Average Error: 11.7 → 1.0
Time: 16.3s
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 r431415 = x;
        double r431416 = y;
        double r431417 = 2.0;
        double r431418 = r431416 * r431417;
        double r431419 = z;
        double r431420 = r431418 * r431419;
        double r431421 = r431419 * r431417;
        double r431422 = r431421 * r431419;
        double r431423 = t;
        double r431424 = r431416 * r431423;
        double r431425 = r431422 - r431424;
        double r431426 = r431420 / r431425;
        double r431427 = r431415 - r431426;
        return r431427;
}
↓
double f(double x, double y, double z, double t) {
        double r431428 = x;
        double r431429 = y;
        double r431430 = z;
        double r431431 = t;
        double r431432 = r431430 / r431431;
        double r431433 = r431429 / r431432;
        double r431434 = 2.0;
        double r431435 = r431433 / r431434;
        double r431436 = r431430 - r431435;
        double r431437 = r431429 / r431436;
        double r431438 = r431428 - r431437;
        return r431438;
}

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

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. Simplified2.8

    \[\leadsto \color{blue}{x - \frac{y}{\frac{z}{1} - \frac{\frac{y \cdot t}{z}}{2}}}\]
  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 2019212 
(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)))))