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

Average Error: 1.4 → 1.5

Time: 16.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r413173 = x;
        double r413174 = y;
        double r413175 = z;
        double r413176 = t;
        double r413177 = r413175 - r413176;
        double r413178 = a;
        double r413179 = r413175 - r413178;
        double r413180 = r413177 / r413179;
        double r413181 = r413174 * r413180;
        double r413182 = r413173 + r413181;
        return r413182;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r413183 = x;
        double r413184 = y;
        double r413185 = z;
        double r413186 = t;
        double r413187 = r413185 - r413186;
        double r413188 = 1.0;
        double r413189 = a;
        double r413190 = r413185 - r413189;
        double r413191 = r413188 / r413190;
        double r413192 = r413187 * r413191;
        double r413193 = r413184 * r413192;
        double r413194 = r413183 + r413193;
        return r413194;
}

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	1.4
Herbie	1.5

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

Derivation

1. Initial program 1.4

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

3. Applied div-inv 1.5

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

4. Final simplification 1.5

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

Reproduce

herbie shell --seed 2019325 
(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)))))