Average Error: 14.8 → 1.4
Time: 22.4s
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 r1443992 = K;
        double r1443993 = m;
        double r1443994 = n;
        double r1443995 = r1443993 + r1443994;
        double r1443996 = r1443992 * r1443995;
        double r1443997 = 2.0;
        double r1443998 = r1443996 / r1443997;
        double r1443999 = M;
        double r1444000 = r1443998 - r1443999;
        double r1444001 = cos(r1444000);
        double r1444002 = r1443995 / r1443997;
        double r1444003 = r1444002 - r1443999;
        double r1444004 = pow(r1444003, r1443997);
        double r1444005 = -r1444004;
        double r1444006 = l;
        double r1444007 = r1443993 - r1443994;
        double r1444008 = fabs(r1444007);
        double r1444009 = r1444006 - r1444008;
        double r1444010 = r1444005 - r1444009;
        double r1444011 = exp(r1444010);
        double r1444012 = r1444001 * r1444011;
        return r1444012;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1444013 = m;
        double r1444014 = n;
        double r1444015 = r1444013 + r1444014;
        double r1444016 = 2.0;
        double r1444017 = r1444015 / r1444016;
        double r1444018 = M;
        double r1444019 = r1444017 - r1444018;
        double r1444020 = pow(r1444019, r1444016);
        double r1444021 = -r1444020;
        double r1444022 = l;
        double r1444023 = r1444013 - r1444014;
        double r1444024 = fabs(r1444023);
        double r1444025 = r1444022 - r1444024;
        double r1444026 = r1444021 - r1444025;
        double r1444027 = exp(r1444026);
        return r1444027;
}

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 14.8

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

  2. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(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)))))))