Average Error: 15.4 → 1.4
Time: 24.3s
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 r5271913 = K;
        double r5271914 = m;
        double r5271915 = n;
        double r5271916 = r5271914 + r5271915;
        double r5271917 = r5271913 * r5271916;
        double r5271918 = 2.0;
        double r5271919 = r5271917 / r5271918;
        double r5271920 = M;
        double r5271921 = r5271919 - r5271920;
        double r5271922 = cos(r5271921);
        double r5271923 = r5271916 / r5271918;
        double r5271924 = r5271923 - r5271920;
        double r5271925 = pow(r5271924, r5271918);
        double r5271926 = -r5271925;
        double r5271927 = l;
        double r5271928 = r5271914 - r5271915;
        double r5271929 = fabs(r5271928);
        double r5271930 = r5271927 - r5271929;
        double r5271931 = r5271926 - r5271930;
        double r5271932 = exp(r5271931);
        double r5271933 = r5271922 * r5271932;
        return r5271933;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5271934 = m;
        double r5271935 = n;
        double r5271936 = r5271934 - r5271935;
        double r5271937 = fabs(r5271936);
        double r5271938 = l;
        double r5271939 = r5271937 - r5271938;
        double r5271940 = r5271934 + r5271935;
        double r5271941 = 2.0;
        double r5271942 = r5271940 / r5271941;
        double r5271943 = M;
        double r5271944 = r5271942 - r5271943;
        double r5271945 = pow(r5271944, r5271941);
        double r5271946 = r5271939 - r5271945;
        double r5271947 = exp(r5271946);
        return r5271947;
}

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 15.4

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

  2. Simplified15.4

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

  3. Taylor expanded around 0 1.4

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

  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 2019169 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))