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

Average Error: 11.1 → 0.6

Time: 4.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -573.259546568546853 \lor \neg \left(t \le 9.77340867370812975 \cdot 10^{-90}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r589773 = x;
        double r589774 = y;
        double r589775 = z;
        double r589776 = r589774 - r589775;
        double r589777 = t;
        double r589778 = r589776 * r589777;
        double r589779 = a;
        double r589780 = r589779 - r589775;
        double r589781 = r589778 / r589780;
        double r589782 = r589773 + r589781;
        return r589782;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r589783 = t;
        double r589784 = -573.2595465685469;
        bool r589785 = r589783 <= r589784;
        double r589786 = 9.77340867370813e-90;
        bool r589787 = r589783 <= r589786;
        double r589788 = !r589787;
        bool r589789 = r589785 || r589788;
        double r589790 = x;
        double r589791 = y;
        double r589792 = z;
        double r589793 = r589791 - r589792;
        double r589794 = a;
        double r589795 = r589794 - r589792;
        double r589796 = r589793 / r589795;
        double r589797 = r589796 * r589783;
        double r589798 = r589790 + r589797;
        double r589799 = r589793 * r589783;
        double r589800 = r589799 / r589795;
        double r589801 = r589790 + r589800;
        double r589802 = r589789 ? r589798 : r589801;
        return r589802;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	11.1
Target	0.7
Herbie	0.6

\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if t < -573.2595465685469 or 9.77340867370813e-90 < t

   1. Initial program 20.0

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

   3. Applied associate-/l* 1.9

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

   5. Applied associate-/r/ 0.7

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

   if -573.2595465685469 < t < 9.77340867370813e-90

   1. Initial program 0.5

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -573.259546568546853 \lor \neg \left(t \le 9.77340867370812975 \cdot 10^{-90}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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