Average Error: 11.7 → 0.1
Time: 15.3s
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 r567368 = x;
        double r567369 = y;
        double r567370 = 2.0;
        double r567371 = r567369 * r567370;
        double r567372 = z;
        double r567373 = r567371 * r567372;
        double r567374 = r567372 * r567370;
        double r567375 = r567374 * r567372;
        double r567376 = t;
        double r567377 = r567369 * r567376;
        double r567378 = r567375 - r567377;
        double r567379 = r567373 / r567378;
        double r567380 = r567368 - r567379;
        return r567380;
}
↓
double f(double x, double y, double z, double t) {
        double r567381 = x;
        double r567382 = 2.0;
        double r567383 = z;
        double r567384 = r567383 * r567382;
        double r567385 = y;
        double r567386 = r567384 / r567385;
        double r567387 = t;
        double r567388 = r567387 / r567383;
        double r567389 = r567386 - r567388;
        double r567390 = r567382 / r567389;
        double r567391 = r567381 - r567390;
        return r567391;
}

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)))))