Average Error: 11.7 → 1.1
Time: 20.8s
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 r24171667 = x;
        double r24171668 = y;
        double r24171669 = 2.0;
        double r24171670 = r24171668 * r24171669;
        double r24171671 = z;
        double r24171672 = r24171670 * r24171671;
        double r24171673 = r24171671 * r24171669;
        double r24171674 = r24171673 * r24171671;
        double r24171675 = t;
        double r24171676 = r24171668 * r24171675;
        double r24171677 = r24171674 - r24171676;
        double r24171678 = r24171672 / r24171677;
        double r24171679 = r24171667 - r24171678;
        return r24171679;
}
↓
double f(double x, double y, double z, double t) {
        double r24171680 = x;
        double r24171681 = 2.0;
        double r24171682 = y;
        double r24171683 = z;
        double r24171684 = r24171681 * r24171683;
        double r24171685 = t;
        double r24171686 = r24171683 / r24171685;
        double r24171687 = r24171682 / r24171686;
        double r24171688 = r24171684 - r24171687;
        double r24171689 = r24171682 / r24171688;
        double r24171690 = r24171681 * r24171689;
        double r24171691 = r24171680 - r24171690;
        return r24171691;
}

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

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. Simplified2.8

    \[\leadsto \color{blue}{x - \frac{y}{2 \cdot z - \frac{y \cdot t}{z}} \cdot 2}\]
  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 2019179 
(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)))))