Average Error: 15.5 → 1.5
Time: 28.5s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[{e}^{\left(\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)\right)}\]
\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(\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r3989047 = K;
        double r3989048 = m;
        double r3989049 = n;
        double r3989050 = r3989048 + r3989049;
        double r3989051 = r3989047 * r3989050;
        double r3989052 = 2.0;
        double r3989053 = r3989051 / r3989052;
        double r3989054 = M;
        double r3989055 = r3989053 - r3989054;
        double r3989056 = cos(r3989055);
        double r3989057 = r3989050 / r3989052;
        double r3989058 = r3989057 - r3989054;
        double r3989059 = pow(r3989058, r3989052);
        double r3989060 = -r3989059;
        double r3989061 = l;
        double r3989062 = r3989048 - r3989049;
        double r3989063 = fabs(r3989062);
        double r3989064 = r3989061 - r3989063;
        double r3989065 = r3989060 - r3989064;
        double r3989066 = exp(r3989065);
        double r3989067 = r3989056 * r3989066;
        return r3989067;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3989068 = exp(1.0);
        double r3989069 = m;
        double r3989070 = n;
        double r3989071 = r3989069 - r3989070;
        double r3989072 = fabs(r3989071);
        double r3989073 = l;
        double r3989074 = r3989069 + r3989070;
        double r3989075 = 2.0;
        double r3989076 = r3989074 / r3989075;
        double r3989077 = M;
        double r3989078 = r3989076 - r3989077;
        double r3989079 = r3989078 * r3989078;
        double r3989080 = r3989073 + r3989079;
        double r3989081 = r3989072 - r3989080;
        double r3989082 = pow(r3989068, r3989081);
        return r3989082;
}

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

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

  3. Taylor expanded around 0 1.5

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

  5. Applied *-un-lft-identity1.5

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

  6. Applied *-un-lft-identity1.5

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

  7. Applied distribute-lft-out--1.5

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

  8. Applied exp-prod1.5

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

  9. Simplified1.5

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

  10. Final simplification1.5

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

Reproduce

herbie shell --seed 2019130 
(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)))))))