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

Average Error: 1.3 → 1.4

Time: 15.0s

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 r662366 = x;
        double r662367 = y;
        double r662368 = z;
        double r662369 = t;
        double r662370 = r662368 - r662369;
        double r662371 = a;
        double r662372 = r662368 - r662371;
        double r662373 = r662370 / r662372;
        double r662374 = r662367 * r662373;
        double r662375 = r662366 + r662374;
        return r662375;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r662376 = z;
        double r662377 = a;
        double r662378 = r662376 - r662377;
        double r662379 = r662376 / r662378;
        double r662380 = 1.0;
        double r662381 = t;
        double r662382 = r662378 / r662381;
        double r662383 = r662380 / r662382;
        double r662384 = r662379 - r662383;
        double r662385 = y;
        double r662386 = x;
        double r662387 = fma(r662384, r662385, r662386);
        return r662387;
}

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)))))