Average Error: 11.8 → 0.1
Time: 23.9s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{\frac{z}{y} - \frac{t}{z \cdot 2}}\]
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 f(double x, double y, double z, double t) {
        double r61203252 = x;
        double r61203253 = y;
        double r61203254 = 2.0;
        double r61203255 = r61203253 * r61203254;
        double r61203256 = z;
        double r61203257 = r61203255 * r61203256;
        double r61203258 = r61203256 * r61203254;
        double r61203259 = r61203258 * r61203256;
        double r61203260 = t;
        double r61203261 = r61203253 * r61203260;
        double r61203262 = r61203259 - r61203261;
        double r61203263 = r61203257 / r61203262;
        double r61203264 = r61203252 - r61203263;
        return r61203264;
}
↓
double f(double x, double y, double z, double t) {
        double r61203265 = x;
        double r61203266 = 1.0;
        double r61203267 = z;
        double r61203268 = y;
        double r61203269 = r61203267 / r61203268;
        double r61203270 = t;
        double r61203271 = 2.0;
        double r61203272 = r61203267 * r61203271;
        double r61203273 = r61203270 / r61203272;
        double r61203274 = r61203269 - r61203273;
        double r61203275 = r61203266 / r61203274;
        double r61203276 = r61203265 - r61203275;
        return r61203276;
}

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

Original11.8
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.8

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

  3. Applied clear-num11.8

    \[\leadsto x - \color{blue}{\frac{1}{\frac{\left(z \cdot 2\right) \cdot z - y \cdot t}{\left(y \cdot 2\right) \cdot z}}}\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"

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

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