Average Error: 15.1 → 1.3
Time: 15.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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 r88727 = K;
        double r88728 = m;
        double r88729 = n;
        double r88730 = r88728 + r88729;
        double r88731 = r88727 * r88730;
        double r88732 = 2.0;
        double r88733 = r88731 / r88732;
        double r88734 = M;
        double r88735 = r88733 - r88734;
        double r88736 = cos(r88735);
        double r88737 = r88730 / r88732;
        double r88738 = r88737 - r88734;
        double r88739 = pow(r88738, r88732);
        double r88740 = -r88739;
        double r88741 = l;
        double r88742 = r88728 - r88729;
        double r88743 = fabs(r88742);
        double r88744 = r88741 - r88743;
        double r88745 = r88740 - r88744;
        double r88746 = exp(r88745);
        double r88747 = r88736 * r88746;
        return r88747;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r88748 = m;
        double r88749 = n;
        double r88750 = r88748 + r88749;
        double r88751 = 2.0;
        double r88752 = r88750 / r88751;
        double r88753 = M;
        double r88754 = r88752 - r88753;
        double r88755 = pow(r88754, r88751);
        double r88756 = -r88755;
        double r88757 = l;
        double r88758 = r88748 - r88749;
        double r88759 = fabs(r88758);
        double r88760 = r88757 - r88759;
        double r88761 = r88756 - r88760;
        double r88762 = exp(r88761);
        return r88762;
}

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 15.1

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

  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 2019304 
(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)))))))