Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

Average Error: 14.5 → 5.9

Time: 34.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -5.6091150268147854 \cdot 10^{+166}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;x \le -2.5758087551247737 \cdot 10^{-191}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \le 3.186901635946382 \cdot 10^{-97}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;x \le 2.487988218208264 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r4878864 = x;
        double r4878865 = y;
        double r4878866 = z;
        double r4878867 = r4878865 / r4878866;
        double r4878868 = t;
        double r4878869 = r4878867 * r4878868;
        double r4878870 = r4878869 / r4878868;
        double r4878871 = r4878864 * r4878870;
        return r4878871;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r4878872 = x;
        double r4878873 = -5.6091150268147854e+166;
        bool r4878874 = r4878872 <= r4878873;
        double r4878875 = y;
        double r4878876 = r4878875 * r4878872;
        double r4878877 = z;
        double r4878878 = r4878876 / r4878877;
        double r4878879 = -2.5758087551247737e-191;
        bool r4878880 = r4878872 <= r4878879;
        double r4878881 = r4878872 / r4878877;
        double r4878882 = r4878875 * r4878881;
        double r4878883 = 3.186901635946382e-97;
        bool r4878884 = r4878872 <= r4878883;
        double r4878885 = 2.487988218208264e+178;
        bool r4878886 = r4878872 <= r4878885;
        double r4878887 = r4878886 ? r4878882 : r4878878;
        double r4878888 = r4878884 ? r4878878 : r4878887;
        double r4878889 = r4878880 ? r4878882 : r4878888;
        double r4878890 = r4878874 ? r4878878 : r4878889;
        return r4878890;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

1. Split input into 2 regimes

2. if x < -5.6091150268147854e+166 or -2.5758087551247737e-191 < x < 3.186901635946382e-97 or 2.487988218208264e+178 < x

   1. Initial program 15.7

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

   2. Simplified 8.3

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y}\]
   3. Using strategy rm

   4. Applied associate-*l/ 8.1

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

   if -5.6091150268147854e+166 < x < -2.5758087551247737e-191 or 3.186901635946382e-97 < x < 2.487988218208264e+178

   1. Initial program 13.3

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

   2. Simplified 3.8

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y}\]
3. Recombined 2 regimes into one program.

4. Final simplification 5.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.6091150268147854 \cdot 10^{+166}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;x \le -2.5758087551247737 \cdot 10^{-191}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \le 3.186901635946382 \cdot 10^{-97}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;x \le 2.487988218208264 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))