Average Error: 12.2 → 0.1
Time: 2.9s
Precision: binary64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x + \frac{-1}{\frac{z}{y} - \frac{t}{z \cdot 2}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x + \frac{-1}{\frac{z}{y} - \frac{t}{z \cdot 2}}
double code(double x, double y, double z, double t) {
	return ((double) (x - (((double) (((double) (y * 2.0)) * z)) / ((double) (((double) (((double) (z * 2.0)) * z)) - ((double) (y * t)))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + (-1.0 / ((double) ((z / y) - (t / ((double) (z * 2.0))))))));
}

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

Original12.2
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 12.2

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"
  :precision binary64

  :herbie-target
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

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