Average Error: 11.9 → 1.1
Time: 32.5s
Precision: 64
\[x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{y}{z - \frac{y \cdot \frac{t}{z}}{2.0}}\]
x - \frac{\left(y \cdot 2.0\right) \cdot z}{\left(z \cdot 2.0\right) \cdot z - y \cdot t}
↓
x - \frac{y}{z - \frac{y \cdot \frac{t}{z}}{2.0}}
double f(double x, double y, double z, double t) {
        double r20335515 = x;
        double r20335516 = y;
        double r20335517 = 2.0;
        double r20335518 = r20335516 * r20335517;
        double r20335519 = z;
        double r20335520 = r20335518 * r20335519;
        double r20335521 = r20335519 * r20335517;
        double r20335522 = r20335521 * r20335519;
        double r20335523 = t;
        double r20335524 = r20335516 * r20335523;
        double r20335525 = r20335522 - r20335524;
        double r20335526 = r20335520 / r20335525;
        double r20335527 = r20335515 - r20335526;
        return r20335527;
}
↓
double f(double x, double y, double z, double t) {
        double r20335528 = x;
        double r20335529 = y;
        double r20335530 = z;
        double r20335531 = t;
        double r20335532 = r20335531 / r20335530;
        double r20335533 = r20335529 * r20335532;
        double r20335534 = 2.0;
        double r20335535 = r20335533 / r20335534;
        double r20335536 = r20335530 - r20335535;
        double r20335537 = r20335529 / r20335536;
        double r20335538 = r20335528 - r20335537;
        return r20335538;
}

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

Original11.9
Target0.1
Herbie1.1
\[x - \frac{1.0}{\frac{z}{y} - \frac{\frac{t}{2.0}}{z}}\]

Derivation

  1. Initial program 11.9

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

  2. Simplified1.1

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

  3. Final simplification1.1

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

Reproduce

herbie shell --seed 2019165 
(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)))))