Average Error: 15.2 → 1.4
Time: 25.9s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)}\]
\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)}
↓
e^{\left(\left|m - n\right| - \ell\right) - \left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right)}
double f(double K, double m, double n, double M, double l) {
        double r3917282 = K;
        double r3917283 = m;
        double r3917284 = n;
        double r3917285 = r3917283 + r3917284;
        double r3917286 = r3917282 * r3917285;
        double r3917287 = 2.0;
        double r3917288 = r3917286 / r3917287;
        double r3917289 = M;
        double r3917290 = r3917288 - r3917289;
        double r3917291 = cos(r3917290);
        double r3917292 = r3917285 / r3917287;
        double r3917293 = r3917292 - r3917289;
        double r3917294 = pow(r3917293, r3917287);
        double r3917295 = -r3917294;
        double r3917296 = l;
        double r3917297 = r3917283 - r3917284;
        double r3917298 = fabs(r3917297);
        double r3917299 = r3917296 - r3917298;
        double r3917300 = r3917295 - r3917299;
        double r3917301 = exp(r3917300);
        double r3917302 = r3917291 * r3917301;
        return r3917302;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3917303 = m;
        double r3917304 = n;
        double r3917305 = r3917303 - r3917304;
        double r3917306 = fabs(r3917305);
        double r3917307 = l;
        double r3917308 = r3917306 - r3917307;
        double r3917309 = r3917304 + r3917303;
        double r3917310 = 2.0;
        double r3917311 = r3917309 / r3917310;
        double r3917312 = M;
        double r3917313 = r3917311 - r3917312;
        double r3917314 = r3917313 * r3917313;
        double r3917315 = r3917308 - r3917314;
        double r3917316 = exp(r3917315);
        return r3917316;
}

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. Simplified15.1

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019135 
(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)))))))