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

Average Error: 1.5 → 1.6

Time: 18.3s

Precision: 64

Math

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

↓

\[x + y \cdot \frac{1}{\frac{a - t}{z - t}}\]

C

double f(double x, double y, double z, double t, double a) {
        double r425740 = x;
        double r425741 = y;
        double r425742 = z;
        double r425743 = t;
        double r425744 = r425742 - r425743;
        double r425745 = a;
        double r425746 = r425745 - r425743;
        double r425747 = r425744 / r425746;
        double r425748 = r425741 * r425747;
        double r425749 = r425740 + r425748;
        return r425749;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r425750 = x;
        double r425751 = y;
        double r425752 = 1.0;
        double r425753 = a;
        double r425754 = t;
        double r425755 = r425753 - r425754;
        double r425756 = z;
        double r425757 = r425756 - r425754;
        double r425758 = r425755 / r425757;
        double r425759 = r425752 / r425758;
        double r425760 = r425751 * r425759;
        double r425761 = r425750 + r425760;
        return r425761;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.5
Target	0.5
Herbie	1.6

\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Initial program 1.5

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

3. Applied clear-num 1.6

   \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]

4. Final simplification 1.6

   \[\leadsto x + y \cdot \frac{1}{\frac{a - t}{z - t}}\]

Reproduce

herbie shell --seed 2019306 
(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 -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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