Average Error: 15.1 → 1.4
Time: 43.1s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{n + m}{2} - M\right)}^{2}}\]
\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)}
↓
e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{n + m}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r4145214 = K;
        double r4145215 = m;
        double r4145216 = n;
        double r4145217 = r4145215 + r4145216;
        double r4145218 = r4145214 * r4145217;
        double r4145219 = 2.0;
        double r4145220 = r4145218 / r4145219;
        double r4145221 = M;
        double r4145222 = r4145220 - r4145221;
        double r4145223 = cos(r4145222);
        double r4145224 = r4145217 / r4145219;
        double r4145225 = r4145224 - r4145221;
        double r4145226 = pow(r4145225, r4145219);
        double r4145227 = -r4145226;
        double r4145228 = l;
        double r4145229 = r4145215 - r4145216;
        double r4145230 = fabs(r4145229);
        double r4145231 = r4145228 - r4145230;
        double r4145232 = r4145227 - r4145231;
        double r4145233 = exp(r4145232);
        double r4145234 = r4145223 * r4145233;
        return r4145234;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4145235 = m;
        double r4145236 = n;
        double r4145237 = r4145235 - r4145236;
        double r4145238 = fabs(r4145237);
        double r4145239 = l;
        double r4145240 = r4145238 - r4145239;
        double r4145241 = r4145236 + r4145235;
        double r4145242 = 2.0;
        double r4145243 = r4145241 / r4145242;
        double r4145244 = M;
        double r4145245 = r4145243 - r4145244;
        double r4145246 = pow(r4145245, r4145242);
        double r4145247 = r4145240 - r4145246;
        double r4145248 = exp(r4145247);
        return r4145248;
}

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 15.1

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

  2. Simplified15.1

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019200 
(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)))))))