Average Error: 14.8 → 1.4
Time: 23.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}\]
\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)}
↓
\frac{1}{e^{\left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}
double f(double K, double m, double n, double M, double l) {
        double r1724822 = K;
        double r1724823 = m;
        double r1724824 = n;
        double r1724825 = r1724823 + r1724824;
        double r1724826 = r1724822 * r1724825;
        double r1724827 = 2.0;
        double r1724828 = r1724826 / r1724827;
        double r1724829 = M;
        double r1724830 = r1724828 - r1724829;
        double r1724831 = cos(r1724830);
        double r1724832 = r1724825 / r1724827;
        double r1724833 = r1724832 - r1724829;
        double r1724834 = pow(r1724833, r1724827);
        double r1724835 = -r1724834;
        double r1724836 = l;
        double r1724837 = r1724823 - r1724824;
        double r1724838 = fabs(r1724837);
        double r1724839 = r1724836 - r1724838;
        double r1724840 = r1724835 - r1724839;
        double r1724841 = exp(r1724840);
        double r1724842 = r1724831 * r1724841;
        return r1724842;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1724843 = 1.0;
        double r1724844 = n;
        double r1724845 = m;
        double r1724846 = r1724844 + r1724845;
        double r1724847 = 2.0;
        double r1724848 = r1724846 / r1724847;
        double r1724849 = M;
        double r1724850 = r1724848 - r1724849;
        double r1724851 = r1724850 * r1724850;
        double r1724852 = l;
        double r1724853 = r1724851 + r1724852;
        double r1724854 = r1724845 - r1724844;
        double r1724855 = fabs(r1724854);
        double r1724856 = r1724853 - r1724855;
        double r1724857 = exp(r1724856);
        double r1724858 = r1724843 / r1724857;
        return r1724858;
}

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

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019153 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))