Average Error: 11.9 → 0.1
Time: 11.2s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}
double f(double x, double y, double z, double t) {
        double r686739 = x;
        double r686740 = y;
        double r686741 = 2.0;
        double r686742 = r686740 * r686741;
        double r686743 = z;
        double r686744 = r686742 * r686743;
        double r686745 = r686743 * r686741;
        double r686746 = r686745 * r686743;
        double r686747 = t;
        double r686748 = r686740 * r686747;
        double r686749 = r686746 - r686748;
        double r686750 = r686744 / r686749;
        double r686751 = r686739 - r686750;
        return r686751;
}
↓
double f(double x, double y, double z, double t) {
        double r686752 = x;
        double r686753 = 1.0;
        double r686754 = z;
        double r686755 = y;
        double r686756 = r686754 / r686755;
        double r686757 = t;
        double r686758 = 2.0;
        double r686759 = r686757 / r686758;
        double r686760 = r686759 / r686754;
        double r686761 = r686756 - r686760;
        double r686762 = r686753 / r686761;
        double r686763 = r686752 - r686762;
        return r686763;
}

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

Original11.9
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.9

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

  3. Applied clear-num11.9

    \[\leadsto x - \color{blue}{\frac{1}{\frac{\left(z \cdot 2\right) \cdot z - y \cdot t}{\left(y \cdot 2\right) \cdot z}}}\]

  4. Simplified0.1

    \[\leadsto x - \frac{1}{\color{blue}{\frac{z}{y} \cdot 1 - \frac{1 \cdot \frac{t}{2}}{z}}}\]

  5. Final simplification0.1

    \[\leadsto x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"
  :precision binary64

  :herbie-target
  (- x (/ 1 (- (/ z y) (/ (/ t 2) z))))

  (- x (/ (* (* y 2) z) (- (* (* z 2) z) (* y t)))))