Average Error: 15.3 → 1.3
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 r125336 = K;
        double r125337 = m;
        double r125338 = n;
        double r125339 = r125337 + r125338;
        double r125340 = r125336 * r125339;
        double r125341 = 2.0;
        double r125342 = r125340 / r125341;
        double r125343 = M;
        double r125344 = r125342 - r125343;
        double r125345 = cos(r125344);
        double r125346 = r125339 / r125341;
        double r125347 = r125346 - r125343;
        double r125348 = pow(r125347, r125341);
        double r125349 = -r125348;
        double r125350 = l;
        double r125351 = r125337 - r125338;
        double r125352 = fabs(r125351);
        double r125353 = r125350 - r125352;
        double r125354 = r125349 - r125353;
        double r125355 = exp(r125354);
        double r125356 = r125345 * r125355;
        return r125356;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r125357 = m;
        double r125358 = n;
        double r125359 = r125357 + r125358;
        double r125360 = 2.0;
        double r125361 = r125359 / r125360;
        double r125362 = M;
        double r125363 = r125361 - r125362;
        double r125364 = pow(r125363, r125360);
        double r125365 = -r125364;
        double r125366 = l;
        double r125367 = r125357 - r125358;
        double r125368 = fabs(r125367);
        double r125369 = r125366 - r125368;
        double r125370 = r125365 - r125369;
        double r125371 = exp(r125370);
        return r125371;
}

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 15.3

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

  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 2020060 +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)))))))