Average Error: 15.2 → 1.4
Time: 23.8s
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 r6057132 = K;
        double r6057133 = m;
        double r6057134 = n;
        double r6057135 = r6057133 + r6057134;
        double r6057136 = r6057132 * r6057135;
        double r6057137 = 2.0;
        double r6057138 = r6057136 / r6057137;
        double r6057139 = M;
        double r6057140 = r6057138 - r6057139;
        double r6057141 = cos(r6057140);
        double r6057142 = r6057135 / r6057137;
        double r6057143 = r6057142 - r6057139;
        double r6057144 = pow(r6057143, r6057137);
        double r6057145 = -r6057144;
        double r6057146 = l;
        double r6057147 = r6057133 - r6057134;
        double r6057148 = fabs(r6057147);
        double r6057149 = r6057146 - r6057148;
        double r6057150 = r6057145 - r6057149;
        double r6057151 = exp(r6057150);
        double r6057152 = r6057141 * r6057151;
        return r6057152;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r6057153 = m;
        double r6057154 = n;
        double r6057155 = r6057153 + r6057154;
        double r6057156 = 2.0;
        double r6057157 = r6057155 / r6057156;
        double r6057158 = M;
        double r6057159 = r6057157 - r6057158;
        double r6057160 = pow(r6057159, r6057156);
        double r6057161 = -r6057160;
        double r6057162 = l;
        double r6057163 = r6057153 - r6057154;
        double r6057164 = fabs(r6057163);
        double r6057165 = r6057162 - r6057164;
        double r6057166 = r6057161 - r6057165;
        double r6057167 = exp(r6057166);
        return r6057167;
}

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 15.2

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

  2. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019168 
(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)))))))