Average Error: 10.9 → 1.3
Time: 2.8s
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 r501876 = x;
        double r501877 = y;
        double r501878 = z;
        double r501879 = t;
        double r501880 = r501878 - r501879;
        double r501881 = r501877 * r501880;
        double r501882 = a;
        double r501883 = r501878 - r501882;
        double r501884 = r501881 / r501883;
        double r501885 = r501876 + r501884;
        return r501885;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r501886 = x;
        double r501887 = y;
        double r501888 = z;
        double r501889 = a;
        double r501890 = r501888 - r501889;
        double r501891 = t;
        double r501892 = r501888 - r501891;
        double r501893 = r501890 / r501892;
        double r501894 = r501887 / r501893;
        double r501895 = r501886 + r501894;
        return r501895;
}

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

Original10.9
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020021 
(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))))