Average Error: 15.6 → 1.4
Time: 35.1s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\left(\sqrt[3]{{e}^{\left(\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell\right)}} \cdot \sqrt[3]{{e}^{\left(\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell\right)}}\right) \cdot \sqrt[3]{e^{\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell}}\]
\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]{{e}^{\left(\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell\right)}} \cdot \sqrt[3]{{e}^{\left(\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell\right)}}\right) \cdot \sqrt[3]{e^{\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell}}
double f(double K, double m, double n, double M, double l) {
        double r6272892 = K;
        double r6272893 = m;
        double r6272894 = n;
        double r6272895 = r6272893 + r6272894;
        double r6272896 = r6272892 * r6272895;
        double r6272897 = 2.0;
        double r6272898 = r6272896 / r6272897;
        double r6272899 = M;
        double r6272900 = r6272898 - r6272899;
        double r6272901 = cos(r6272900);
        double r6272902 = r6272895 / r6272897;
        double r6272903 = r6272902 - r6272899;
        double r6272904 = pow(r6272903, r6272897);
        double r6272905 = -r6272904;
        double r6272906 = l;
        double r6272907 = r6272893 - r6272894;
        double r6272908 = fabs(r6272907);
        double r6272909 = r6272906 - r6272908;
        double r6272910 = r6272905 - r6272909;
        double r6272911 = exp(r6272910);
        double r6272912 = r6272901 * r6272911;
        return r6272912;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r6272913 = exp(1.0);
        double r6272914 = m;
        double r6272915 = n;
        double r6272916 = r6272914 - r6272915;
        double r6272917 = fabs(r6272916);
        double r6272918 = r6272914 + r6272915;
        double r6272919 = 2.0;
        double r6272920 = r6272918 / r6272919;
        double r6272921 = M;
        double r6272922 = r6272920 - r6272921;
        double r6272923 = pow(r6272922, r6272919);
        double r6272924 = r6272917 - r6272923;
        double r6272925 = l;
        double r6272926 = r6272924 - r6272925;
        double r6272927 = pow(r6272913, r6272926);
        double r6272928 = cbrt(r6272927);
        double r6272929 = r6272928 * r6272928;
        double r6272930 = exp(r6272926);
        double r6272931 = cbrt(r6272930);
        double r6272932 = r6272929 * r6272931;
        return r6272932;
}

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 15.6

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

  2. Simplified15.6

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

  3. Taylor expanded around 0 1.4

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

  5. Applied *-un-lft-identity1.4

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

  6. Applied exp-prod1.4

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

  7. Simplified1.4

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

  9. Applied add-cube-cbrt1.4

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

  11. Applied e-exp-11.4

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

  12. Applied pow-exp1.4

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

  13. Final simplification1.4

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

Reproduce

herbie shell --seed 2019172 
(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)))))))