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

Average Error: 14.5 → 1.4

Time: 12.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.96646549046934189 \cdot 10^{230}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2270242891442878 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.933654612229097 \cdot 10^{80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r82978 = x;
        double r82979 = y;
        double r82980 = z;
        double r82981 = r82979 / r82980;
        double r82982 = t;
        double r82983 = r82981 * r82982;
        double r82984 = r82983 / r82982;
        double r82985 = r82978 * r82984;
        return r82985;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r82986 = y;
        double r82987 = z;
        double r82988 = r82986 / r82987;
        double r82989 = -1.966465490469342e+230;
        bool r82990 = r82988 <= r82989;
        double r82991 = x;
        double r82992 = r82987 / r82991;
        double r82993 = r82986 / r82992;
        double r82994 = -3.2270242891442878e-105;
        bool r82995 = r82988 <= r82994;
        double r82996 = r82988 * r82991;
        double r82997 = -0.0;
        bool r82998 = r82988 <= r82997;
        double r82999 = r82986 * r82991;
        double r83000 = r82999 / r82987;
        double r83001 = 6.933654612229097e+80;
        bool r83002 = r82988 <= r83001;
        double r83003 = r83002 ? r82996 : r82993;
        double r83004 = r82998 ? r83000 : r83003;
        double r83005 = r82995 ? r82996 : r83004;
        double r83006 = r82990 ? r82993 : r83005;
        return r83006;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -1.966465490469342e+230 or 6.933654612229097e+80 < (/ y z)

   1. Initial program 32.0

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

   2. Simplified 3.2

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

   4. Applied associate-/l* 4.4

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]

   if -1.966465490469342e+230 < (/ y z) < -3.2270242891442878e-105 or -0.0 < (/ y z) < 6.933654612229097e+80

   1. Initial program 9.0

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

   2. Simplified 8.3

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

   4. Applied associate-/l* 8.7

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

   6. Applied associate-/r/ 2.5

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]

   if -3.2270242891442878e-105 < (/ y z) < -0.0

   1. Initial program 15.3

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

   2. Simplified 1.8

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

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.96646549046934189 \cdot 10^{230}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -3.2270242891442878 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.933654612229097 \cdot 10^{80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))