Average Error: 15.4 → 1.4
Time: 23.8s
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 r5690760 = K;
        double r5690761 = m;
        double r5690762 = n;
        double r5690763 = r5690761 + r5690762;
        double r5690764 = r5690760 * r5690763;
        double r5690765 = 2.0;
        double r5690766 = r5690764 / r5690765;
        double r5690767 = M;
        double r5690768 = r5690766 - r5690767;
        double r5690769 = cos(r5690768);
        double r5690770 = r5690763 / r5690765;
        double r5690771 = r5690770 - r5690767;
        double r5690772 = pow(r5690771, r5690765);
        double r5690773 = -r5690772;
        double r5690774 = l;
        double r5690775 = r5690761 - r5690762;
        double r5690776 = fabs(r5690775);
        double r5690777 = r5690774 - r5690776;
        double r5690778 = r5690773 - r5690777;
        double r5690779 = exp(r5690778);
        double r5690780 = r5690769 * r5690779;
        return r5690780;
}

double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5690781 = m;
        double r5690782 = n;
        double r5690783 = r5690781 - r5690782;
        double r5690784 = fabs(r5690783);
        double r5690785 = l;
        double r5690786 = r5690784 - r5690785;
        double r5690787 = r5690781 + r5690782;
        double r5690788 = 2.0;
        double r5690789 = r5690787 / r5690788;
        double r5690790 = M;
        double r5690791 = r5690789 - r5690790;
        double r5690792 = pow(r5690791, r5690788);
        double r5690793 = r5690786 - r5690792;
        double r5690794 = exp(r5690793);
        return r5690794;
}

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 15.4

    \[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
  2. Simplified15.4

    \[\leadsto \color{blue}{\cos \left(\frac{\left(m + n\right) \cdot K}{2} - M\right) \cdot e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}}\]
  3. Taylor expanded around 0 1.4

    \[\leadsto \color{blue}{1} \cdot e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(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)))))))