Average Error: 15.4 → 1.4
Time: 8.6s
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 r185323 = K;
        double r185324 = m;
        double r185325 = n;
        double r185326 = r185324 + r185325;
        double r185327 = r185323 * r185326;
        double r185328 = 2.0;
        double r185329 = r185327 / r185328;
        double r185330 = M;
        double r185331 = r185329 - r185330;
        double r185332 = cos(r185331);
        double r185333 = r185326 / r185328;
        double r185334 = r185333 - r185330;
        double r185335 = pow(r185334, r185328);
        double r185336 = -r185335;
        double r185337 = l;
        double r185338 = r185324 - r185325;
        double r185339 = fabs(r185338);
        double r185340 = r185337 - r185339;
        double r185341 = r185336 - r185340;
        double r185342 = exp(r185341);
        double r185343 = r185332 * r185342;
        return r185343;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r185344 = m;
        double r185345 = n;
        double r185346 = r185344 + r185345;
        double r185347 = 2.0;
        double r185348 = r185346 / r185347;
        double r185349 = M;
        double r185350 = r185348 - r185349;
        double r185351 = pow(r185350, r185347);
        double r185352 = -r185351;
        double r185353 = l;
        double r185354 = r185344 - r185345;
        double r185355 = fabs(r185354);
        double r185356 = r185353 - r185355;
        double r185357 = r185352 - r185356;
        double r185358 = exp(r185357);
        return r185358;
}

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 15.4

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

  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 2020002 +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)))))))