Average Error: 15.6 → 1.3
Time: 16.3s
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 r146164 = K;
        double r146165 = m;
        double r146166 = n;
        double r146167 = r146165 + r146166;
        double r146168 = r146164 * r146167;
        double r146169 = 2.0;
        double r146170 = r146168 / r146169;
        double r146171 = M;
        double r146172 = r146170 - r146171;
        double r146173 = cos(r146172);
        double r146174 = r146167 / r146169;
        double r146175 = r146174 - r146171;
        double r146176 = pow(r146175, r146169);
        double r146177 = -r146176;
        double r146178 = l;
        double r146179 = r146165 - r146166;
        double r146180 = fabs(r146179);
        double r146181 = r146178 - r146180;
        double r146182 = r146177 - r146181;
        double r146183 = exp(r146182);
        double r146184 = r146173 * r146183;
        return r146184;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r146185 = m;
        double r146186 = n;
        double r146187 = r146185 + r146186;
        double r146188 = 2.0;
        double r146189 = r146187 / r146188;
        double r146190 = M;
        double r146191 = r146189 - r146190;
        double r146192 = pow(r146191, r146188);
        double r146193 = -r146192;
        double r146194 = l;
        double r146195 = r146185 - r146186;
        double r146196 = fabs(r146195);
        double r146197 = r146194 - r146196;
        double r146198 = r146193 - r146197;
        double r146199 = exp(r146198);
        return r146199;
}

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 1.3

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

  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 2019350 
(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)))))))