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

Average Error: 1.3 → 1.3

Time: 27.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r1365084 = x;
        double r1365085 = y;
        double r1365086 = z;
        double r1365087 = t;
        double r1365088 = r1365086 - r1365087;
        double r1365089 = a;
        double r1365090 = r1365086 - r1365089;
        double r1365091 = r1365088 / r1365090;
        double r1365092 = r1365085 * r1365091;
        double r1365093 = r1365084 + r1365092;
        return r1365093;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r1365094 = x;
        double r1365095 = z;
        double r1365096 = a;
        double r1365097 = r1365095 - r1365096;
        double r1365098 = r1365095 / r1365097;
        double r1365099 = t;
        double r1365100 = r1365099 / r1365097;
        double r1365101 = r1365098 - r1365100;
        double r1365102 = y;
        double r1365103 = r1365101 * r1365102;
        double r1365104 = r1365094 + r1365103;
        return r1365104;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 1.3

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

3. Applied div-sub 1.3

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

4. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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