Average Error: 11.6 → 1.0
Time: 14.0s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{y}{z - \frac{\frac{y}{\frac{z}{t}}}{2}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{y}{z - \frac{\frac{y}{\frac{z}{t}}}{2}}
double f(double x, double y, double z, double t) {
        double r322374 = x;
        double r322375 = y;
        double r322376 = 2.0;
        double r322377 = r322375 * r322376;
        double r322378 = z;
        double r322379 = r322377 * r322378;
        double r322380 = r322378 * r322376;
        double r322381 = r322380 * r322378;
        double r322382 = t;
        double r322383 = r322375 * r322382;
        double r322384 = r322381 - r322383;
        double r322385 = r322379 / r322384;
        double r322386 = r322374 - r322385;
        return r322386;
}
↓
double f(double x, double y, double z, double t) {
        double r322387 = x;
        double r322388 = y;
        double r322389 = z;
        double r322390 = t;
        double r322391 = r322389 / r322390;
        double r322392 = r322388 / r322391;
        double r322393 = 2.0;
        double r322394 = r322392 / r322393;
        double r322395 = r322389 - r322394;
        double r322396 = r322388 / r322395;
        double r322397 = r322387 - r322396;
        return r322397;
}

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
Herbie1.0
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

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. Simplified2.9

    \[\leadsto \color{blue}{x - \frac{y}{\frac{z}{1} - \frac{\frac{y \cdot t}{z}}{2}}}\]
  3. Using strategy rm

  4. Applied associate-/l*1.0

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

  5. Final simplification1.0

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

Reproduce

herbie shell --seed 2019235 
(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)))))