Average Error: 10.9 → 1.3
Time: 6.3s
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 r396883 = x;
        double r396884 = y;
        double r396885 = z;
        double r396886 = t;
        double r396887 = r396885 - r396886;
        double r396888 = r396884 * r396887;
        double r396889 = a;
        double r396890 = r396889 - r396886;
        double r396891 = r396888 / r396890;
        double r396892 = r396883 + r396891;
        return r396892;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r396893 = x;
        double r396894 = y;
        double r396895 = a;
        double r396896 = t;
        double r396897 = r396895 - r396896;
        double r396898 = z;
        double r396899 = r396898 - r396896;
        double r396900 = r396897 / r396899;
        double r396901 = r396894 / r396900;
        double r396902 = r396893 + r396901;
        return r396902;
}

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

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
  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 1978988140 
(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))))