Average Error: 14.5 → 1.2
Time: 23.5s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}\]
\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|m - n\right| - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right) - \ell}
double f(double K, double m, double n, double M, double l) {
        double r5118675 = K;
        double r5118676 = m;
        double r5118677 = n;
        double r5118678 = r5118676 + r5118677;
        double r5118679 = r5118675 * r5118678;
        double r5118680 = 2.0;
        double r5118681 = r5118679 / r5118680;
        double r5118682 = M;
        double r5118683 = r5118681 - r5118682;
        double r5118684 = cos(r5118683);
        double r5118685 = r5118678 / r5118680;
        double r5118686 = r5118685 - r5118682;
        double r5118687 = pow(r5118686, r5118680);
        double r5118688 = -r5118687;
        double r5118689 = l;
        double r5118690 = r5118676 - r5118677;
        double r5118691 = fabs(r5118690);
        double r5118692 = r5118689 - r5118691;
        double r5118693 = r5118688 - r5118692;
        double r5118694 = exp(r5118693);
        double r5118695 = r5118684 * r5118694;
        return r5118695;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5118696 = m;
        double r5118697 = n;
        double r5118698 = r5118696 - r5118697;
        double r5118699 = fabs(r5118698);
        double r5118700 = r5118697 + r5118696;
        double r5118701 = 2.0;
        double r5118702 = r5118700 / r5118701;
        double r5118703 = M;
        double r5118704 = r5118702 - r5118703;
        double r5118705 = r5118704 * r5118704;
        double r5118706 = r5118699 - r5118705;
        double r5118707 = l;
        double r5118708 = r5118706 - r5118707;
        double r5118709 = exp(r5118708);
        return r5118709;
}

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 14.5

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

  2. Simplified14.5

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

  3. Taylor expanded around 0 1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019163 
(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)))))))