Average Error: 14.8 → 1.3
Time: 25.5s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}\]
\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)}
↓
\frac{1}{e^{\left(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}
double f(double K, double m, double n, double M, double l) {
        double r2649678 = K;
        double r2649679 = m;
        double r2649680 = n;
        double r2649681 = r2649679 + r2649680;
        double r2649682 = r2649678 * r2649681;
        double r2649683 = 2.0;
        double r2649684 = r2649682 / r2649683;
        double r2649685 = M;
        double r2649686 = r2649684 - r2649685;
        double r2649687 = cos(r2649686);
        double r2649688 = r2649681 / r2649683;
        double r2649689 = r2649688 - r2649685;
        double r2649690 = pow(r2649689, r2649683);
        double r2649691 = -r2649690;
        double r2649692 = l;
        double r2649693 = r2649679 - r2649680;
        double r2649694 = fabs(r2649693);
        double r2649695 = r2649692 - r2649694;
        double r2649696 = r2649691 - r2649695;
        double r2649697 = exp(r2649696);
        double r2649698 = r2649687 * r2649697;
        return r2649698;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r2649699 = 1.0;
        double r2649700 = l;
        double r2649701 = m;
        double r2649702 = n;
        double r2649703 = r2649701 - r2649702;
        double r2649704 = fabs(r2649703);
        double r2649705 = r2649700 - r2649704;
        double r2649706 = r2649701 + r2649702;
        double r2649707 = 2.0;
        double r2649708 = r2649706 / r2649707;
        double r2649709 = M;
        double r2649710 = r2649708 - r2649709;
        double r2649711 = r2649710 * r2649710;
        double r2649712 = r2649705 + r2649711;
        double r2649713 = exp(r2649712);
        double r2649714 = r2649699 / r2649713;
        return r2649714;
}

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. Simplified14.8

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019142 
(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)))))))