Average Error: 15.7 → 1.5
Time: 30.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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 r3425126 = K;
        double r3425127 = m;
        double r3425128 = n;
        double r3425129 = r3425127 + r3425128;
        double r3425130 = r3425126 * r3425129;
        double r3425131 = 2.0;
        double r3425132 = r3425130 / r3425131;
        double r3425133 = M;
        double r3425134 = r3425132 - r3425133;
        double r3425135 = cos(r3425134);
        double r3425136 = r3425129 / r3425131;
        double r3425137 = r3425136 - r3425133;
        double r3425138 = pow(r3425137, r3425131);
        double r3425139 = -r3425138;
        double r3425140 = l;
        double r3425141 = r3425127 - r3425128;
        double r3425142 = fabs(r3425141);
        double r3425143 = r3425140 - r3425142;
        double r3425144 = r3425139 - r3425143;
        double r3425145 = exp(r3425144);
        double r3425146 = r3425135 * r3425145;
        return r3425146;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3425147 = m;
        double r3425148 = n;
        double r3425149 = r3425147 + r3425148;
        double r3425150 = 2.0;
        double r3425151 = r3425149 / r3425150;
        double r3425152 = M;
        double r3425153 = r3425151 - r3425152;
        double r3425154 = pow(r3425153, r3425150);
        double r3425155 = -r3425154;
        double r3425156 = l;
        double r3425157 = r3425147 - r3425148;
        double r3425158 = fabs(r3425157);
        double r3425159 = r3425156 - r3425158;
        double r3425160 = r3425155 - r3425159;
        double r3425161 = exp(r3425160);
        return r3425161;
}

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 15.7

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

  2. Taylor expanded around 0 1.5

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

  3. Final simplification1.5

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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)))))))