Average Error: 15.3 → 1.3
Time: 11.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\left(\sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}} \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}\right) \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}\]
\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)}
↓
\left(\sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}} \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}\right) \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}
double f(double K, double m, double n, double M, double l) {
        double r178808 = K;
        double r178809 = m;
        double r178810 = n;
        double r178811 = r178809 + r178810;
        double r178812 = r178808 * r178811;
        double r178813 = 2.0;
        double r178814 = r178812 / r178813;
        double r178815 = M;
        double r178816 = r178814 - r178815;
        double r178817 = cos(r178816);
        double r178818 = r178811 / r178813;
        double r178819 = r178818 - r178815;
        double r178820 = pow(r178819, r178813);
        double r178821 = -r178820;
        double r178822 = l;
        double r178823 = r178809 - r178810;
        double r178824 = fabs(r178823);
        double r178825 = r178822 - r178824;
        double r178826 = r178821 - r178825;
        double r178827 = exp(r178826);
        double r178828 = r178817 * r178827;
        return r178828;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r178829 = 1.0;
        double r178830 = m;
        double r178831 = n;
        double r178832 = r178830 + r178831;
        double r178833 = 2.0;
        double r178834 = r178832 / r178833;
        double r178835 = M;
        double r178836 = r178834 - r178835;
        double r178837 = pow(r178836, r178833);
        double r178838 = l;
        double r178839 = r178830 - r178831;
        double r178840 = fabs(r178839);
        double r178841 = r178838 - r178840;
        double r178842 = r178837 + r178841;
        double r178843 = exp(r178842);
        double r178844 = r178829 / r178843;
        double r178845 = cbrt(r178844);
        double r178846 = r178845 * r178845;
        double r178847 = r178846 * r178845;
        return r178847;
}

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 15.3

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

  2. Simplified15.3

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

  3. Taylor expanded around 0 1.3

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

  5. Applied add-cube-cbrt1.3

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}} \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}\right) \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}}\]

  6. Final simplification1.3

    \[\leadsto \left(\sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}} \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}\right) \cdot \sqrt[3]{\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}}\]

Reproduce

herbie shell --seed 2020036 
(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)))))))