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

Average Error: 14.8 → 1.8

Time: 3.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r93680 = x;
        double r93681 = y;
        double r93682 = z;
        double r93683 = r93681 / r93682;
        double r93684 = t;
        double r93685 = r93683 * r93684;
        double r93686 = r93685 / r93684;
        double r93687 = r93680 * r93686;
        return r93687;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r93688 = y;
        double r93689 = z;
        double r93690 = r93688 / r93689;
        double r93691 = -7.71513312838218e+306;
        bool r93692 = r93690 <= r93691;
        double r93693 = -6.11823401185594e-307;
        bool r93694 = r93690 <= r93693;
        double r93695 = 1.161601004338193e-258;
        bool r93696 = r93690 <= r93695;
        double r93697 = !r93696;
        bool r93698 = r93694 || r93697;
        double r93699 = !r93698;
        bool r93700 = r93692 || r93699;
        double r93701 = x;
        double r93702 = r93701 * r93688;
        double r93703 = 1.0;
        double r93704 = r93703 / r93689;
        double r93705 = r93702 * r93704;
        double r93706 = r93701 * r93690;
        double r93707 = r93700 ? r93705 : r93706;
        return r93707;
}

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

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

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)))