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

Average Error: 11.2 → 1.1

Time: 10.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot x}{t - z} \le 2.164785590368067654753045725339164066048 \cdot 10^{245}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r410551 = x;
        double r410552 = y;
        double r410553 = z;
        double r410554 = r410552 - r410553;
        double r410555 = r410551 * r410554;
        double r410556 = t;
        double r410557 = r410556 - r410553;
        double r410558 = r410555 / r410557;
        return r410558;
}

↓

double f(double x, double y, double z, double t) {
        double r410559 = y;
        double r410560 = z;
        double r410561 = r410559 - r410560;
        double r410562 = x;
        double r410563 = r410561 * r410562;
        double r410564 = t;
        double r410565 = r410564 - r410560;
        double r410566 = r410563 / r410565;
        double r410567 = -inf.0;
        bool r410568 = r410566 <= r410567;
        double r410569 = 2.1647855903680677e+245;
        bool r410570 = r410566 <= r410569;
        double r410571 = !r410570;
        bool r410572 = r410568 || r410571;
        double r410573 = r410565 / r410561;
        double r410574 = r410562 / r410573;
        double r410575 = r410572 ? r410574 : r410566;
        return r410575;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.2
Target	2.0
Herbie	1.1

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (- y z)) (- t z)) < -inf.0 or 2.1647855903680677e+245 < (/ (* x (- y z)) (- t z))

   1. Initial program 59.1

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

   3. Applied associate-/l* 0.6

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

   if -inf.0 < (/ (* x (- y z)) (- t z)) < 2.1647855903680677e+245

   1. Initial program 1.2

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot x}{t - z} \le 2.164785590368067654753045725339164066048 \cdot 10^{245}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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)))