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

Average Error: 10.9 → 0.4

Time: 5.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -1.3990348901059605 \cdot 10^{295}:\\ \;\;\;\;x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 6.1068988768212615 \cdot 10^{266}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r686726 = x;
        double r686727 = y;
        double r686728 = z;
        double r686729 = t;
        double r686730 = r686728 - r686729;
        double r686731 = r686727 * r686730;
        double r686732 = a;
        double r686733 = r686728 - r686732;
        double r686734 = r686731 / r686733;
        double r686735 = r686726 + r686734;
        return r686735;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r686736 = y;
        double r686737 = z;
        double r686738 = t;
        double r686739 = r686737 - r686738;
        double r686740 = r686736 * r686739;
        double r686741 = a;
        double r686742 = r686737 - r686741;
        double r686743 = r686740 / r686742;
        double r686744 = -1.3990348901059605e+295;
        bool r686745 = r686743 <= r686744;
        double r686746 = x;
        double r686747 = 1.0;
        double r686748 = r686747 / r686739;
        double r686749 = r686742 * r686748;
        double r686750 = r686736 / r686749;
        double r686751 = r686746 + r686750;
        double r686752 = 6.106898876821261e+266;
        bool r686753 = r686743 <= r686752;
        double r686754 = r686746 + r686743;
        double r686755 = r686742 / r686739;
        double r686756 = r686736 / r686755;
        double r686757 = r686746 + r686756;
        double r686758 = r686753 ? r686754 : r686757;
        double r686759 = r686745 ? r686751 : r686758;
        return r686759;
}

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	0.4

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

Derivation

1. Split input into 3 regimes

2. if (/ (* y (- z t)) (- z a)) < -1.3990348901059605e+295

   1. Initial program 61.6

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

   3. Applied associate-/l* 0.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
   4. Using strategy rm

   5. Applied div-inv 0.8

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

   if -1.3990348901059605e+295 < (/ (* y (- z t)) (- z a)) < 6.106898876821261e+266

   1. Initial program 0.3

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

   if 6.106898876821261e+266 < (/ (* y (- z t)) (- z a))

   1. Initial program 57.8

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

   3. Applied associate-/l* 0.8

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
3. Recombined 3 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -1.3990348901059605 \cdot 10^{295}:\\ \;\;\;\;x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 6.1068988768212615 \cdot 10^{266}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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))))