Average Error: 11.7 → 0.1
Time: 13.8s
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 r188442 = x;
        double r188443 = y;
        double r188444 = 2.0;
        double r188445 = r188443 * r188444;
        double r188446 = z;
        double r188447 = r188445 * r188446;
        double r188448 = r188446 * r188444;
        double r188449 = r188448 * r188446;
        double r188450 = t;
        double r188451 = r188443 * r188450;
        double r188452 = r188449 - r188451;
        double r188453 = r188447 / r188452;
        double r188454 = r188442 - r188453;
        return r188454;
}
↓
double f(double x, double y, double z, double t) {
        double r188455 = x;
        double r188456 = 2.0;
        double r188457 = z;
        double r188458 = r188457 * r188456;
        double r188459 = y;
        double r188460 = r188458 / r188459;
        double r188461 = t;
        double r188462 = r188461 / r188457;
        double r188463 = r188460 - r188462;
        double r188464 = r188456 / r188463;
        double r188465 = r188455 - r188464;
        return r188465;
}

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

Original11.7
Target0.1
Herbie0.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 11.7

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

  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 2020042 +o rules:numerics
(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)))))