Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 11.5 → 2.0

Time: 15.2s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r29874773 = x;
        double r29874774 = y;
        double r29874775 = z;
        double r29874776 = r29874774 - r29874775;
        double r29874777 = r29874773 * r29874776;
        double r29874778 = t;
        double r29874779 = r29874778 - r29874775;
        double r29874780 = r29874777 / r29874779;
        return r29874780;
}

↓

double f(double x, double y, double z, double t) {
        double r29874781 = z;
        double r29874782 = -1.5211504248577889e-190;
        bool r29874783 = r29874781 <= r29874782;
        double r29874784 = x;
        double r29874785 = t;
        double r29874786 = y;
        double r29874787 = r29874786 - r29874781;
        double r29874788 = r29874785 / r29874787;
        double r29874789 = r29874781 / r29874787;
        double r29874790 = r29874788 - r29874789;
        double r29874791 = r29874784 / r29874790;
        double r29874792 = 4.5513352917512905e-204;
        bool r29874793 = r29874781 <= r29874792;
        double r29874794 = r29874784 * r29874787;
        double r29874795 = r29874785 - r29874781;
        double r29874796 = r29874794 / r29874795;
        double r29874797 = r29874793 ? r29874796 : r29874791;
        double r29874798 = r29874783 ? r29874791 : r29874797;
        return r29874798;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.5
Target	2.0
Herbie	2.0

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

Derivation

1. Split input into 2 regimes

2. if z < -1.5211504248577889e-190 or 4.5513352917512905e-204 < z

   1. Initial program 12.6

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

   3. Applied associate-/l* 1.3

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

   5. Applied div-sub 1.3

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

   if -1.5211504248577889e-190 < z < 4.5513352917512905e-204

   1. Initial program 5.8

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

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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