Average Error: 14.8 → 1.4
Time: 38.4s
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 r1694727 = K;
        double r1694728 = m;
        double r1694729 = n;
        double r1694730 = r1694728 + r1694729;
        double r1694731 = r1694727 * r1694730;
        double r1694732 = 2.0;
        double r1694733 = r1694731 / r1694732;
        double r1694734 = M;
        double r1694735 = r1694733 - r1694734;
        double r1694736 = cos(r1694735);
        double r1694737 = r1694730 / r1694732;
        double r1694738 = r1694737 - r1694734;
        double r1694739 = pow(r1694738, r1694732);
        double r1694740 = -r1694739;
        double r1694741 = l;
        double r1694742 = r1694728 - r1694729;
        double r1694743 = fabs(r1694742);
        double r1694744 = r1694741 - r1694743;
        double r1694745 = r1694740 - r1694744;
        double r1694746 = exp(r1694745);
        double r1694747 = r1694736 * r1694746;
        return r1694747;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1694748 = m;
        double r1694749 = n;
        double r1694750 = r1694748 + r1694749;
        double r1694751 = 2.0;
        double r1694752 = r1694750 / r1694751;
        double r1694753 = M;
        double r1694754 = r1694752 - r1694753;
        double r1694755 = pow(r1694754, r1694751);
        double r1694756 = -r1694755;
        double r1694757 = l;
        double r1694758 = r1694748 - r1694749;
        double r1694759 = fabs(r1694758);
        double r1694760 = r1694757 - r1694759;
        double r1694761 = r1694756 - r1694760;
        double r1694762 = exp(r1694761);
        return r1694762;
}

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 14.8

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

  2. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(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)))))))