Average Error: 11.4 → 1.1
Time: 4.8s
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 r657997 = x;
        double r657998 = y;
        double r657999 = 2.0;
        double r658000 = r657998 * r657999;
        double r658001 = z;
        double r658002 = r658000 * r658001;
        double r658003 = r658001 * r657999;
        double r658004 = r658003 * r658001;
        double r658005 = t;
        double r658006 = r657998 * r658005;
        double r658007 = r658004 - r658006;
        double r658008 = r658002 / r658007;
        double r658009 = r657997 - r658008;
        return r658009;
}
↓
double f(double x, double y, double z, double t) {
        double r658010 = x;
        double r658011 = z;
        double r658012 = y;
        double r658013 = r658012 / r658011;
        double r658014 = r658011 / r658013;
        double r658015 = t;
        double r658016 = 2.0;
        double r658017 = r658015 / r658016;
        double r658018 = r658014 - r658017;
        double r658019 = r658011 / r658018;
        double r658020 = r658010 - r658019;
        return r658020;
}

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

Derivation

  1. Initial program 11.4

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

  2. Simplified3.5

    \[\leadsto \color{blue}{x - \frac{z}{\frac{z \cdot z}{y} - \frac{t}{2}}}\]
  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 2020047 
(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)))))