Average Error: 14.8 → 1.4
Time: 17.0s
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 r113720 = K;
        double r113721 = m;
        double r113722 = n;
        double r113723 = r113721 + r113722;
        double r113724 = r113720 * r113723;
        double r113725 = 2.0;
        double r113726 = r113724 / r113725;
        double r113727 = M;
        double r113728 = r113726 - r113727;
        double r113729 = cos(r113728);
        double r113730 = r113723 / r113725;
        double r113731 = r113730 - r113727;
        double r113732 = pow(r113731, r113725);
        double r113733 = -r113732;
        double r113734 = l;
        double r113735 = r113721 - r113722;
        double r113736 = fabs(r113735);
        double r113737 = r113734 - r113736;
        double r113738 = r113733 - r113737;
        double r113739 = exp(r113738);
        double r113740 = r113729 * r113739;
        return r113740;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r113741 = m;
        double r113742 = n;
        double r113743 = r113741 + r113742;
        double r113744 = 2.0;
        double r113745 = r113743 / r113744;
        double r113746 = M;
        double r113747 = r113745 - r113746;
        double r113748 = pow(r113747, r113744);
        double r113749 = -r113748;
        double r113750 = l;
        double r113751 = r113741 - r113742;
        double r113752 = fabs(r113751);
        double r113753 = r113750 - r113752;
        double r113754 = r113749 - r113753;
        double r113755 = exp(r113754);
        return r113755;
}

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 2019298 
(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)))))))