Average Error: 14.9 → 1.3
Time: 30.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\sqrt[3]{\frac{m + n}{2} - M} \cdot \left(\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right) \cdot \left(\frac{m + n}{2} - M\right)\right) + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{\sqrt[3]{\frac{m + n}{2} - M} \cdot \left(\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right) \cdot \left(\frac{m + n}{2} - M\right)\right) + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r1924841 = K;
        double r1924842 = m;
        double r1924843 = n;
        double r1924844 = r1924842 + r1924843;
        double r1924845 = r1924841 * r1924844;
        double r1924846 = 2.0;
        double r1924847 = r1924845 / r1924846;
        double r1924848 = M;
        double r1924849 = r1924847 - r1924848;
        double r1924850 = cos(r1924849);
        double r1924851 = r1924844 / r1924846;
        double r1924852 = r1924851 - r1924848;
        double r1924853 = pow(r1924852, r1924846);
        double r1924854 = -r1924853;
        double r1924855 = l;
        double r1924856 = r1924842 - r1924843;
        double r1924857 = fabs(r1924856);
        double r1924858 = r1924855 - r1924857;
        double r1924859 = r1924854 - r1924858;
        double r1924860 = exp(r1924859);
        double r1924861 = r1924850 * r1924860;
        return r1924861;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1924862 = 1.0;
        double r1924863 = m;
        double r1924864 = n;
        double r1924865 = r1924863 + r1924864;
        double r1924866 = 2.0;
        double r1924867 = r1924865 / r1924866;
        double r1924868 = M;
        double r1924869 = r1924867 - r1924868;
        double r1924870 = cbrt(r1924869);
        double r1924871 = r1924870 * r1924870;
        double r1924872 = r1924871 * r1924869;
        double r1924873 = r1924870 * r1924872;
        double r1924874 = l;
        double r1924875 = r1924863 - r1924864;
        double r1924876 = fabs(r1924875);
        double r1924877 = r1924874 - r1924876;
        double r1924878 = r1924873 + r1924877;
        double r1924879 = exp(r1924878);
        double r1924880 = r1924862 / r1924879;
        return r1924880;
}

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

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

  3. Taylor expanded around 0 1.3

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

  5. Applied add-cube-cbrt1.3

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

  6. Applied associate-*r*1.3

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

  7. Final simplification1.3

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

Reproduce

herbie shell --seed 2019143 
(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)))))))