Average Error: 14.9 → 1.3
Time: 23.4s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right)}\]
\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|m - n\right| - \left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right)}
double f(double K, double m, double n, double M, double l) {
        double r2500956 = K;
        double r2500957 = m;
        double r2500958 = n;
        double r2500959 = r2500957 + r2500958;
        double r2500960 = r2500956 * r2500959;
        double r2500961 = 2.0;
        double r2500962 = r2500960 / r2500961;
        double r2500963 = M;
        double r2500964 = r2500962 - r2500963;
        double r2500965 = cos(r2500964);
        double r2500966 = r2500959 / r2500961;
        double r2500967 = r2500966 - r2500963;
        double r2500968 = pow(r2500967, r2500961);
        double r2500969 = -r2500968;
        double r2500970 = l;
        double r2500971 = r2500957 - r2500958;
        double r2500972 = fabs(r2500971);
        double r2500973 = r2500970 - r2500972;
        double r2500974 = r2500969 - r2500973;
        double r2500975 = exp(r2500974);
        double r2500976 = r2500965 * r2500975;
        return r2500976;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r2500977 = m;
        double r2500978 = n;
        double r2500979 = r2500977 - r2500978;
        double r2500980 = fabs(r2500979);
        double r2500981 = r2500978 + r2500977;
        double r2500982 = 2.0;
        double r2500983 = r2500981 / r2500982;
        double r2500984 = M;
        double r2500985 = r2500983 - r2500984;
        double r2500986 = r2500985 * r2500985;
        double r2500987 = l;
        double r2500988 = r2500986 + r2500987;
        double r2500989 = r2500980 - r2500988;
        double r2500990 = exp(r2500989);
        return r2500990;
}

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

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019133 
(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)))))))