Average Error: 14.7 → 1.3
Time: 19.9s
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 r93722 = K;
        double r93723 = m;
        double r93724 = n;
        double r93725 = r93723 + r93724;
        double r93726 = r93722 * r93725;
        double r93727 = 2.0;
        double r93728 = r93726 / r93727;
        double r93729 = M;
        double r93730 = r93728 - r93729;
        double r93731 = cos(r93730);
        double r93732 = r93725 / r93727;
        double r93733 = r93732 - r93729;
        double r93734 = pow(r93733, r93727);
        double r93735 = -r93734;
        double r93736 = l;
        double r93737 = r93723 - r93724;
        double r93738 = fabs(r93737);
        double r93739 = r93736 - r93738;
        double r93740 = r93735 - r93739;
        double r93741 = exp(r93740);
        double r93742 = r93731 * r93741;
        return r93742;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r93743 = m;
        double r93744 = n;
        double r93745 = r93743 + r93744;
        double r93746 = 2.0;
        double r93747 = r93745 / r93746;
        double r93748 = M;
        double r93749 = r93747 - r93748;
        double r93750 = pow(r93749, r93746);
        double r93751 = -r93750;
        double r93752 = l;
        double r93753 = r93743 - r93744;
        double r93754 = fabs(r93753);
        double r93755 = r93752 - r93754;
        double r93756 = r93751 - r93755;
        double r93757 = exp(r93756);
        return r93757;
}

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 14.7

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

  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 2019212 
(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)))))))