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

Average Error: 1.4 → 1.4

Time: 12.2s

Precision: 64

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 r608960 = x;
        double r608961 = y;
        double r608962 = z;
        double r608963 = t;
        double r608964 = r608962 - r608963;
        double r608965 = a;
        double r608966 = r608962 - r608965;
        double r608967 = r608964 / r608966;
        double r608968 = r608961 * r608967;
        double r608969 = r608960 + r608968;
        return r608969;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r608970 = x;
        double r608971 = y;
        double r608972 = z;
        double r608973 = a;
        double r608974 = r608972 - r608973;
        double r608975 = r608972 / r608974;
        double r608976 = t;
        double r608977 = r608976 / r608974;
        double r608978 = r608975 - r608977;
        double r608979 = r608971 * r608978;
        double r608980 = r608970 + r608979;
        return r608980;
}

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	1.3
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 2019353 +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)))))