Average Error: 11.4 → 0.1
Time: 10.2s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{2}{\frac{z \cdot 2}{y} - \frac{t}{z}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{2}{\frac{z \cdot 2}{y} - \frac{t}{z}}
double f(double x, double y, double z, double t) {
        double r443784 = x;
        double r443785 = y;
        double r443786 = 2.0;
        double r443787 = r443785 * r443786;
        double r443788 = z;
        double r443789 = r443787 * r443788;
        double r443790 = r443788 * r443786;
        double r443791 = r443790 * r443788;
        double r443792 = t;
        double r443793 = r443785 * r443792;
        double r443794 = r443791 - r443793;
        double r443795 = r443789 / r443794;
        double r443796 = r443784 - r443795;
        return r443796;
}
↓
double f(double x, double y, double z, double t) {
        double r443797 = x;
        double r443798 = 2.0;
        double r443799 = z;
        double r443800 = r443799 * r443798;
        double r443801 = y;
        double r443802 = r443800 / r443801;
        double r443803 = t;
        double r443804 = r443803 / r443799;
        double r443805 = r443802 - r443804;
        double r443806 = r443798 / r443805;
        double r443807 = r443797 - r443806;
        return r443807;
}

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

Original11.4
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.4

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))))