Average Error: 14.7 → 1.4
Time: 45.2s
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 r22393128 = K;
        double r22393129 = m;
        double r22393130 = n;
        double r22393131 = r22393129 + r22393130;
        double r22393132 = r22393128 * r22393131;
        double r22393133 = 2.0;
        double r22393134 = r22393132 / r22393133;
        double r22393135 = M;
        double r22393136 = r22393134 - r22393135;
        double r22393137 = cos(r22393136);
        double r22393138 = r22393131 / r22393133;
        double r22393139 = r22393138 - r22393135;
        double r22393140 = pow(r22393139, r22393133);
        double r22393141 = -r22393140;
        double r22393142 = l;
        double r22393143 = r22393129 - r22393130;
        double r22393144 = fabs(r22393143);
        double r22393145 = r22393142 - r22393144;
        double r22393146 = r22393141 - r22393145;
        double r22393147 = exp(r22393146);
        double r22393148 = r22393137 * r22393147;
        return r22393148;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r22393149 = m;
        double r22393150 = n;
        double r22393151 = r22393149 + r22393150;
        double r22393152 = 2.0;
        double r22393153 = r22393151 / r22393152;
        double r22393154 = M;
        double r22393155 = r22393153 - r22393154;
        double r22393156 = pow(r22393155, r22393152);
        double r22393157 = -r22393156;
        double r22393158 = l;
        double r22393159 = r22393149 - r22393150;
        double r22393160 = fabs(r22393159);
        double r22393161 = r22393158 - r22393160;
        double r22393162 = r22393157 - r22393161;
        double r22393163 = exp(r22393162);
        return r22393163;
}

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 14.7

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

  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 2019119 
(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)))))))