Average Error: 15.1 → 1.3
Time: 9.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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)}
↓
e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r147754 = K;
        double r147755 = m;
        double r147756 = n;
        double r147757 = r147755 + r147756;
        double r147758 = r147754 * r147757;
        double r147759 = 2.0;
        double r147760 = r147758 / r147759;
        double r147761 = M;
        double r147762 = r147760 - r147761;
        double r147763 = cos(r147762);
        double r147764 = r147757 / r147759;
        double r147765 = r147764 - r147761;
        double r147766 = pow(r147765, r147759);
        double r147767 = -r147766;
        double r147768 = l;
        double r147769 = r147755 - r147756;
        double r147770 = fabs(r147769);
        double r147771 = r147768 - r147770;
        double r147772 = r147767 - r147771;
        double r147773 = exp(r147772);
        double r147774 = r147763 * r147773;
        return r147774;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r147775 = m;
        double r147776 = n;
        double r147777 = r147775 + r147776;
        double r147778 = 2.0;
        double r147779 = r147777 / r147778;
        double r147780 = M;
        double r147781 = r147779 - r147780;
        double r147782 = pow(r147781, r147778);
        double r147783 = -r147782;
        double r147784 = l;
        double r147785 = r147775 - r147776;
        double r147786 = fabs(r147785);
        double r147787 = r147784 - r147786;
        double r147788 = r147783 - r147787;
        double r147789 = exp(r147788);
        return r147789;
}

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. Taylor expanded around 0 1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(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)))))))