Average Error: 15.4 → 1.3
Time: 15.3s
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 r153769 = K;
        double r153770 = m;
        double r153771 = n;
        double r153772 = r153770 + r153771;
        double r153773 = r153769 * r153772;
        double r153774 = 2.0;
        double r153775 = r153773 / r153774;
        double r153776 = M;
        double r153777 = r153775 - r153776;
        double r153778 = cos(r153777);
        double r153779 = r153772 / r153774;
        double r153780 = r153779 - r153776;
        double r153781 = pow(r153780, r153774);
        double r153782 = -r153781;
        double r153783 = l;
        double r153784 = r153770 - r153771;
        double r153785 = fabs(r153784);
        double r153786 = r153783 - r153785;
        double r153787 = r153782 - r153786;
        double r153788 = exp(r153787);
        double r153789 = r153778 * r153788;
        return r153789;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r153790 = m;
        double r153791 = n;
        double r153792 = r153790 + r153791;
        double r153793 = 2.0;
        double r153794 = r153792 / r153793;
        double r153795 = M;
        double r153796 = r153794 - r153795;
        double r153797 = pow(r153796, r153793);
        double r153798 = -r153797;
        double r153799 = l;
        double r153800 = r153790 - r153791;
        double r153801 = fabs(r153800);
        double r153802 = r153799 - r153801;
        double r153803 = r153798 - r153802;
        double r153804 = exp(r153803);
        return r153804;
}

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 1.3

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

  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 2020042 
(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)))))))