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

Average Error: 14.8 → 1.8

Time: 13.7s

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 r108373 = x;
        double r108374 = y;
        double r108375 = z;
        double r108376 = r108374 / r108375;
        double r108377 = t;
        double r108378 = r108376 * r108377;
        double r108379 = r108378 / r108377;
        double r108380 = r108373 * r108379;
        return r108380;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r108381 = y;
        double r108382 = z;
        double r108383 = r108381 / r108382;
        double r108384 = -7.71513312838218e+306;
        bool r108385 = r108383 <= r108384;
        double r108386 = -6.11823401185594e-307;
        bool r108387 = r108383 <= r108386;
        double r108388 = !r108387;
        double r108389 = 1.161601004338193e-258;
        bool r108390 = r108383 <= r108389;
        bool r108391 = r108388 && r108390;
        bool r108392 = r108385 || r108391;
        double r108393 = x;
        double r108394 = r108393 * r108381;
        double r108395 = 1.0;
        double r108396 = r108395 / r108382;
        double r108397 = r108394 * r108396;
        double r108398 = r108393 * r108383;
        double r108399 = r108392 ? r108397 : r108398;
        return r108399;
}

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 +o rules:numerics
(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)))