Average Error: 15.5 → 1.3
Time: 36.2s
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 r138747 = K;
        double r138748 = m;
        double r138749 = n;
        double r138750 = r138748 + r138749;
        double r138751 = r138747 * r138750;
        double r138752 = 2.0;
        double r138753 = r138751 / r138752;
        double r138754 = M;
        double r138755 = r138753 - r138754;
        double r138756 = cos(r138755);
        double r138757 = r138750 / r138752;
        double r138758 = r138757 - r138754;
        double r138759 = pow(r138758, r138752);
        double r138760 = -r138759;
        double r138761 = l;
        double r138762 = r138748 - r138749;
        double r138763 = fabs(r138762);
        double r138764 = r138761 - r138763;
        double r138765 = r138760 - r138764;
        double r138766 = exp(r138765);
        double r138767 = r138756 * r138766;
        return r138767;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r138768 = m;
        double r138769 = n;
        double r138770 = r138768 + r138769;
        double r138771 = 2.0;
        double r138772 = r138770 / r138771;
        double r138773 = M;
        double r138774 = r138772 - r138773;
        double r138775 = pow(r138774, r138771);
        double r138776 = -r138775;
        double r138777 = l;
        double r138778 = r138768 - r138769;
        double r138779 = fabs(r138778);
        double r138780 = r138777 - r138779;
        double r138781 = r138776 - r138780;
        double r138782 = exp(r138781);
        return r138782;
}

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 15.5

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

  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 2019303 +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)))))))