Average Error: 11.7 → 0.1
Time: 14.5s
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 r616005 = x;
        double r616006 = y;
        double r616007 = 2.0;
        double r616008 = r616006 * r616007;
        double r616009 = z;
        double r616010 = r616008 * r616009;
        double r616011 = r616009 * r616007;
        double r616012 = r616011 * r616009;
        double r616013 = t;
        double r616014 = r616006 * r616013;
        double r616015 = r616012 - r616014;
        double r616016 = r616010 / r616015;
        double r616017 = r616005 - r616016;
        return r616017;
}
↓
double f(double x, double y, double z, double t) {
        double r616018 = x;
        double r616019 = 2.0;
        double r616020 = z;
        double r616021 = r616020 * r616019;
        double r616022 = y;
        double r616023 = r616021 / r616022;
        double r616024 = t;
        double r616025 = r616024 / r616020;
        double r616026 = r616023 - r616025;
        double r616027 = r616019 / r616026;
        double r616028 = r616018 - r616027;
        return r616028;
}

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

Original11.7
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.7

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

  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 2020042 
(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)))))