Average Error: 15.5 → 1.4
Time: 24.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r86040 = K;
        double r86041 = m;
        double r86042 = n;
        double r86043 = r86041 + r86042;
        double r86044 = r86040 * r86043;
        double r86045 = 2.0;
        double r86046 = r86044 / r86045;
        double r86047 = M;
        double r86048 = r86046 - r86047;
        double r86049 = cos(r86048);
        double r86050 = r86043 / r86045;
        double r86051 = r86050 - r86047;
        double r86052 = pow(r86051, r86045);
        double r86053 = -r86052;
        double r86054 = l;
        double r86055 = r86041 - r86042;
        double r86056 = fabs(r86055);
        double r86057 = r86054 - r86056;
        double r86058 = r86053 - r86057;
        double r86059 = exp(r86058);
        double r86060 = r86049 * r86059;
        return r86060;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r86061 = m;
        double r86062 = n;
        double r86063 = r86061 - r86062;
        double r86064 = fabs(r86063);
        double r86065 = l;
        double r86066 = r86064 - r86065;
        double r86067 = r86061 + r86062;
        double r86068 = 2.0;
        double r86069 = r86067 / r86068;
        double r86070 = M;
        double r86071 = r86069 - r86070;
        double r86072 = pow(r86071, r86068);
        double r86073 = r86066 - r86072;
        double r86074 = exp(r86073);
        return r86074;
}

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

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019326 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))