Average Error: 12.0 → 1.1
Time: 16.7s
Precision: 64
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
↓
\[x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}\]
x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}
↓
x - 2 \cdot \frac{y}{2 \cdot z - \frac{y}{\frac{z}{t}}}
double f(double x, double y, double z, double t) {
        double r27907401 = x;
        double r27907402 = y;
        double r27907403 = 2.0;
        double r27907404 = r27907402 * r27907403;
        double r27907405 = z;
        double r27907406 = r27907404 * r27907405;
        double r27907407 = r27907405 * r27907403;
        double r27907408 = r27907407 * r27907405;
        double r27907409 = t;
        double r27907410 = r27907402 * r27907409;
        double r27907411 = r27907408 - r27907410;
        double r27907412 = r27907406 / r27907411;
        double r27907413 = r27907401 - r27907412;
        return r27907413;
}
↓
double f(double x, double y, double z, double t) {
        double r27907414 = x;
        double r27907415 = 2.0;
        double r27907416 = y;
        double r27907417 = z;
        double r27907418 = r27907415 * r27907417;
        double r27907419 = t;
        double r27907420 = r27907417 / r27907419;
        double r27907421 = r27907416 / r27907420;
        double r27907422 = r27907418 - r27907421;
        double r27907423 = r27907416 / r27907422;
        double r27907424 = r27907415 * r27907423;
        double r27907425 = r27907414 - r27907424;
        return r27907425;
}

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

Original12.0
Target0.1
Herbie1.1
\[x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}}\]

Derivation

  1. Initial program 12.0

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

  2. Simplified2.7

    \[\leadsto \color{blue}{x - \frac{y}{2 \cdot z - \frac{y \cdot t}{z}} \cdot 2}\]
  3. Using strategy rm

  4. Applied associate-/l*1.1

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

  5. Final simplification1.1

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

Reproduce

herbie shell --seed 2019171 
(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)))))