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

Average Error: 14.8 → 1.8

Time: 13.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -7.7151331283821803 \cdot 10^{306} \lor \neg \left(\frac{y}{z} \le -6.11823401185594017 \cdot 10^{-307}\right) \land \frac{y}{z} \le 1.1616010043381929 \cdot 10^{-258}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r140352 = x;
        double r140353 = y;
        double r140354 = z;
        double r140355 = r140353 / r140354;
        double r140356 = t;
        double r140357 = r140355 * r140356;
        double r140358 = r140357 / r140356;
        double r140359 = r140352 * r140358;
        return r140359;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r140360 = y;
        double r140361 = z;
        double r140362 = r140360 / r140361;
        double r140363 = -7.71513312838218e+306;
        bool r140364 = r140362 <= r140363;
        double r140365 = -6.11823401185594e-307;
        bool r140366 = r140362 <= r140365;
        double r140367 = !r140366;
        double r140368 = 1.161601004338193e-258;
        bool r140369 = r140362 <= r140368;
        bool r140370 = r140367 && r140369;
        bool r140371 = r140364 || r140370;
        double r140372 = x;
        double r140373 = r140372 * r140360;
        double r140374 = 1.0;
        double r140375 = r140374 / r140361;
        double r140376 = r140373 * r140375;
        double r140377 = r140372 * r140362;
        double r140378 = r140371 ? r140376 : r140377;
        return r140378;
}

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 (/ y z) < -7.71513312838218e+306 or -6.11823401185594e-307 < (/ y z) < 1.161601004338193e-258

   1. Initial program 24.4

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

   2. Simplified 21.7

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

   4. Applied div-inv 21.7

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

   5. Applied associate-*r* 0.2

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]

   if -7.71513312838218e+306 < (/ y z) < -6.11823401185594e-307 or 1.161601004338193e-258 < (/ y z)

   1. Initial program 12.2

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

   2. Simplified 2.2

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

4. Final simplification 1.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -7.7151331283821803 \cdot 10^{306} \lor \neg \left(\frac{y}{z} \le -6.11823401185594017 \cdot 10^{-307}\right) \land \frac{y}{z} \le 1.1616010043381929 \cdot 10^{-258}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))