Average Error: 15.6 → 1.4
Time: 45.4s
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 r6402774 = K;
        double r6402775 = m;
        double r6402776 = n;
        double r6402777 = r6402775 + r6402776;
        double r6402778 = r6402774 * r6402777;
        double r6402779 = 2.0;
        double r6402780 = r6402778 / r6402779;
        double r6402781 = M;
        double r6402782 = r6402780 - r6402781;
        double r6402783 = cos(r6402782);
        double r6402784 = r6402777 / r6402779;
        double r6402785 = r6402784 - r6402781;
        double r6402786 = pow(r6402785, r6402779);
        double r6402787 = -r6402786;
        double r6402788 = l;
        double r6402789 = r6402775 - r6402776;
        double r6402790 = fabs(r6402789);
        double r6402791 = r6402788 - r6402790;
        double r6402792 = r6402787 - r6402791;
        double r6402793 = exp(r6402792);
        double r6402794 = r6402783 * r6402793;
        return r6402794;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r6402795 = m;
        double r6402796 = n;
        double r6402797 = r6402795 + r6402796;
        double r6402798 = 2.0;
        double r6402799 = r6402797 / r6402798;
        double r6402800 = M;
        double r6402801 = r6402799 - r6402800;
        double r6402802 = pow(r6402801, r6402798);
        double r6402803 = -r6402802;
        double r6402804 = l;
        double r6402805 = r6402795 - r6402796;
        double r6402806 = fabs(r6402805);
        double r6402807 = r6402804 - r6402806;
        double r6402808 = r6402803 - r6402807;
        double r6402809 = exp(r6402808);
        return r6402809;
}

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)))))))