Average Error: 15.6 → 1.4
Time: 8.4s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r155349 = K;
        double r155350 = m;
        double r155351 = n;
        double r155352 = r155350 + r155351;
        double r155353 = r155349 * r155352;
        double r155354 = 2.0;
        double r155355 = r155353 / r155354;
        double r155356 = M;
        double r155357 = r155355 - r155356;
        double r155358 = cos(r155357);
        double r155359 = r155352 / r155354;
        double r155360 = r155359 - r155356;
        double r155361 = pow(r155360, r155354);
        double r155362 = -r155361;
        double r155363 = l;
        double r155364 = r155350 - r155351;
        double r155365 = fabs(r155364);
        double r155366 = r155363 - r155365;
        double r155367 = r155362 - r155366;
        double r155368 = exp(r155367);
        double r155369 = r155358 * r155368;
        return r155369;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r155370 = 1.0;
        double r155371 = m;
        double r155372 = n;
        double r155373 = r155371 + r155372;
        double r155374 = 2.0;
        double r155375 = r155373 / r155374;
        double r155376 = M;
        double r155377 = r155375 - r155376;
        double r155378 = pow(r155377, r155374);
        double r155379 = l;
        double r155380 = r155371 - r155372;
        double r155381 = fabs(r155380);
        double r155382 = r155379 - r155381;
        double r155383 = r155378 + r155382;
        double r155384 = exp(r155383);
        double r155385 = r155370 / r155384;
        return r155385;
}

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

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020021 
(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)))))))