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

Average Error: 1.6 → 1.6

Time: 13.6s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r748988 = x;
        double r748989 = y;
        double r748990 = z;
        double r748991 = t;
        double r748992 = r748990 - r748991;
        double r748993 = a;
        double r748994 = r748993 - r748991;
        double r748995 = r748992 / r748994;
        double r748996 = r748989 * r748995;
        double r748997 = r748988 + r748996;
        return r748997;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r748998 = z;
        double r748999 = t;
        double r749000 = r748998 - r748999;
        double r749001 = a;
        double r749002 = r749001 - r748999;
        double r749003 = r749000 / r749002;
        double r749004 = y;
        double r749005 = x;
        double r749006 = fma(r749003, r749004, r749005);
        return r749006;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.6
Target	0.5
Herbie	1.6

\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Initial program 1.6

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

2. Simplified 1.6

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

3. Final simplification 1.6

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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