Average Error: 15.4 → 1.3
Time: 18.9s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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)}
↓
e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r87830 = K;
        double r87831 = m;
        double r87832 = n;
        double r87833 = r87831 + r87832;
        double r87834 = r87830 * r87833;
        double r87835 = 2.0;
        double r87836 = r87834 / r87835;
        double r87837 = M;
        double r87838 = r87836 - r87837;
        double r87839 = cos(r87838);
        double r87840 = r87833 / r87835;
        double r87841 = r87840 - r87837;
        double r87842 = pow(r87841, r87835);
        double r87843 = -r87842;
        double r87844 = l;
        double r87845 = r87831 - r87832;
        double r87846 = fabs(r87845);
        double r87847 = r87844 - r87846;
        double r87848 = r87843 - r87847;
        double r87849 = exp(r87848);
        double r87850 = r87839 * r87849;
        return r87850;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r87851 = m;
        double r87852 = n;
        double r87853 = r87851 + r87852;
        double r87854 = 2.0;
        double r87855 = r87853 / r87854;
        double r87856 = M;
        double r87857 = r87855 - r87856;
        double r87858 = pow(r87857, r87854);
        double r87859 = -r87858;
        double r87860 = l;
        double r87861 = r87851 - r87852;
        double r87862 = fabs(r87861);
        double r87863 = r87860 - r87862;
        double r87864 = r87859 - r87863;
        double r87865 = exp(r87864);
        return r87865;
}

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. Taylor expanded around 0 1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(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)))))))