Average Error: 11.6 → 0.1
Time: 19.3s
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 r397292 = x;
        double r397293 = y;
        double r397294 = 2.0;
        double r397295 = r397293 * r397294;
        double r397296 = z;
        double r397297 = r397295 * r397296;
        double r397298 = r397296 * r397294;
        double r397299 = r397298 * r397296;
        double r397300 = t;
        double r397301 = r397293 * r397300;
        double r397302 = r397299 - r397301;
        double r397303 = r397297 / r397302;
        double r397304 = r397292 - r397303;
        return r397304;
}
↓
double f(double x, double y, double z, double t) {
        double r397305 = x;
        double r397306 = 2.0;
        double r397307 = z;
        double r397308 = r397307 * r397306;
        double r397309 = y;
        double r397310 = r397308 / r397309;
        double r397311 = t;
        double r397312 = r397311 / r397307;
        double r397313 = r397310 - r397312;
        double r397314 = r397306 / r397313;
        double r397315 = r397305 - r397314;
        return r397315;
}

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)))))