Average Error: 15.7 → 1.2
Time: 6.3s
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 r142803 = K;
        double r142804 = m;
        double r142805 = n;
        double r142806 = r142804 + r142805;
        double r142807 = r142803 * r142806;
        double r142808 = 2.0;
        double r142809 = r142807 / r142808;
        double r142810 = M;
        double r142811 = r142809 - r142810;
        double r142812 = cos(r142811);
        double r142813 = r142806 / r142808;
        double r142814 = r142813 - r142810;
        double r142815 = pow(r142814, r142808);
        double r142816 = -r142815;
        double r142817 = l;
        double r142818 = r142804 - r142805;
        double r142819 = fabs(r142818);
        double r142820 = r142817 - r142819;
        double r142821 = r142816 - r142820;
        double r142822 = exp(r142821);
        double r142823 = r142812 * r142822;
        return r142823;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r142824 = m;
        double r142825 = n;
        double r142826 = r142824 + r142825;
        double r142827 = 2.0;
        double r142828 = r142826 / r142827;
        double r142829 = M;
        double r142830 = r142828 - r142829;
        double r142831 = pow(r142830, r142827);
        double r142832 = -r142831;
        double r142833 = l;
        double r142834 = r142824 - r142825;
        double r142835 = fabs(r142834);
        double r142836 = r142833 - r142835;
        double r142837 = r142832 - r142836;
        double r142838 = exp(r142837);
        return r142838;
}

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 15.7

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

  2. Taylor expanded around 0 1.2

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

  3. Final simplification1.2

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(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)))))))