Average Error: 15.2 → 1.3
Time: 13.9s
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 r243280 = K;
        double r243281 = m;
        double r243282 = n;
        double r243283 = r243281 + r243282;
        double r243284 = r243280 * r243283;
        double r243285 = 2.0;
        double r243286 = r243284 / r243285;
        double r243287 = M;
        double r243288 = r243286 - r243287;
        double r243289 = cos(r243288);
        double r243290 = r243283 / r243285;
        double r243291 = r243290 - r243287;
        double r243292 = pow(r243291, r243285);
        double r243293 = -r243292;
        double r243294 = l;
        double r243295 = r243281 - r243282;
        double r243296 = fabs(r243295);
        double r243297 = r243294 - r243296;
        double r243298 = r243293 - r243297;
        double r243299 = exp(r243298);
        double r243300 = r243289 * r243299;
        return r243300;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r243301 = m;
        double r243302 = n;
        double r243303 = r243301 + r243302;
        double r243304 = 2.0;
        double r243305 = r243303 / r243304;
        double r243306 = M;
        double r243307 = r243305 - r243306;
        double r243308 = pow(r243307, r243304);
        double r243309 = -r243308;
        double r243310 = l;
        double r243311 = r243301 - r243302;
        double r243312 = fabs(r243311);
        double r243313 = r243310 - r243312;
        double r243314 = r243309 - r243313;
        double r243315 = exp(r243314);
        return r243315;
}

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 15.2

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

  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 2020047 
(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)))))))