Average Error: 15.3 → 1.3
Time: 9.4s
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 r151712 = K;
        double r151713 = m;
        double r151714 = n;
        double r151715 = r151713 + r151714;
        double r151716 = r151712 * r151715;
        double r151717 = 2.0;
        double r151718 = r151716 / r151717;
        double r151719 = M;
        double r151720 = r151718 - r151719;
        double r151721 = cos(r151720);
        double r151722 = r151715 / r151717;
        double r151723 = r151722 - r151719;
        double r151724 = pow(r151723, r151717);
        double r151725 = -r151724;
        double r151726 = l;
        double r151727 = r151713 - r151714;
        double r151728 = fabs(r151727);
        double r151729 = r151726 - r151728;
        double r151730 = r151725 - r151729;
        double r151731 = exp(r151730);
        double r151732 = r151721 * r151731;
        return r151732;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r151733 = m;
        double r151734 = n;
        double r151735 = r151733 + r151734;
        double r151736 = 2.0;
        double r151737 = r151735 / r151736;
        double r151738 = M;
        double r151739 = r151737 - r151738;
        double r151740 = pow(r151739, r151736);
        double r151741 = -r151740;
        double r151742 = l;
        double r151743 = r151733 - r151734;
        double r151744 = fabs(r151743);
        double r151745 = r151742 - r151744;
        double r151746 = r151741 - r151745;
        double r151747 = exp(r151746);
        return r151747;
}

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 15.3

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

  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 2020060 
(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)))))))