Average Error: 11.4 → 0.1
Time: 11.4s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{2}{\frac{z \cdot 2}{y} - \frac{t}{z}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - \frac{2}{\frac{z \cdot 2}{y} - \frac{t}{z}}
double f(double x, double y, double z, double t) {
        double r1141311 = x;
        double r1141312 = y;
        double r1141313 = 2.0;
        double r1141314 = r1141312 * r1141313;
        double r1141315 = z;
        double r1141316 = r1141314 * r1141315;
        double r1141317 = r1141315 * r1141313;
        double r1141318 = r1141317 * r1141315;
        double r1141319 = t;
        double r1141320 = r1141312 * r1141319;
        double r1141321 = r1141318 - r1141320;
        double r1141322 = r1141316 / r1141321;
        double r1141323 = r1141311 - r1141322;
        return r1141323;
}
↓
double f(double x, double y, double z, double t) {
        double r1141324 = x;
        double r1141325 = 2.0;
        double r1141326 = z;
        double r1141327 = r1141326 * r1141325;
        double r1141328 = y;
        double r1141329 = r1141327 / r1141328;
        double r1141330 = t;
        double r1141331 = r1141330 / r1141326;
        double r1141332 = r1141329 - r1141331;
        double r1141333 = r1141325 / r1141332;
        double r1141334 = r1141324 - r1141333;
        return r1141334;
}

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

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. Simplified0.1

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

  3. Final simplification0.1

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

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)))))