Average Error: 15.2 → 1.3
Time: 16.4s
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 r78872 = K;
        double r78873 = m;
        double r78874 = n;
        double r78875 = r78873 + r78874;
        double r78876 = r78872 * r78875;
        double r78877 = 2.0;
        double r78878 = r78876 / r78877;
        double r78879 = M;
        double r78880 = r78878 - r78879;
        double r78881 = cos(r78880);
        double r78882 = r78875 / r78877;
        double r78883 = r78882 - r78879;
        double r78884 = pow(r78883, r78877);
        double r78885 = -r78884;
        double r78886 = l;
        double r78887 = r78873 - r78874;
        double r78888 = fabs(r78887);
        double r78889 = r78886 - r78888;
        double r78890 = r78885 - r78889;
        double r78891 = exp(r78890);
        double r78892 = r78881 * r78891;
        return r78892;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r78893 = m;
        double r78894 = n;
        double r78895 = r78893 + r78894;
        double r78896 = 2.0;
        double r78897 = r78895 / r78896;
        double r78898 = M;
        double r78899 = r78897 - r78898;
        double r78900 = pow(r78899, r78896);
        double r78901 = -r78900;
        double r78902 = l;
        double r78903 = r78893 - r78894;
        double r78904 = fabs(r78903);
        double r78905 = r78902 - r78904;
        double r78906 = r78901 - r78905;
        double r78907 = exp(r78906);
        return r78907;
}

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 15.2

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

  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 2019305 
(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)))))))