Average Error: 11.4 → 1.1
Time: 9.5s
Precision: 64
\[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{y}{z - \frac{t}{2.0 \cdot z} \cdot y}\]
x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}
↓
x - \frac{y}{z - \frac{t}{2.0 \cdot z} \cdot y}
double f(double x, double y, double z, double t) {
        double r9544984 = x;
        double r9544985 = y;
        double r9544986 = 2.0;
        double r9544987 = r9544985 * r9544986;
        double r9544988 = z;
        double r9544989 = r9544987 * r9544988;
        double r9544990 = r9544988 * r9544986;
        double r9544991 = r9544990 * r9544988;
        double r9544992 = t;
        double r9544993 = r9544985 * r9544992;
        double r9544994 = r9544991 - r9544993;
        double r9544995 = r9544989 / r9544994;
        double r9544996 = r9544984 - r9544995;
        return r9544996;
}
↓
double f(double x, double y, double z, double t) {
        double r9544997 = x;
        double r9544998 = y;
        double r9544999 = z;
        double r9545000 = t;
        double r9545001 = 2.0;
        double r9545002 = r9545001 * r9544999;
        double r9545003 = r9545000 / r9545002;
        double r9545004 = r9545003 * r9544998;
        double r9545005 = r9544999 - r9545004;
        double r9545006 = r9544998 / r9545005;
        double r9545007 = r9544997 - r9545006;
        return r9545007;
}

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
Herbie1.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2.0}}{z}}\]

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. Simplified2.4

    \[\leadsto \color{blue}{x - \frac{y}{z - \frac{t}{\frac{z \cdot 2.0}{y}}}}\]
  3. Using strategy rm

  4. Applied associate-/r/1.1

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

  5. Final simplification1.1

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

Reproduce

herbie shell --seed 2019156 
(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)))))