Average Error: 15.6 → 1.3
Time: 19.3s
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 r110119 = K;
        double r110120 = m;
        double r110121 = n;
        double r110122 = r110120 + r110121;
        double r110123 = r110119 * r110122;
        double r110124 = 2.0;
        double r110125 = r110123 / r110124;
        double r110126 = M;
        double r110127 = r110125 - r110126;
        double r110128 = cos(r110127);
        double r110129 = r110122 / r110124;
        double r110130 = r110129 - r110126;
        double r110131 = pow(r110130, r110124);
        double r110132 = -r110131;
        double r110133 = l;
        double r110134 = r110120 - r110121;
        double r110135 = fabs(r110134);
        double r110136 = r110133 - r110135;
        double r110137 = r110132 - r110136;
        double r110138 = exp(r110137);
        double r110139 = r110128 * r110138;
        return r110139;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r110140 = m;
        double r110141 = n;
        double r110142 = r110140 + r110141;
        double r110143 = 2.0;
        double r110144 = r110142 / r110143;
        double r110145 = M;
        double r110146 = r110144 - r110145;
        double r110147 = pow(r110146, r110143);
        double r110148 = -r110147;
        double r110149 = l;
        double r110150 = r110140 - r110141;
        double r110151 = fabs(r110150);
        double r110152 = r110149 - r110151;
        double r110153 = r110148 - r110152;
        double r110154 = exp(r110153);
        return r110154;
}

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 15.6

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

  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 2019350 +o rules:numerics
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))