Average Error: 15.5 → 1.3
Time: 21.6s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r5001122 = K;
        double r5001123 = m;
        double r5001124 = n;
        double r5001125 = r5001123 + r5001124;
        double r5001126 = r5001122 * r5001125;
        double r5001127 = 2.0;
        double r5001128 = r5001126 / r5001127;
        double r5001129 = M;
        double r5001130 = r5001128 - r5001129;
        double r5001131 = cos(r5001130);
        double r5001132 = r5001125 / r5001127;
        double r5001133 = r5001132 - r5001129;
        double r5001134 = pow(r5001133, r5001127);
        double r5001135 = -r5001134;
        double r5001136 = l;
        double r5001137 = r5001123 - r5001124;
        double r5001138 = fabs(r5001137);
        double r5001139 = r5001136 - r5001138;
        double r5001140 = r5001135 - r5001139;
        double r5001141 = exp(r5001140);
        double r5001142 = r5001131 * r5001141;
        return r5001142;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5001143 = m;
        double r5001144 = n;
        double r5001145 = r5001143 + r5001144;
        double r5001146 = 2.0;
        double r5001147 = r5001145 / r5001146;
        double r5001148 = M;
        double r5001149 = r5001147 - r5001148;
        double r5001150 = pow(r5001149, r5001146);
        double r5001151 = -r5001150;
        double r5001152 = l;
        double r5001153 = r5001143 - r5001144;
        double r5001154 = fabs(r5001153);
        double r5001155 = r5001152 - r5001154;
        double r5001156 = r5001151 - r5001155;
        double r5001157 = exp(r5001156);
        return r5001157;
}

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. Taylor expanded around 0 1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2019149 
(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)))))))