Average Error: 14.9 → 1.3
Time: 32.1s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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 r85876 = K;
        double r85877 = m;
        double r85878 = n;
        double r85879 = r85877 + r85878;
        double r85880 = r85876 * r85879;
        double r85881 = 2.0;
        double r85882 = r85880 / r85881;
        double r85883 = M;
        double r85884 = r85882 - r85883;
        double r85885 = cos(r85884);
        double r85886 = r85879 / r85881;
        double r85887 = r85886 - r85883;
        double r85888 = pow(r85887, r85881);
        double r85889 = -r85888;
        double r85890 = l;
        double r85891 = r85877 - r85878;
        double r85892 = fabs(r85891);
        double r85893 = r85890 - r85892;
        double r85894 = r85889 - r85893;
        double r85895 = exp(r85894);
        double r85896 = r85885 * r85895;
        return r85896;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r85897 = m;
        double r85898 = n;
        double r85899 = r85897 + r85898;
        double r85900 = 2.0;
        double r85901 = r85899 / r85900;
        double r85902 = M;
        double r85903 = r85901 - r85902;
        double r85904 = pow(r85903, r85900);
        double r85905 = -r85904;
        double r85906 = l;
        double r85907 = r85897 - r85898;
        double r85908 = fabs(r85907);
        double r85909 = r85906 - r85908;
        double r85910 = r85905 - r85909;
        double r85911 = exp(r85910);
        return r85911;
}

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. 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 2019323 +o rules:numerics
(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)))))))