Average Error: 11.5 → 0.1
Time: 19.6s
Precision: 64
\[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{\frac{z}{y} - \frac{t}{2.0 \cdot z}}\]
x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}
↓
x - \frac{1}{\frac{z}{y} - \frac{t}{2.0 \cdot z}}
double f(double x, double y, double z, double t) {
        double r26020298 = x;
        double r26020299 = y;
        double r26020300 = 2.0;
        double r26020301 = r26020299 * r26020300;
        double r26020302 = z;
        double r26020303 = r26020301 * r26020302;
        double r26020304 = r26020302 * r26020300;
        double r26020305 = r26020304 * r26020302;
        double r26020306 = t;
        double r26020307 = r26020299 * r26020306;
        double r26020308 = r26020305 - r26020307;
        double r26020309 = r26020303 / r26020308;
        double r26020310 = r26020298 - r26020309;
        return r26020310;
}
↓
double f(double x, double y, double z, double t) {
        double r26020311 = x;
        double r26020312 = 1.0;
        double r26020313 = z;
        double r26020314 = y;
        double r26020315 = r26020313 / r26020314;
        double r26020316 = t;
        double r26020317 = 2.0;
        double r26020318 = r26020317 * r26020313;
        double r26020319 = r26020316 / r26020318;
        double r26020320 = r26020315 - r26020319;
        double r26020321 = r26020312 / r26020320;
        double r26020322 = r26020311 - r26020321;
        return r26020322;
}

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

Derivation

  1. Initial program 11.5

    \[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
  2. Using strategy rm

  3. Applied clear-num11.5

    \[\leadsto x - \color{blue}{\frac{1}{\frac{\left(z \cdot 2.0\right) \cdot z - y \cdot t}{\left(y \cdot 2.0\right) \cdot z}}}\]

  4. Simplified0.1

    \[\leadsto x - \frac{1}{\color{blue}{\frac{z}{y} \cdot 1 - 1 \cdot \frac{t}{2.0 \cdot z}}}\]

  5. Final simplification0.1

    \[\leadsto x - \frac{1}{\frac{z}{y} - \frac{t}{2.0 \cdot z}}\]

Reproduce

herbie shell --seed 2019168 
(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)))))