Average Error: 10.5 → 1.3
Time: 3.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r473867 = x;
        double r473868 = y;
        double r473869 = z;
        double r473870 = t;
        double r473871 = r473869 - r473870;
        double r473872 = r473868 * r473871;
        double r473873 = a;
        double r473874 = r473873 - r473870;
        double r473875 = r473872 / r473874;
        double r473876 = r473867 + r473875;
        return r473876;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r473877 = x;
        double r473878 = y;
        double r473879 = a;
        double r473880 = t;
        double r473881 = r473879 - r473880;
        double r473882 = z;
        double r473883 = r473882 - r473880;
        double r473884 = r473881 / r473883;
        double r473885 = r473878 / r473884;
        double r473886 = r473877 + r473885;
        return r473886;
}

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

Original10.5
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.5

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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