Average Error: 15.6 → 1.4
Time: 7.1s
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 r125247 = K;
        double r125248 = m;
        double r125249 = n;
        double r125250 = r125248 + r125249;
        double r125251 = r125247 * r125250;
        double r125252 = 2.0;
        double r125253 = r125251 / r125252;
        double r125254 = M;
        double r125255 = r125253 - r125254;
        double r125256 = cos(r125255);
        double r125257 = r125250 / r125252;
        double r125258 = r125257 - r125254;
        double r125259 = pow(r125258, r125252);
        double r125260 = -r125259;
        double r125261 = l;
        double r125262 = r125248 - r125249;
        double r125263 = fabs(r125262);
        double r125264 = r125261 - r125263;
        double r125265 = r125260 - r125264;
        double r125266 = exp(r125265);
        double r125267 = r125256 * r125266;
        return r125267;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r125268 = m;
        double r125269 = n;
        double r125270 = r125268 + r125269;
        double r125271 = 2.0;
        double r125272 = r125270 / r125271;
        double r125273 = M;
        double r125274 = r125272 - r125273;
        double r125275 = pow(r125274, r125271);
        double r125276 = -r125275;
        double r125277 = l;
        double r125278 = r125268 - r125269;
        double r125279 = fabs(r125278);
        double r125280 = r125277 - r125279;
        double r125281 = r125276 - r125280;
        double r125282 = exp(r125281);
        return r125282;
}

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 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2020083 +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)))))))