Average Error: 14.7 → 1.3
Time: 1.4m
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{\cos \left(-M\right)}{e^{\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{\cos \left(-M\right)}{e^{\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r18772703 = K;
        double r18772704 = m;
        double r18772705 = n;
        double r18772706 = r18772704 + r18772705;
        double r18772707 = r18772703 * r18772706;
        double r18772708 = 2.0;
        double r18772709 = r18772707 / r18772708;
        double r18772710 = M;
        double r18772711 = r18772709 - r18772710;
        double r18772712 = cos(r18772711);
        double r18772713 = r18772706 / r18772708;
        double r18772714 = r18772713 - r18772710;
        double r18772715 = pow(r18772714, r18772708);
        double r18772716 = -r18772715;
        double r18772717 = l;
        double r18772718 = r18772704 - r18772705;
        double r18772719 = fabs(r18772718);
        double r18772720 = r18772717 - r18772719;
        double r18772721 = r18772716 - r18772720;
        double r18772722 = exp(r18772721);
        double r18772723 = r18772712 * r18772722;
        return r18772723;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r18772724 = M;
        double r18772725 = -r18772724;
        double r18772726 = cos(r18772725);
        double r18772727 = n;
        double r18772728 = m;
        double r18772729 = r18772727 + r18772728;
        double r18772730 = 2.0;
        double r18772731 = r18772729 / r18772730;
        double r18772732 = r18772731 - r18772724;
        double r18772733 = r18772732 * r18772732;
        double r18772734 = l;
        double r18772735 = r18772728 - r18772727;
        double r18772736 = fabs(r18772735);
        double r18772737 = r18772734 - r18772736;
        double r18772738 = r18772733 + r18772737;
        double r18772739 = exp(r18772738);
        double r18772740 = r18772726 / r18772739;
        return r18772740;
}

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 14.7

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

  2. Simplified14.7

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

  3. Taylor expanded around 0 1.3

    \[\leadsto \frac{\cos \left(\frac{\color{blue}{0}}{2} - M\right)}{e^{\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right)}}\]

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019112 
(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)))))))