Average Error: 15.0 → 1.3
Time: 27.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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)}
↓
e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r4574156 = K;
        double r4574157 = m;
        double r4574158 = n;
        double r4574159 = r4574157 + r4574158;
        double r4574160 = r4574156 * r4574159;
        double r4574161 = 2.0;
        double r4574162 = r4574160 / r4574161;
        double r4574163 = M;
        double r4574164 = r4574162 - r4574163;
        double r4574165 = cos(r4574164);
        double r4574166 = r4574159 / r4574161;
        double r4574167 = r4574166 - r4574163;
        double r4574168 = pow(r4574167, r4574161);
        double r4574169 = -r4574168;
        double r4574170 = l;
        double r4574171 = r4574157 - r4574158;
        double r4574172 = fabs(r4574171);
        double r4574173 = r4574170 - r4574172;
        double r4574174 = r4574169 - r4574173;
        double r4574175 = exp(r4574174);
        double r4574176 = r4574165 * r4574175;
        return r4574176;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4574177 = m;
        double r4574178 = n;
        double r4574179 = r4574177 - r4574178;
        double r4574180 = fabs(r4574179);
        double r4574181 = l;
        double r4574182 = r4574180 - r4574181;
        double r4574183 = r4574177 + r4574178;
        double r4574184 = 2.0;
        double r4574185 = r4574183 / r4574184;
        double r4574186 = M;
        double r4574187 = r4574185 - r4574186;
        double r4574188 = pow(r4574187, r4574184);
        double r4574189 = r4574182 - r4574188;
        double r4574190 = exp(r4574189);
        return r4574190;
}

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 15.0

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

  2. Simplified15.0

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(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)))))))