Average Error: 11.5 → 1.1
Time: 15.9s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}} \cdot y\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}} \cdot y
double f(double x, double y, double z, double t) {
        double r17704798 = x;
        double r17704799 = y;
        double r17704800 = 2.0;
        double r17704801 = r17704799 * r17704800;
        double r17704802 = z;
        double r17704803 = r17704801 * r17704802;
        double r17704804 = r17704802 * r17704800;
        double r17704805 = r17704804 * r17704802;
        double r17704806 = t;
        double r17704807 = r17704799 * r17704806;
        double r17704808 = r17704805 - r17704807;
        double r17704809 = r17704803 / r17704808;
        double r17704810 = r17704798 - r17704809;
        return r17704810;
}
↓
double f(double x, double y, double z, double t) {
        double r17704811 = x;
        double r17704812 = 1.0;
        double r17704813 = z;
        double r17704814 = t;
        double r17704815 = r17704814 / r17704813;
        double r17704816 = y;
        double r17704817 = r17704815 * r17704816;
        double r17704818 = 2.0;
        double r17704819 = r17704817 / r17704818;
        double r17704820 = r17704813 - r17704819;
        double r17704821 = r17704812 / r17704820;
        double r17704822 = r17704821 * r17704816;
        double r17704823 = r17704811 - r17704822;
        return r17704823;
}

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

Original11.5
Target0.1
Herbie1.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.5

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

  2. Simplified1.0

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

  4. Applied div-inv1.1

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

  5. Final simplification1.1

    \[\leadsto x - \frac{1}{z - \frac{\frac{t}{z} \cdot y}{2}} \cdot y\]

Reproduce

herbie shell --seed 2019172 
(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)))))