Average Error: 15.2 → 1.2
Time: 35.9s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}\]
\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(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}
double f(double K, double m, double n, double M, double l) {
        double r5881299 = K;
        double r5881300 = m;
        double r5881301 = n;
        double r5881302 = r5881300 + r5881301;
        double r5881303 = r5881299 * r5881302;
        double r5881304 = 2.0;
        double r5881305 = r5881303 / r5881304;
        double r5881306 = M;
        double r5881307 = r5881305 - r5881306;
        double r5881308 = cos(r5881307);
        double r5881309 = r5881302 / r5881304;
        double r5881310 = r5881309 - r5881306;
        double r5881311 = pow(r5881310, r5881304);
        double r5881312 = -r5881311;
        double r5881313 = l;
        double r5881314 = r5881300 - r5881301;
        double r5881315 = fabs(r5881314);
        double r5881316 = r5881313 - r5881315;
        double r5881317 = r5881312 - r5881316;
        double r5881318 = exp(r5881317);
        double r5881319 = r5881308 * r5881318;
        return r5881319;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5881320 = 1.0;
        double r5881321 = l;
        double r5881322 = m;
        double r5881323 = n;
        double r5881324 = r5881322 - r5881323;
        double r5881325 = fabs(r5881324);
        double r5881326 = r5881321 - r5881325;
        double r5881327 = r5881322 + r5881323;
        double r5881328 = 2.0;
        double r5881329 = r5881327 / r5881328;
        double r5881330 = M;
        double r5881331 = r5881329 - r5881330;
        double r5881332 = r5881331 * r5881331;
        double r5881333 = r5881326 + r5881332;
        double r5881334 = exp(r5881333);
        double r5881335 = r5881320 / r5881334;
        return r5881335;
}

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 15.2

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

  2. Simplified15.2

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

  3. Taylor expanded around 0 1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019151 
(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)))))))