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

Average Error: 1.4 → 1.4

Time: 10.5s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r650699 = x;
        double r650700 = y;
        double r650701 = z;
        double r650702 = t;
        double r650703 = r650701 - r650702;
        double r650704 = a;
        double r650705 = r650701 - r650704;
        double r650706 = r650703 / r650705;
        double r650707 = r650700 * r650706;
        double r650708 = r650699 + r650707;
        return r650708;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r650709 = x;
        double r650710 = y;
        double r650711 = z;
        double r650712 = a;
        double r650713 = r650711 - r650712;
        double r650714 = r650711 / r650713;
        double r650715 = t;
        double r650716 = r650715 / r650713;
        double r650717 = r650714 - r650716;
        double r650718 = r650710 * r650717;
        double r650719 = r650709 + r650718;
        return r650719;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.4
Target	1.2
Herbie	1.4

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

Derivation

1. Initial program 1.4

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

3. Applied div-sub 1.4

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

4. Final simplification 1.4

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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