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

Average Error: 1.3 → 1.4

Time: 14.5s

Precision: 64

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

Math

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

↓

\[\mathsf{fma}\left(\frac{z}{z - a} - \frac{1}{\frac{z - a}{t}}, y, x\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r713036 = x;
        double r713037 = y;
        double r713038 = z;
        double r713039 = t;
        double r713040 = r713038 - r713039;
        double r713041 = a;
        double r713042 = r713038 - r713041;
        double r713043 = r713040 / r713042;
        double r713044 = r713037 * r713043;
        double r713045 = r713036 + r713044;
        return r713045;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r713046 = z;
        double r713047 = a;
        double r713048 = r713046 - r713047;
        double r713049 = r713046 / r713048;
        double r713050 = 1.0;
        double r713051 = t;
        double r713052 = r713048 / r713051;
        double r713053 = r713050 / r713052;
        double r713054 = r713049 - r713053;
        double r713055 = y;
        double r713056 = x;
        double r713057 = fma(r713054, r713055, r713056);
        return r713057;
}

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	1.4

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

Derivation

1. Initial program 1.3

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

2. Simplified 1.3

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)}\]
3. Using strategy rm

4. Applied div-sub 1.3

   \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{z - a} - \frac{t}{z - a}}, y, x\right)\]
5. Using strategy rm

6. Applied clear-num 1.4

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

7. Final simplification 1.4

   \[\leadsto \mathsf{fma}\left(\frac{z}{z - a} - \frac{1}{\frac{z - a}{t}}, y, x\right)\]

Reproduce

herbie shell --seed 2020047 +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)))))