Average Error: 11.6 → 1.4
Time: 58.3s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{z}{\frac{z}{y} \cdot z - \frac{t}{2}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{z}{\frac{z}{y} \cdot z - \frac{t}{2}}
double f(double x, double y, double z, double t) {
        double r22297798 = x;
        double r22297799 = y;
        double r22297800 = 2.0;
        double r22297801 = r22297799 * r22297800;
        double r22297802 = z;
        double r22297803 = r22297801 * r22297802;
        double r22297804 = r22297802 * r22297800;
        double r22297805 = r22297804 * r22297802;
        double r22297806 = t;
        double r22297807 = r22297799 * r22297806;
        double r22297808 = r22297805 - r22297807;
        double r22297809 = r22297803 / r22297808;
        double r22297810 = r22297798 - r22297809;
        return r22297810;
}
↓
double f(double x, double y, double z, double t) {
        double r22297811 = x;
        double r22297812 = z;
        double r22297813 = y;
        double r22297814 = r22297812 / r22297813;
        double r22297815 = r22297814 * r22297812;
        double r22297816 = t;
        double r22297817 = 2.0;
        double r22297818 = r22297816 / r22297817;
        double r22297819 = r22297815 - r22297818;
        double r22297820 = r22297812 / r22297819;
        double r22297821 = r22297811 - r22297820;
        return r22297821;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.6
Target0.1
Herbie1.4
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.6

    \[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]

  2. Simplified1.4

    \[\leadsto \color{blue}{x - \frac{z}{\frac{z}{y} \cdot z - \frac{t}{2}}}\]

  3. Final simplification1.4

    \[\leadsto x - \frac{z}{\frac{z}{y} \cdot z - \frac{t}{2}}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

  :herbie-target
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

  (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))