Average Error: 15.7 → 1.2
Time: 18.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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 r84169 = K;
        double r84170 = m;
        double r84171 = n;
        double r84172 = r84170 + r84171;
        double r84173 = r84169 * r84172;
        double r84174 = 2.0;
        double r84175 = r84173 / r84174;
        double r84176 = M;
        double r84177 = r84175 - r84176;
        double r84178 = cos(r84177);
        double r84179 = r84172 / r84174;
        double r84180 = r84179 - r84176;
        double r84181 = pow(r84180, r84174);
        double r84182 = -r84181;
        double r84183 = l;
        double r84184 = r84170 - r84171;
        double r84185 = fabs(r84184);
        double r84186 = r84183 - r84185;
        double r84187 = r84182 - r84186;
        double r84188 = exp(r84187);
        double r84189 = r84178 * r84188;
        return r84189;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r84190 = m;
        double r84191 = n;
        double r84192 = r84190 + r84191;
        double r84193 = 2.0;
        double r84194 = r84192 / r84193;
        double r84195 = M;
        double r84196 = r84194 - r84195;
        double r84197 = pow(r84196, r84193);
        double r84198 = -r84197;
        double r84199 = l;
        double r84200 = r84190 - r84191;
        double r84201 = fabs(r84200);
        double r84202 = r84199 - r84201;
        double r84203 = r84198 - r84202;
        double r84204 = exp(r84203);
        return r84204;
}

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 15.7

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

  2. Taylor expanded around 0 1.2

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

  3. Final simplification1.2

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

Reproduce

herbie shell --seed 2019208 
(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)))))))