Average Error: 15.1 → 1.3
Time: 26.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r119686 = K;
        double r119687 = m;
        double r119688 = n;
        double r119689 = r119687 + r119688;
        double r119690 = r119686 * r119689;
        double r119691 = 2.0;
        double r119692 = r119690 / r119691;
        double r119693 = M;
        double r119694 = r119692 - r119693;
        double r119695 = cos(r119694);
        double r119696 = r119689 / r119691;
        double r119697 = r119696 - r119693;
        double r119698 = pow(r119697, r119691);
        double r119699 = -r119698;
        double r119700 = l;
        double r119701 = r119687 - r119688;
        double r119702 = fabs(r119701);
        double r119703 = r119700 - r119702;
        double r119704 = r119699 - r119703;
        double r119705 = exp(r119704);
        double r119706 = r119695 * r119705;
        return r119706;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r119707 = m;
        double r119708 = n;
        double r119709 = r119707 - r119708;
        double r119710 = fabs(r119709);
        double r119711 = l;
        double r119712 = r119710 - r119711;
        double r119713 = r119707 + r119708;
        double r119714 = 2.0;
        double r119715 = r119713 / r119714;
        double r119716 = M;
        double r119717 = r119715 - r119716;
        double r119718 = pow(r119717, r119714);
        double r119719 = r119712 - r119718;
        double r119720 = exp(r119719);
        return r119720;
}

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 15.1

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

  2. Simplified15.1

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019304 
(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)))))))