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

Average Error: 1.2 → 1.1

Time: 19.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r369100 = x;
        double r369101 = y;
        double r369102 = z;
        double r369103 = t;
        double r369104 = r369102 - r369103;
        double r369105 = a;
        double r369106 = r369102 - r369105;
        double r369107 = r369104 / r369106;
        double r369108 = r369101 * r369107;
        double r369109 = r369100 + r369108;
        return r369109;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r369110 = x;
        double r369111 = y;
        double r369112 = z;
        double r369113 = a;
        double r369114 = r369112 - r369113;
        double r369115 = t;
        double r369116 = r369112 - r369115;
        double r369117 = r369114 / r369116;
        double r369118 = r369111 / r369117;
        double r369119 = r369110 + r369118;
        return r369119;
}

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	1.1
Herbie	1.1

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

Derivation

1. Initial program 1.2

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

3. Applied associate-*r/ 10.9

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

5. Applied associate-/l* 1.1

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

6. Final simplification 1.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(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)))))