Average Error: 15.3 → 1.3
Time: 11.1s
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 r156153 = K;
        double r156154 = m;
        double r156155 = n;
        double r156156 = r156154 + r156155;
        double r156157 = r156153 * r156156;
        double r156158 = 2.0;
        double r156159 = r156157 / r156158;
        double r156160 = M;
        double r156161 = r156159 - r156160;
        double r156162 = cos(r156161);
        double r156163 = r156156 / r156158;
        double r156164 = r156163 - r156160;
        double r156165 = pow(r156164, r156158);
        double r156166 = -r156165;
        double r156167 = l;
        double r156168 = r156154 - r156155;
        double r156169 = fabs(r156168);
        double r156170 = r156167 - r156169;
        double r156171 = r156166 - r156170;
        double r156172 = exp(r156171);
        double r156173 = r156162 * r156172;
        return r156173;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r156174 = m;
        double r156175 = n;
        double r156176 = r156174 + r156175;
        double r156177 = 2.0;
        double r156178 = r156176 / r156177;
        double r156179 = M;
        double r156180 = r156178 - r156179;
        double r156181 = pow(r156180, r156177);
        double r156182 = -r156181;
        double r156183 = l;
        double r156184 = r156174 - r156175;
        double r156185 = fabs(r156184);
        double r156186 = r156183 - r156185;
        double r156187 = r156182 - r156186;
        double r156188 = exp(r156187);
        return r156188;
}

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 15.3

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

  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 2020060 +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)))))))