Average Error: 14.8 → 1.4
Time: 22.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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 r95849 = K;
        double r95850 = m;
        double r95851 = n;
        double r95852 = r95850 + r95851;
        double r95853 = r95849 * r95852;
        double r95854 = 2.0;
        double r95855 = r95853 / r95854;
        double r95856 = M;
        double r95857 = r95855 - r95856;
        double r95858 = cos(r95857);
        double r95859 = r95852 / r95854;
        double r95860 = r95859 - r95856;
        double r95861 = pow(r95860, r95854);
        double r95862 = -r95861;
        double r95863 = l;
        double r95864 = r95850 - r95851;
        double r95865 = fabs(r95864);
        double r95866 = r95863 - r95865;
        double r95867 = r95862 - r95866;
        double r95868 = exp(r95867);
        double r95869 = r95858 * r95868;
        return r95869;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r95870 = m;
        double r95871 = n;
        double r95872 = r95870 - r95871;
        double r95873 = fabs(r95872);
        double r95874 = l;
        double r95875 = r95873 - r95874;
        double r95876 = r95870 + r95871;
        double r95877 = 2.0;
        double r95878 = r95876 / r95877;
        double r95879 = M;
        double r95880 = r95878 - r95879;
        double r95881 = pow(r95880, r95877);
        double r95882 = r95875 - r95881;
        double r95883 = exp(r95882);
        return r95883;
}

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 14.8

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

  2. Simplified14.8

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019306 
(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)))))))