Average Error: 10.6 → 1.2
Time: 10.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r393863 = x;
        double r393864 = y;
        double r393865 = z;
        double r393866 = t;
        double r393867 = r393865 - r393866;
        double r393868 = r393864 * r393867;
        double r393869 = a;
        double r393870 = r393865 - r393869;
        double r393871 = r393868 / r393870;
        double r393872 = r393863 + r393871;
        return r393872;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r393873 = x;
        double r393874 = y;
        double r393875 = z;
        double r393876 = a;
        double r393877 = r393875 - r393876;
        double r393878 = t;
        double r393879 = r393875 - r393878;
        double r393880 = r393877 / r393879;
        double r393881 = r393874 / r393880;
        double r393882 = r393873 + r393881;
        return r393882;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  2. Using strategy rm

  3. Applied associate-/l*1.2

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]

  4. Final simplification1.2

    \[\leadsto x + \frac{y}{\frac{z - a}{z - t}}\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))