Average Error: 15.2 → 1.3
Time: 5.5s
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 r208057 = K;
        double r208058 = m;
        double r208059 = n;
        double r208060 = r208058 + r208059;
        double r208061 = r208057 * r208060;
        double r208062 = 2.0;
        double r208063 = r208061 / r208062;
        double r208064 = M;
        double r208065 = r208063 - r208064;
        double r208066 = cos(r208065);
        double r208067 = r208060 / r208062;
        double r208068 = r208067 - r208064;
        double r208069 = pow(r208068, r208062);
        double r208070 = -r208069;
        double r208071 = l;
        double r208072 = r208058 - r208059;
        double r208073 = fabs(r208072);
        double r208074 = r208071 - r208073;
        double r208075 = r208070 - r208074;
        double r208076 = exp(r208075);
        double r208077 = r208066 * r208076;
        return r208077;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r208078 = m;
        double r208079 = n;
        double r208080 = r208078 + r208079;
        double r208081 = 2.0;
        double r208082 = r208080 / r208081;
        double r208083 = M;
        double r208084 = r208082 - r208083;
        double r208085 = pow(r208084, r208081);
        double r208086 = -r208085;
        double r208087 = l;
        double r208088 = r208078 - r208079;
        double r208089 = fabs(r208088);
        double r208090 = r208087 - r208089;
        double r208091 = r208086 - r208090;
        double r208092 = exp(r208091);
        return r208092;
}

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 1.3

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

  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 2019347 +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)))))))