Average Error: 15.6 → 1.4
Time: 47.6s
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 r3363739 = K;
        double r3363740 = m;
        double r3363741 = n;
        double r3363742 = r3363740 + r3363741;
        double r3363743 = r3363739 * r3363742;
        double r3363744 = 2.0;
        double r3363745 = r3363743 / r3363744;
        double r3363746 = M;
        double r3363747 = r3363745 - r3363746;
        double r3363748 = cos(r3363747);
        double r3363749 = r3363742 / r3363744;
        double r3363750 = r3363749 - r3363746;
        double r3363751 = pow(r3363750, r3363744);
        double r3363752 = -r3363751;
        double r3363753 = l;
        double r3363754 = r3363740 - r3363741;
        double r3363755 = fabs(r3363754);
        double r3363756 = r3363753 - r3363755;
        double r3363757 = r3363752 - r3363756;
        double r3363758 = exp(r3363757);
        double r3363759 = r3363748 * r3363758;
        return r3363759;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3363760 = m;
        double r3363761 = n;
        double r3363762 = r3363760 + r3363761;
        double r3363763 = 2.0;
        double r3363764 = r3363762 / r3363763;
        double r3363765 = M;
        double r3363766 = r3363764 - r3363765;
        double r3363767 = pow(r3363766, r3363763);
        double r3363768 = -r3363767;
        double r3363769 = l;
        double r3363770 = r3363760 - r3363761;
        double r3363771 = fabs(r3363770);
        double r3363772 = r3363769 - r3363771;
        double r3363773 = r3363768 - r3363772;
        double r3363774 = exp(r3363773);
        return r3363774;
}

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 15.6

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

  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 2019174 +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)))))))