Average Error: 15.4 → 1.3
Time: 18.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - {\left(\frac{n + m}{2} - M\right)}^{2}\right) - \ell}\]
\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)}
↓
e^{\left(\left|m - n\right| - {\left(\frac{n + m}{2} - M\right)}^{2}\right) - \ell}
double f(double K, double m, double n, double M, double l) {
        double r128953 = K;
        double r128954 = m;
        double r128955 = n;
        double r128956 = r128954 + r128955;
        double r128957 = r128953 * r128956;
        double r128958 = 2.0;
        double r128959 = r128957 / r128958;
        double r128960 = M;
        double r128961 = r128959 - r128960;
        double r128962 = cos(r128961);
        double r128963 = r128956 / r128958;
        double r128964 = r128963 - r128960;
        double r128965 = pow(r128964, r128958);
        double r128966 = -r128965;
        double r128967 = l;
        double r128968 = r128954 - r128955;
        double r128969 = fabs(r128968);
        double r128970 = r128967 - r128969;
        double r128971 = r128966 - r128970;
        double r128972 = exp(r128971);
        double r128973 = r128962 * r128972;
        return r128973;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r128974 = m;
        double r128975 = n;
        double r128976 = r128974 - r128975;
        double r128977 = fabs(r128976);
        double r128978 = r128975 + r128974;
        double r128979 = 2.0;
        double r128980 = r128978 / r128979;
        double r128981 = M;
        double r128982 = r128980 - r128981;
        double r128983 = pow(r128982, r128979);
        double r128984 = r128977 - r128983;
        double r128985 = l;
        double r128986 = r128984 - r128985;
        double r128987 = exp(r128986);
        return r128987;
}

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. Simplified15.4

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019196 
(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)))))))