Average Error: 11.7 → 1.1
Time: 14.2s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}
double f(double x, double y, double z, double t) {
        double r414411 = x;
        double r414412 = y;
        double r414413 = 2.0;
        double r414414 = r414412 * r414413;
        double r414415 = z;
        double r414416 = r414414 * r414415;
        double r414417 = r414415 * r414413;
        double r414418 = r414417 * r414415;
        double r414419 = t;
        double r414420 = r414412 * r414419;
        double r414421 = r414418 - r414420;
        double r414422 = r414416 / r414421;
        double r414423 = r414411 - r414422;
        return r414423;
}
↓
double f(double x, double y, double z, double t) {
        double r414424 = x;
        double r414425 = 2.0;
        double r414426 = y;
        double r414427 = z;
        double r414428 = r414425 * r414427;
        double r414429 = t;
        double r414430 = r414427 / r414429;
        double r414431 = r414426 / r414430;
        double r414432 = r414428 - r414431;
        double r414433 = r414426 / r414432;
        double r414434 = r414425 * r414433;
        double r414435 = r414424 - r414434;
        return r414435;
}

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

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. Simplified2.8

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

  4. Applied associate-/l*1.1

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

  5. Final simplification1.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

  :herbie-target
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

  (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))