Average Error: 11.3 → 1.1
Time: 19.3s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{z}{\frac{z}{\frac{y}{z}} - \frac{t}{2}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{z}{\frac{z}{\frac{y}{z}} - \frac{t}{2}}
double f(double x, double y, double z, double t) {
        double r297548 = x;
        double r297549 = y;
        double r297550 = 2.0;
        double r297551 = r297549 * r297550;
        double r297552 = z;
        double r297553 = r297551 * r297552;
        double r297554 = r297552 * r297550;
        double r297555 = r297554 * r297552;
        double r297556 = t;
        double r297557 = r297549 * r297556;
        double r297558 = r297555 - r297557;
        double r297559 = r297553 / r297558;
        double r297560 = r297548 - r297559;
        return r297560;
}
↓
double f(double x, double y, double z, double t) {
        double r297561 = x;
        double r297562 = z;
        double r297563 = y;
        double r297564 = r297563 / r297562;
        double r297565 = r297562 / r297564;
        double r297566 = t;
        double r297567 = 2.0;
        double r297568 = r297566 / r297567;
        double r297569 = r297565 - r297568;
        double r297570 = r297562 / r297569;
        double r297571 = r297561 - r297570;
        return r297571;
}

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

Original11.3
Target0.1
Herbie1.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.3

    \[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]

  2. Simplified3.1

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

  4. Applied associate-/l*1.1

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

  5. Final simplification1.1

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

Reproduce

herbie shell --seed 2019326 
(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)))))