Average Error: 11.6 → 0.1
Time: 13.8s
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 r516522 = x;
        double r516523 = y;
        double r516524 = 2.0;
        double r516525 = r516523 * r516524;
        double r516526 = z;
        double r516527 = r516525 * r516526;
        double r516528 = r516526 * r516524;
        double r516529 = r516528 * r516526;
        double r516530 = t;
        double r516531 = r516523 * r516530;
        double r516532 = r516529 - r516531;
        double r516533 = r516527 / r516532;
        double r516534 = r516522 - r516533;
        return r516534;
}
↓
double f(double x, double y, double z, double t) {
        double r516535 = x;
        double r516536 = 2.0;
        double r516537 = z;
        double r516538 = r516537 * r516536;
        double r516539 = y;
        double r516540 = r516538 / r516539;
        double r516541 = t;
        double r516542 = r516541 / r516537;
        double r516543 = r516540 - r516542;
        double r516544 = r516536 / r516543;
        double r516545 = r516535 - r516544;
        return r516545;
}

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 2020043 
(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)))))