M

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

    \[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

  2. Taylor expanded around 0 1.3

    \[\leadsto \color{blue}{1} \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

  3. Final simplification1.3

    \[\leadsto e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

Reproduce

herbie shell --seed 2020089 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))