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

Average Error: 1.2 → 1.2

Time: 12.0s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r545431 = x;
        double r545432 = y;
        double r545433 = z;
        double r545434 = t;
        double r545435 = r545433 - r545434;
        double r545436 = a;
        double r545437 = r545433 - r545436;
        double r545438 = r545435 / r545437;
        double r545439 = r545432 * r545438;
        double r545440 = r545431 + r545439;
        return r545440;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r545441 = z;
        double r545442 = t;
        double r545443 = r545441 - r545442;
        double r545444 = a;
        double r545445 = r545441 - r545444;
        double r545446 = r545443 / r545445;
        double r545447 = y;
        double r545448 = x;
        double r545449 = fma(r545446, r545447, r545448);
        return r545449;
}

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	1.2

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

Derivation

1. Initial program 1.2

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

2. Simplified 1.2

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

3. Final simplification 1.2

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

Reproduce

herbie shell --seed 2020046 +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)))))