Average Error: 15.7 → 1.6
Time: 6.7s
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 r113275 = K;
        double r113276 = m;
        double r113277 = n;
        double r113278 = r113276 + r113277;
        double r113279 = r113275 * r113278;
        double r113280 = 2.0;
        double r113281 = r113279 / r113280;
        double r113282 = M;
        double r113283 = r113281 - r113282;
        double r113284 = cos(r113283);
        double r113285 = r113278 / r113280;
        double r113286 = r113285 - r113282;
        double r113287 = pow(r113286, r113280);
        double r113288 = -r113287;
        double r113289 = l;
        double r113290 = r113276 - r113277;
        double r113291 = fabs(r113290);
        double r113292 = r113289 - r113291;
        double r113293 = r113288 - r113292;
        double r113294 = exp(r113293);
        double r113295 = r113284 * r113294;
        return r113295;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r113296 = m;
        double r113297 = n;
        double r113298 = r113296 + r113297;
        double r113299 = 2.0;
        double r113300 = r113298 / r113299;
        double r113301 = M;
        double r113302 = r113300 - r113301;
        double r113303 = pow(r113302, r113299);
        double r113304 = -r113303;
        double r113305 = l;
        double r113306 = r113296 - r113297;
        double r113307 = fabs(r113306);
        double r113308 = r113305 - r113307;
        double r113309 = r113304 - r113308;
        double r113310 = exp(r113309);
        return r113310;
}

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 1.6

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

  3. Final simplification1.6

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

Reproduce

herbie shell --seed 2020057 +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)))))))