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

Average Error: 14.8 → 1.8

Time: 9.3s

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 r153349 = x;
        double r153350 = y;
        double r153351 = z;
        double r153352 = r153350 / r153351;
        double r153353 = t;
        double r153354 = r153352 * r153353;
        double r153355 = r153354 / r153353;
        double r153356 = r153349 * r153355;
        return r153356;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r153357 = y;
        double r153358 = z;
        double r153359 = r153357 / r153358;
        double r153360 = -7.71513312838218e+306;
        bool r153361 = r153359 <= r153360;
        double r153362 = -6.11823401185594e-307;
        bool r153363 = r153359 <= r153362;
        double r153364 = !r153363;
        double r153365 = 1.161601004338193e-258;
        bool r153366 = r153359 <= r153365;
        bool r153367 = r153364 && r153366;
        bool r153368 = r153361 || r153367;
        double r153369 = x;
        double r153370 = r153369 * r153357;
        double r153371 = 1.0;
        double r153372 = r153371 / r153358;
        double r153373 = r153370 * r153372;
        double r153374 = r153369 * r153359;
        double r153375 = r153368 ? r153373 : r153374;
        return r153375;
}

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)))