Average Error: 11.4 → 0.1
Time: 11.9s
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 r529094 = x;
        double r529095 = y;
        double r529096 = 2.0;
        double r529097 = r529095 * r529096;
        double r529098 = z;
        double r529099 = r529097 * r529098;
        double r529100 = r529098 * r529096;
        double r529101 = r529100 * r529098;
        double r529102 = t;
        double r529103 = r529095 * r529102;
        double r529104 = r529101 - r529103;
        double r529105 = r529099 / r529104;
        double r529106 = r529094 - r529105;
        return r529106;
}
↓
double f(double x, double y, double z, double t) {
        double r529107 = x;
        double r529108 = 2.0;
        double r529109 = z;
        double r529110 = r529109 * r529108;
        double r529111 = y;
        double r529112 = r529110 / r529111;
        double r529113 = t;
        double r529114 = r529113 / r529109;
        double r529115 = r529112 - r529114;
        double r529116 = r529108 / r529115;
        double r529117 = r529107 - r529116;
        return r529117;
}

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 2020047 
(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)))))