Average Error: 11.7 → 1.1
Time: 10.7s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}
double f(double x, double y, double z, double t) {
        double r21365612 = x;
        double r21365613 = y;
        double r21365614 = 2.0;
        double r21365615 = r21365613 * r21365614;
        double r21365616 = z;
        double r21365617 = r21365615 * r21365616;
        double r21365618 = r21365616 * r21365614;
        double r21365619 = r21365618 * r21365616;
        double r21365620 = t;
        double r21365621 = r21365613 * r21365620;
        double r21365622 = r21365619 - r21365621;
        double r21365623 = r21365617 / r21365622;
        double r21365624 = r21365612 - r21365623;
        return r21365624;
}
↓
double f(double x, double y, double z, double t) {
        double r21365625 = x;
        double r21365626 = 2.0;
        double r21365627 = y;
        double r21365628 = z;
        double r21365629 = r21365626 * r21365628;
        double r21365630 = t;
        double r21365631 = r21365628 / r21365630;
        double r21365632 = r21365627 / r21365631;
        double r21365633 = r21365629 - r21365632;
        double r21365634 = r21365627 / r21365633;
        double r21365635 = r21365626 * r21365634;
        double r21365636 = r21365625 - r21365635;
        return r21365636;
}

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
Herbie1.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

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. Simplified3.0

    \[\leadsto \color{blue}{x - \frac{y}{2 \cdot z - \frac{y \cdot t}{z}} \cdot 2}\]
  3. Using strategy rm

  4. Applied associate-/l*1.1

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

  5. Final simplification1.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

  :herbie-target
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

  (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))