Average Error: 14.9 → 1.3
Time: 24.7s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r87842 = K;
        double r87843 = m;
        double r87844 = n;
        double r87845 = r87843 + r87844;
        double r87846 = r87842 * r87845;
        double r87847 = 2.0;
        double r87848 = r87846 / r87847;
        double r87849 = M;
        double r87850 = r87848 - r87849;
        double r87851 = cos(r87850);
        double r87852 = r87845 / r87847;
        double r87853 = r87852 - r87849;
        double r87854 = pow(r87853, r87847);
        double r87855 = -r87854;
        double r87856 = l;
        double r87857 = r87843 - r87844;
        double r87858 = fabs(r87857);
        double r87859 = r87856 - r87858;
        double r87860 = r87855 - r87859;
        double r87861 = exp(r87860);
        double r87862 = r87851 * r87861;
        return r87862;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r87863 = m;
        double r87864 = n;
        double r87865 = r87863 - r87864;
        double r87866 = fabs(r87865);
        double r87867 = l;
        double r87868 = r87866 - r87867;
        double r87869 = r87863 + r87864;
        double r87870 = 2.0;
        double r87871 = r87869 / r87870;
        double r87872 = M;
        double r87873 = r87871 - r87872;
        double r87874 = pow(r87873, r87870);
        double r87875 = r87868 - r87874;
        double r87876 = exp(r87875);
        return r87876;
}

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 14.9

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

  2. Simplified14.9

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019323 
(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)))))))