Average Error: 15.5 → 1.3
Time: 23.4s
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 r140901 = K;
        double r140902 = m;
        double r140903 = n;
        double r140904 = r140902 + r140903;
        double r140905 = r140901 * r140904;
        double r140906 = 2.0;
        double r140907 = r140905 / r140906;
        double r140908 = M;
        double r140909 = r140907 - r140908;
        double r140910 = cos(r140909);
        double r140911 = r140904 / r140906;
        double r140912 = r140911 - r140908;
        double r140913 = pow(r140912, r140906);
        double r140914 = -r140913;
        double r140915 = l;
        double r140916 = r140902 - r140903;
        double r140917 = fabs(r140916);
        double r140918 = r140915 - r140917;
        double r140919 = r140914 - r140918;
        double r140920 = exp(r140919);
        double r140921 = r140910 * r140920;
        return r140921;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r140922 = m;
        double r140923 = n;
        double r140924 = r140922 + r140923;
        double r140925 = 2.0;
        double r140926 = r140924 / r140925;
        double r140927 = M;
        double r140928 = r140926 - r140927;
        double r140929 = pow(r140928, r140925);
        double r140930 = -r140929;
        double r140931 = l;
        double r140932 = r140922 - r140923;
        double r140933 = fabs(r140932);
        double r140934 = r140931 - r140933;
        double r140935 = r140930 - r140934;
        double r140936 = exp(r140935);
        return r140936;
}

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 15.5

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

  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 2019303 
(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)))))))