Average Error: 15.5 → 1.4
Time: 26.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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 r86313 = K;
        double r86314 = m;
        double r86315 = n;
        double r86316 = r86314 + r86315;
        double r86317 = r86313 * r86316;
        double r86318 = 2.0;
        double r86319 = r86317 / r86318;
        double r86320 = M;
        double r86321 = r86319 - r86320;
        double r86322 = cos(r86321);
        double r86323 = r86316 / r86318;
        double r86324 = r86323 - r86320;
        double r86325 = pow(r86324, r86318);
        double r86326 = -r86325;
        double r86327 = l;
        double r86328 = r86314 - r86315;
        double r86329 = fabs(r86328);
        double r86330 = r86327 - r86329;
        double r86331 = r86326 - r86330;
        double r86332 = exp(r86331);
        double r86333 = r86322 * r86332;
        return r86333;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r86334 = 1.0;
        double r86335 = m;
        double r86336 = n;
        double r86337 = r86335 + r86336;
        double r86338 = 2.0;
        double r86339 = r86337 / r86338;
        double r86340 = M;
        double r86341 = r86339 - r86340;
        double r86342 = pow(r86341, r86338);
        double r86343 = l;
        double r86344 = r86335 - r86336;
        double r86345 = fabs(r86344);
        double r86346 = r86343 - r86345;
        double r86347 = r86342 + r86346;
        double r86348 = exp(r86347);
        double r86349 = r86334 / r86348;
        return r86349;
}

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 15.5

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

  2. Simplified15.5

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

  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 2019199 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))