Average Error: 15.5 → 1.3
Time: 35.5s
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 r129168 = K;
        double r129169 = m;
        double r129170 = n;
        double r129171 = r129169 + r129170;
        double r129172 = r129168 * r129171;
        double r129173 = 2.0;
        double r129174 = r129172 / r129173;
        double r129175 = M;
        double r129176 = r129174 - r129175;
        double r129177 = cos(r129176);
        double r129178 = r129171 / r129173;
        double r129179 = r129178 - r129175;
        double r129180 = pow(r129179, r129173);
        double r129181 = -r129180;
        double r129182 = l;
        double r129183 = r129169 - r129170;
        double r129184 = fabs(r129183);
        double r129185 = r129182 - r129184;
        double r129186 = r129181 - r129185;
        double r129187 = exp(r129186);
        double r129188 = r129177 * r129187;
        return r129188;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r129189 = m;
        double r129190 = n;
        double r129191 = r129189 + r129190;
        double r129192 = 2.0;
        double r129193 = r129191 / r129192;
        double r129194 = M;
        double r129195 = r129193 - r129194;
        double r129196 = pow(r129195, r129192);
        double r129197 = -r129196;
        double r129198 = l;
        double r129199 = r129189 - r129190;
        double r129200 = fabs(r129199);
        double r129201 = r129198 - r129200;
        double r129202 = r129197 - r129201;
        double r129203 = exp(r129202);
        return r129203;
}

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 15.5

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

  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 2019303 +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)))))))