Average Error: 15.4 → 1.4
Time: 1.1m
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left(\ell + \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right)}\]
\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)}
↓
e^{\left|m - n\right| - \left(\ell + \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r10125267 = K;
        double r10125268 = m;
        double r10125269 = n;
        double r10125270 = r10125268 + r10125269;
        double r10125271 = r10125267 * r10125270;
        double r10125272 = 2.0;
        double r10125273 = r10125271 / r10125272;
        double r10125274 = M;
        double r10125275 = r10125273 - r10125274;
        double r10125276 = cos(r10125275);
        double r10125277 = r10125270 / r10125272;
        double r10125278 = r10125277 - r10125274;
        double r10125279 = pow(r10125278, r10125272);
        double r10125280 = -r10125279;
        double r10125281 = l;
        double r10125282 = r10125268 - r10125269;
        double r10125283 = fabs(r10125282);
        double r10125284 = r10125281 - r10125283;
        double r10125285 = r10125280 - r10125284;
        double r10125286 = exp(r10125285);
        double r10125287 = r10125276 * r10125286;
        return r10125287;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r10125288 = m;
        double r10125289 = n;
        double r10125290 = r10125288 - r10125289;
        double r10125291 = fabs(r10125290);
        double r10125292 = l;
        double r10125293 = r10125289 + r10125288;
        double r10125294 = 2.0;
        double r10125295 = r10125293 / r10125294;
        double r10125296 = M;
        double r10125297 = r10125295 - r10125296;
        double r10125298 = r10125297 * r10125297;
        double r10125299 = r10125292 + r10125298;
        double r10125300 = r10125291 - r10125299;
        double r10125301 = exp(r10125300);
        return r10125301;
}

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 15.4

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

  2. Simplified15.4

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

  3. Taylor expanded around 0 1.4

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

  5. Applied 1-exp1.4

    \[\leadsto \frac{\color{blue}{e^{0}}}{e^{\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right)}}\]

  6. Applied div-exp1.4

    \[\leadsto \color{blue}{e^{0 - \left(\left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right) + \left(\ell - \left|m - n\right|\right)\right)}}\]

  7. Simplified1.4

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

  8. Final simplification1.4

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

Reproduce

herbie shell --seed 2019124 
(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)))))))