Average Error: 14.6 → 1.4
Time: 19.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}\]
\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)}
↓
\frac{1}{e^{\left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}
double f(double K, double m, double n, double M, double l) {
        double r2832334 = K;
        double r2832335 = m;
        double r2832336 = n;
        double r2832337 = r2832335 + r2832336;
        double r2832338 = r2832334 * r2832337;
        double r2832339 = 2.0;
        double r2832340 = r2832338 / r2832339;
        double r2832341 = M;
        double r2832342 = r2832340 - r2832341;
        double r2832343 = cos(r2832342);
        double r2832344 = r2832337 / r2832339;
        double r2832345 = r2832344 - r2832341;
        double r2832346 = pow(r2832345, r2832339);
        double r2832347 = -r2832346;
        double r2832348 = l;
        double r2832349 = r2832335 - r2832336;
        double r2832350 = fabs(r2832349);
        double r2832351 = r2832348 - r2832350;
        double r2832352 = r2832347 - r2832351;
        double r2832353 = exp(r2832352);
        double r2832354 = r2832343 * r2832353;
        return r2832354;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r2832355 = 1.0;
        double r2832356 = n;
        double r2832357 = m;
        double r2832358 = r2832356 + r2832357;
        double r2832359 = 2.0;
        double r2832360 = r2832358 / r2832359;
        double r2832361 = M;
        double r2832362 = r2832360 - r2832361;
        double r2832363 = r2832362 * r2832362;
        double r2832364 = l;
        double r2832365 = r2832363 + r2832364;
        double r2832366 = r2832357 - r2832356;
        double r2832367 = fabs(r2832366);
        double r2832368 = r2832365 - r2832367;
        double r2832369 = exp(r2832368);
        double r2832370 = r2832355 / r2832369;
        return r2832370;
}

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 14.6

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

  2. Simplified14.6

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019152 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))