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

Average Error: 11.5 → 2.0

Time: 16.6s

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 r24102784 = x;
        double r24102785 = y;
        double r24102786 = z;
        double r24102787 = r24102785 - r24102786;
        double r24102788 = r24102784 * r24102787;
        double r24102789 = t;
        double r24102790 = r24102789 - r24102786;
        double r24102791 = r24102788 / r24102790;
        return r24102791;
}

↓

double f(double x, double y, double z, double t) {
        double r24102792 = z;
        double r24102793 = -1.5211504248577889e-190;
        bool r24102794 = r24102792 <= r24102793;
        double r24102795 = x;
        double r24102796 = t;
        double r24102797 = y;
        double r24102798 = r24102797 - r24102792;
        double r24102799 = r24102796 / r24102798;
        double r24102800 = r24102792 / r24102798;
        double r24102801 = r24102799 - r24102800;
        double r24102802 = r24102795 / r24102801;
        double r24102803 = 4.5513352917512905e-204;
        bool r24102804 = r24102792 <= r24102803;
        double r24102805 = r24102795 * r24102798;
        double r24102806 = r24102796 - r24102792;
        double r24102807 = r24102805 / r24102806;
        double r24102808 = r24102804 ? r24102807 : r24102802;
        double r24102809 = r24102794 ? r24102802 : r24102808;
        return r24102809;
}

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 +o rules:numerics
(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)))