Average Error: 15.5 → 1.3
Time: 31.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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 r5703816 = K;
        double r5703817 = m;
        double r5703818 = n;
        double r5703819 = r5703817 + r5703818;
        double r5703820 = r5703816 * r5703819;
        double r5703821 = 2.0;
        double r5703822 = r5703820 / r5703821;
        double r5703823 = M;
        double r5703824 = r5703822 - r5703823;
        double r5703825 = cos(r5703824);
        double r5703826 = r5703819 / r5703821;
        double r5703827 = r5703826 - r5703823;
        double r5703828 = pow(r5703827, r5703821);
        double r5703829 = -r5703828;
        double r5703830 = l;
        double r5703831 = r5703817 - r5703818;
        double r5703832 = fabs(r5703831);
        double r5703833 = r5703830 - r5703832;
        double r5703834 = r5703829 - r5703833;
        double r5703835 = exp(r5703834);
        double r5703836 = r5703825 * r5703835;
        return r5703836;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5703837 = m;
        double r5703838 = n;
        double r5703839 = r5703837 - r5703838;
        double r5703840 = fabs(r5703839);
        double r5703841 = l;
        double r5703842 = r5703840 - r5703841;
        double r5703843 = r5703837 + r5703838;
        double r5703844 = 2.0;
        double r5703845 = r5703843 / r5703844;
        double r5703846 = M;
        double r5703847 = r5703845 - r5703846;
        double r5703848 = pow(r5703847, r5703844);
        double r5703849 = r5703842 - r5703848;
        double r5703850 = exp(r5703849);
        return r5703850;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.3

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

  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 2019170 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))