Average Error: 11.8 → 0.1
Time: 33.8s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - \frac{1}{\frac{z}{y} - \frac{t}{2 \cdot z}}\]
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}{2 \cdot z}}
double f(double x, double y, double z, double t) {
        double r23166519 = x;
        double r23166520 = y;
        double r23166521 = 2.0;
        double r23166522 = r23166520 * r23166521;
        double r23166523 = z;
        double r23166524 = r23166522 * r23166523;
        double r23166525 = r23166523 * r23166521;
        double r23166526 = r23166525 * r23166523;
        double r23166527 = t;
        double r23166528 = r23166520 * r23166527;
        double r23166529 = r23166526 - r23166528;
        double r23166530 = r23166524 / r23166529;
        double r23166531 = r23166519 - r23166530;
        return r23166531;
}
↓
double f(double x, double y, double z, double t) {
        double r23166532 = x;
        double r23166533 = 1.0;
        double r23166534 = z;
        double r23166535 = y;
        double r23166536 = r23166534 / r23166535;
        double r23166537 = t;
        double r23166538 = 2.0;
        double r23166539 = r23166538 * r23166534;
        double r23166540 = r23166537 / r23166539;
        double r23166541 = r23166536 - r23166540;
        double r23166542 = r23166533 / r23166541;
        double r23166543 = r23166532 - r23166542;
        return r23166543;
}

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

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

Reproduce

herbie shell --seed 2019168 
(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)))))