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

Average Error: 10.9 → 1.3

Time: 22.5s

Precision: 64

Math

\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r24484571 = x;
        double r24484572 = y;
        double r24484573 = z;
        double r24484574 = t;
        double r24484575 = r24484573 - r24484574;
        double r24484576 = r24484572 * r24484575;
        double r24484577 = a;
        double r24484578 = r24484573 - r24484577;
        double r24484579 = r24484576 / r24484578;
        double r24484580 = r24484571 + r24484579;
        return r24484580;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r24484581 = x;
        double r24484582 = y;
        double r24484583 = z;
        double r24484584 = a;
        double r24484585 = r24484583 - r24484584;
        double r24484586 = t;
        double r24484587 = r24484583 - r24484586;
        double r24484588 = r24484585 / r24484587;
        double r24484589 = r24484582 / r24484588;
        double r24484590 = r24484581 + r24484589;
        return r24484590;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.9
Target	1.3
Herbie	1.3

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

Derivation

1. Initial program 10.9

   \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
2. Using strategy rm

3. Applied associate-/l* 1.3

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

4. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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