Average Error: 15.4 → 1.2
Time: 30.6s
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 r167974 = K;
        double r167975 = m;
        double r167976 = n;
        double r167977 = r167975 + r167976;
        double r167978 = r167974 * r167977;
        double r167979 = 2.0;
        double r167980 = r167978 / r167979;
        double r167981 = M;
        double r167982 = r167980 - r167981;
        double r167983 = cos(r167982);
        double r167984 = r167977 / r167979;
        double r167985 = r167984 - r167981;
        double r167986 = pow(r167985, r167979);
        double r167987 = -r167986;
        double r167988 = l;
        double r167989 = r167975 - r167976;
        double r167990 = fabs(r167989);
        double r167991 = r167988 - r167990;
        double r167992 = r167987 - r167991;
        double r167993 = exp(r167992);
        double r167994 = r167983 * r167993;
        return r167994;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r167995 = m;
        double r167996 = n;
        double r167997 = r167995 + r167996;
        double r167998 = 2.0;
        double r167999 = r167997 / r167998;
        double r168000 = M;
        double r168001 = r167999 - r168000;
        double r168002 = pow(r168001, r167998);
        double r168003 = -r168002;
        double r168004 = l;
        double r168005 = r167995 - r167996;
        double r168006 = fabs(r168005);
        double r168007 = r168004 - r168006;
        double r168008 = r168003 - r168007;
        double r168009 = exp(r168008);
        return r168009;
}

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 1.2

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

  3. Final simplification1.2

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

Reproduce

herbie shell --seed 2020046 +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)))))))