Average Error: 14.9 → 1.3
Time: 24.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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)}
↓
e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r93281 = K;
        double r93282 = m;
        double r93283 = n;
        double r93284 = r93282 + r93283;
        double r93285 = r93281 * r93284;
        double r93286 = 2.0;
        double r93287 = r93285 / r93286;
        double r93288 = M;
        double r93289 = r93287 - r93288;
        double r93290 = cos(r93289);
        double r93291 = r93284 / r93286;
        double r93292 = r93291 - r93288;
        double r93293 = pow(r93292, r93286);
        double r93294 = -r93293;
        double r93295 = l;
        double r93296 = r93282 - r93283;
        double r93297 = fabs(r93296);
        double r93298 = r93295 - r93297;
        double r93299 = r93294 - r93298;
        double r93300 = exp(r93299);
        double r93301 = r93290 * r93300;
        return r93301;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r93302 = m;
        double r93303 = n;
        double r93304 = r93302 - r93303;
        double r93305 = fabs(r93304);
        double r93306 = l;
        double r93307 = r93305 - r93306;
        double r93308 = r93302 + r93303;
        double r93309 = 2.0;
        double r93310 = r93308 / r93309;
        double r93311 = M;
        double r93312 = r93310 - r93311;
        double r93313 = pow(r93312, r93309);
        double r93314 = r93307 - r93313;
        double r93315 = exp(r93314);
        return r93315;
}

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 14.9

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

  2. Simplified14.9

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019323 
(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)))))))