Average Error: 11.0 → 1.3
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r584905 = x;
        double r584906 = y;
        double r584907 = z;
        double r584908 = t;
        double r584909 = r584907 - r584908;
        double r584910 = r584906 * r584909;
        double r584911 = a;
        double r584912 = r584911 - r584908;
        double r584913 = r584910 / r584912;
        double r584914 = r584905 + r584913;
        return r584914;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r584915 = x;
        double r584916 = y;
        double r584917 = a;
        double r584918 = z;
        double r584919 = t;
        double r584920 = r584918 - r584919;
        double r584921 = r584917 / r584920;
        double r584922 = r584919 / r584920;
        double r584923 = r584921 - r584922;
        double r584924 = r584916 / r584923;
        double r584925 = r584915 + r584924;
        return r584925;
}

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

Original11.0
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.3

    \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied div-sub1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020039 
(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))))