Average Error: 15.2 → 1.4
Time: 29.1s
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 r107916 = K;
        double r107917 = m;
        double r107918 = n;
        double r107919 = r107917 + r107918;
        double r107920 = r107916 * r107919;
        double r107921 = 2.0;
        double r107922 = r107920 / r107921;
        double r107923 = M;
        double r107924 = r107922 - r107923;
        double r107925 = cos(r107924);
        double r107926 = r107919 / r107921;
        double r107927 = r107926 - r107923;
        double r107928 = pow(r107927, r107921);
        double r107929 = -r107928;
        double r107930 = l;
        double r107931 = r107917 - r107918;
        double r107932 = fabs(r107931);
        double r107933 = r107930 - r107932;
        double r107934 = r107929 - r107933;
        double r107935 = exp(r107934);
        double r107936 = r107925 * r107935;
        return r107936;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r107937 = m;
        double r107938 = n;
        double r107939 = r107937 + r107938;
        double r107940 = 2.0;
        double r107941 = r107939 / r107940;
        double r107942 = M;
        double r107943 = r107941 - r107942;
        double r107944 = pow(r107943, r107940);
        double r107945 = -r107944;
        double r107946 = l;
        double r107947 = r107937 - r107938;
        double r107948 = fabs(r107947);
        double r107949 = r107946 - r107948;
        double r107950 = r107945 - r107949;
        double r107951 = exp(r107950);
        return r107951;
}

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 15.2

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

  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 2019235 
(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)))))))