Average Error: 11.6 → 0.1
Time: 11.5s
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 r590887 = x;
        double r590888 = y;
        double r590889 = 2.0;
        double r590890 = r590888 * r590889;
        double r590891 = z;
        double r590892 = r590890 * r590891;
        double r590893 = r590891 * r590889;
        double r590894 = r590893 * r590891;
        double r590895 = t;
        double r590896 = r590888 * r590895;
        double r590897 = r590894 - r590896;
        double r590898 = r590892 / r590897;
        double r590899 = r590887 - r590898;
        return r590899;
}
↓
double f(double x, double y, double z, double t) {
        double r590900 = x;
        double r590901 = 2.0;
        double r590902 = z;
        double r590903 = r590902 * r590901;
        double r590904 = y;
        double r590905 = r590903 / r590904;
        double r590906 = t;
        double r590907 = r590906 / r590902;
        double r590908 = r590905 - r590907;
        double r590909 = r590901 / r590908;
        double r590910 = r590900 - r590909;
        return r590910;
}

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

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. 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 2020046 
(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)))))