Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Average Error: 1.2 → 1.2

Time: 7.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r1235859 = x;
        double r1235860 = y;
        double r1235861 = z;
        double r1235862 = t;
        double r1235863 = r1235861 - r1235862;
        double r1235864 = a;
        double r1235865 = r1235864 - r1235862;
        double r1235866 = r1235863 / r1235865;
        double r1235867 = r1235860 * r1235866;
        double r1235868 = r1235859 + r1235867;
        return r1235868;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r1235869 = x;
        double r1235870 = y;
        double r1235871 = z;
        double r1235872 = t;
        double r1235873 = r1235871 - r1235872;
        double r1235874 = 1.0;
        double r1235875 = a;
        double r1235876 = r1235875 - r1235872;
        double r1235877 = r1235874 / r1235876;
        double r1235878 = r1235873 * r1235877;
        double r1235879 = r1235870 * r1235878;
        double r1235880 = r1235869 + r1235879;
        return r1235880;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.2
Target	0.4
Herbie	1.2

\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Initial program 1.2

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

3. Applied div-inv 1.2

   \[\leadsto x + y \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{a - t}\right)}\]

4. Final simplification 1.2

   \[\leadsto x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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