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

Average Error: 10.9 → 1.2

Time: 9.2s

Precision: 64

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

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 r1169660 = x;
        double r1169661 = y;
        double r1169662 = z;
        double r1169663 = t;
        double r1169664 = r1169662 - r1169663;
        double r1169665 = r1169661 * r1169664;
        double r1169666 = a;
        double r1169667 = r1169662 - r1169666;
        double r1169668 = r1169665 / r1169667;
        double r1169669 = r1169660 + r1169668;
        return r1169669;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r1169670 = x;
        double r1169671 = y;
        double r1169672 = z;
        double r1169673 = a;
        double r1169674 = r1169672 - r1169673;
        double r1169675 = t;
        double r1169676 = r1169672 - r1169675;
        double r1169677 = r1169674 / r1169676;
        double r1169678 = r1169671 / r1169677;
        double r1169679 = r1169670 + r1169678;
        return r1169679;
}

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	1.2
Herbie	1.2

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

Derivation

1. Initial program 10.9

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

3. Applied associate-/l* 1.2

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

4. Final simplification 1.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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