Average Error: 11.3 → 0.1
Time: 15.5s
Precision: 64
\[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{\frac{z}{y} - \frac{t}{2.0 \cdot z}}\]
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 r25039244 = x;
        double r25039245 = y;
        double r25039246 = 2.0;
        double r25039247 = r25039245 * r25039246;
        double r25039248 = z;
        double r25039249 = r25039247 * r25039248;
        double r25039250 = r25039248 * r25039246;
        double r25039251 = r25039250 * r25039248;
        double r25039252 = t;
        double r25039253 = r25039245 * r25039252;
        double r25039254 = r25039251 - r25039253;
        double r25039255 = r25039249 / r25039254;
        double r25039256 = r25039244 - r25039255;
        return r25039256;
}
↓
double f(double x, double y, double z, double t) {
        double r25039257 = x;
        double r25039258 = 1.0;
        double r25039259 = z;
        double r25039260 = y;
        double r25039261 = r25039259 / r25039260;
        double r25039262 = t;
        double r25039263 = 2.0;
        double r25039264 = r25039263 * r25039259;
        double r25039265 = r25039262 / r25039264;
        double r25039266 = r25039261 - r25039265;
        double r25039267 = r25039258 / r25039266;
        double r25039268 = r25039257 - r25039267;
        return r25039268;
}

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

Original11.3
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2.0}}{z}}\]

Derivation

  1. Initial program 11.3

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

  3. Applied clear-num11.3

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

  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 2019158 
(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)))))