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

Average Error: 14.8 → 1.8

Time: 10.9s

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 r136242 = x;
        double r136243 = y;
        double r136244 = z;
        double r136245 = r136243 / r136244;
        double r136246 = t;
        double r136247 = r136245 * r136246;
        double r136248 = r136247 / r136246;
        double r136249 = r136242 * r136248;
        return r136249;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r136250 = y;
        double r136251 = z;
        double r136252 = r136250 / r136251;
        double r136253 = -7.71513312838218e+306;
        bool r136254 = r136252 <= r136253;
        double r136255 = -6.11823401185594e-307;
        bool r136256 = r136252 <= r136255;
        double r136257 = !r136256;
        double r136258 = 1.161601004338193e-258;
        bool r136259 = r136252 <= r136258;
        bool r136260 = r136257 && r136259;
        bool r136261 = r136254 || r136260;
        double r136262 = x;
        double r136263 = r136262 * r136250;
        double r136264 = 1.0;
        double r136265 = r136264 / r136251;
        double r136266 = r136263 * r136265;
        double r136267 = r136262 * r136252;
        double r136268 = r136261 ? r136266 : r136267;
        return r136268;
}

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)))