Average Error: 11.4 → 0.1
Time: 12.8s
Precision: 64
\[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{2.0}{\frac{z \cdot 2.0}{y} - \frac{t}{z}}\]
x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}
↓
x - \frac{2.0}{\frac{z \cdot 2.0}{y} - \frac{t}{z}}
double f(double x, double y, double z, double t) {
        double r8604507 = x;
        double r8604508 = y;
        double r8604509 = 2.0;
        double r8604510 = r8604508 * r8604509;
        double r8604511 = z;
        double r8604512 = r8604510 * r8604511;
        double r8604513 = r8604511 * r8604509;
        double r8604514 = r8604513 * r8604511;
        double r8604515 = t;
        double r8604516 = r8604508 * r8604515;
        double r8604517 = r8604514 - r8604516;
        double r8604518 = r8604512 / r8604517;
        double r8604519 = r8604507 - r8604518;
        return r8604519;
}
↓
double f(double x, double y, double z, double t) {
        double r8604520 = x;
        double r8604521 = 2.0;
        double r8604522 = z;
        double r8604523 = r8604522 * r8604521;
        double r8604524 = y;
        double r8604525 = r8604523 / r8604524;
        double r8604526 = t;
        double r8604527 = r8604526 / r8604522;
        double r8604528 = r8604525 - r8604527;
        double r8604529 = r8604521 / r8604528;
        double r8604530 = r8604520 - r8604529;
        return r8604530;
}

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

Original11.4
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2.0}}{z}}\]

Derivation

  1. Initial program 11.4

    \[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x - \frac{2.0}{\frac{2.0 \cdot z}{y} - \frac{t}{z}}}\]

  3. Final simplification0.1

    \[\leadsto x - \frac{2.0}{\frac{z \cdot 2.0}{y} - \frac{t}{z}}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

  :herbie-target
  (- x (/ 1 (- (/ z y) (/ (/ t 2.0) z))))

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