Average Error: 15.3 → 1.5
Time: 20.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[{e}^{\left(\left(\left|m - n\right| - \ell\right) - \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}\]
\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(\left|m - n\right| - \ell\right) - \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r2034123 = K;
        double r2034124 = m;
        double r2034125 = n;
        double r2034126 = r2034124 + r2034125;
        double r2034127 = r2034123 * r2034126;
        double r2034128 = 2.0;
        double r2034129 = r2034127 / r2034128;
        double r2034130 = M;
        double r2034131 = r2034129 - r2034130;
        double r2034132 = cos(r2034131);
        double r2034133 = r2034126 / r2034128;
        double r2034134 = r2034133 - r2034130;
        double r2034135 = pow(r2034134, r2034128);
        double r2034136 = -r2034135;
        double r2034137 = l;
        double r2034138 = r2034124 - r2034125;
        double r2034139 = fabs(r2034138);
        double r2034140 = r2034137 - r2034139;
        double r2034141 = r2034136 - r2034140;
        double r2034142 = exp(r2034141);
        double r2034143 = r2034132 * r2034142;
        return r2034143;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r2034144 = exp(1.0);
        double r2034145 = m;
        double r2034146 = n;
        double r2034147 = r2034145 - r2034146;
        double r2034148 = fabs(r2034147);
        double r2034149 = l;
        double r2034150 = r2034148 - r2034149;
        double r2034151 = r2034145 + r2034146;
        double r2034152 = 2.0;
        double r2034153 = r2034151 / r2034152;
        double r2034154 = M;
        double r2034155 = r2034153 - r2034154;
        double r2034156 = r2034155 * r2034155;
        double r2034157 = r2034150 - r2034156;
        double r2034158 = pow(r2034144, r2034157);
        return r2034158;
}

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 15.3

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

  2. Simplified15.2

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

  3. Taylor expanded around 0 1.5

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

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

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

  6. Applied exp-prod1.5

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

  7. Simplified1.5

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

  8. Final simplification1.5

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

Reproduce

herbie shell --seed 2019128 
(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)))))))