Average Error: 11.5 → 0.1
Time: 18.7s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}
double f(double x, double y, double z, double t) {
        double r455209 = x;
        double r455210 = y;
        double r455211 = 2.0;
        double r455212 = r455210 * r455211;
        double r455213 = z;
        double r455214 = r455212 * r455213;
        double r455215 = r455213 * r455211;
        double r455216 = r455215 * r455213;
        double r455217 = t;
        double r455218 = r455210 * r455217;
        double r455219 = r455216 - r455218;
        double r455220 = r455214 / r455219;
        double r455221 = r455209 - r455220;
        return r455221;
}
↓
double f(double x, double y, double z, double t) {
        double r455222 = x;
        double r455223 = 1.0;
        double r455224 = z;
        double r455225 = y;
        double r455226 = r455224 / r455225;
        double r455227 = t;
        double r455228 = 2.0;
        double r455229 = r455227 / r455228;
        double r455230 = r455229 / r455224;
        double r455231 = r455226 - r455230;
        double r455232 = r455223 / r455231;
        double r455233 = r455222 - r455232;
        return r455233;
}

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

Original11.5
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.5

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

  2. Simplified3.5

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

  4. Applied clear-num3.5

    \[\leadsto x - \color{blue}{\frac{1}{\frac{\frac{z \cdot z}{y} - \frac{t}{2}}{z}}}\]

  5. Simplified0.1

    \[\leadsto x - \frac{1}{\color{blue}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}}\]

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(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)))))