Average Error: 15.6 → 1.5
Time: 21.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right)}\]
\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|m - n\right| - \left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right)}
double f(double K, double m, double n, double M, double l) {
        double r3477341 = K;
        double r3477342 = m;
        double r3477343 = n;
        double r3477344 = r3477342 + r3477343;
        double r3477345 = r3477341 * r3477344;
        double r3477346 = 2.0;
        double r3477347 = r3477345 / r3477346;
        double r3477348 = M;
        double r3477349 = r3477347 - r3477348;
        double r3477350 = cos(r3477349);
        double r3477351 = r3477344 / r3477346;
        double r3477352 = r3477351 - r3477348;
        double r3477353 = pow(r3477352, r3477346);
        double r3477354 = -r3477353;
        double r3477355 = l;
        double r3477356 = r3477342 - r3477343;
        double r3477357 = fabs(r3477356);
        double r3477358 = r3477355 - r3477357;
        double r3477359 = r3477354 - r3477358;
        double r3477360 = exp(r3477359);
        double r3477361 = r3477350 * r3477360;
        return r3477361;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3477362 = m;
        double r3477363 = n;
        double r3477364 = r3477362 - r3477363;
        double r3477365 = fabs(r3477364);
        double r3477366 = r3477363 + r3477362;
        double r3477367 = 2.0;
        double r3477368 = r3477366 / r3477367;
        double r3477369 = M;
        double r3477370 = r3477368 - r3477369;
        double r3477371 = r3477370 * r3477370;
        double r3477372 = l;
        double r3477373 = r3477371 + r3477372;
        double r3477374 = r3477365 - r3477373;
        double r3477375 = exp(r3477374);
        return r3477375;
}

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. Simplified15.6

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

  3. Taylor expanded around 0 1.5

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

  4. Final simplification1.5

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

Reproduce

herbie shell --seed 2019132 
(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)))))))