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

Average Error: 1.3 → 1.3

Time: 23.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r31291498 = x;
        double r31291499 = y;
        double r31291500 = z;
        double r31291501 = t;
        double r31291502 = r31291500 - r31291501;
        double r31291503 = a;
        double r31291504 = r31291500 - r31291503;
        double r31291505 = r31291502 / r31291504;
        double r31291506 = r31291499 * r31291505;
        double r31291507 = r31291498 + r31291506;
        return r31291507;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r31291508 = z;
        double r31291509 = a;
        double r31291510 = r31291508 - r31291509;
        double r31291511 = r31291508 / r31291510;
        double r31291512 = t;
        double r31291513 = r31291512 / r31291510;
        double r31291514 = r31291511 - r31291513;
        double r31291515 = y;
        double r31291516 = x;
        double r31291517 = fma(r31291514, r31291515, r31291516);
        return r31291517;
}

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	1.3

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

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. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))