Average Error: 15.6 → 1.4
Time: 47.6s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[{e}^{\left(\left(-{\left(\frac{n + m}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}\]
\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(-{\left(\frac{n + m}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r115153 = K;
        double r115154 = m;
        double r115155 = n;
        double r115156 = r115154 + r115155;
        double r115157 = r115153 * r115156;
        double r115158 = 2.0;
        double r115159 = r115157 / r115158;
        double r115160 = M;
        double r115161 = r115159 - r115160;
        double r115162 = cos(r115161);
        double r115163 = r115156 / r115158;
        double r115164 = r115163 - r115160;
        double r115165 = pow(r115164, r115158);
        double r115166 = -r115165;
        double r115167 = l;
        double r115168 = r115154 - r115155;
        double r115169 = fabs(r115168);
        double r115170 = r115167 - r115169;
        double r115171 = r115166 - r115170;
        double r115172 = exp(r115171);
        double r115173 = r115162 * r115172;
        return r115173;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r115174 = exp(1.0);
        double r115175 = n;
        double r115176 = m;
        double r115177 = r115175 + r115176;
        double r115178 = 2.0;
        double r115179 = r115177 / r115178;
        double r115180 = M;
        double r115181 = r115179 - r115180;
        double r115182 = pow(r115181, r115178);
        double r115183 = -r115182;
        double r115184 = l;
        double r115185 = r115176 - r115175;
        double r115186 = fabs(r115185);
        double r115187 = r115184 - r115186;
        double r115188 = r115183 - r115187;
        double r115189 = pow(r115174, r115188);
        return r115189;
}

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. Using strategy rm

  4. Applied *-un-lft-identity1.4

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

  5. Applied exp-prod1.4

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

  6. Simplified1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2019174 
(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)))))))