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

Average Error: 14.1 → 2.1

Time: 4.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.339100113054096077367478108920979716351 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.95252516672997235341255034294577097892 \cdot 10^{-323}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.425467457487989591337114825286942269211 \cdot 10^{307}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r169059 = x;
        double r169060 = y;
        double r169061 = z;
        double r169062 = r169060 / r169061;
        double r169063 = t;
        double r169064 = r169062 * r169063;
        double r169065 = r169064 / r169063;
        double r169066 = r169059 * r169065;
        return r169066;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r169067 = y;
        double r169068 = z;
        double r169069 = r169067 / r169068;
        double r169070 = -3.339100113054096e-121;
        bool r169071 = r169069 <= r169070;
        double r169072 = x;
        double r169073 = r169072 * r169069;
        double r169074 = 3.95252516673e-323;
        bool r169075 = r169069 <= r169074;
        double r169076 = r169072 * r169067;
        double r169077 = r169076 / r169068;
        double r169078 = 2.4254674574879896e+307;
        bool r169079 = r169069 <= r169078;
        double r169080 = 1.0;
        double r169081 = r169080 / r169068;
        double r169082 = r169076 * r169081;
        double r169083 = r169079 ? r169073 : r169082;
        double r169084 = r169075 ? r169077 : r169083;
        double r169085 = r169071 ? r169073 : r169084;
        return r169085;
}

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) < -3.339100113054096e-121 or 3.95252516673e-323 < (/ y z) < 2.4254674574879896e+307

   1. Initial program 11.5

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

   2. Simplified 2.4

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

   if -3.339100113054096e-121 < (/ y z) < 3.95252516673e-323

   1. Initial program 16.9

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

   2. Simplified 11.2

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

   4. Applied associate-*r/ 1.2

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

   if 2.4254674574879896e+307 < (/ y z)

   1. Initial program 64.0

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

   2. Simplified 63.3

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

   4. Applied div-inv 63.3

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

   5. Applied associate-*r* 0.4

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
3. Recombined 3 regimes into one program.

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.339100113054096077367478108920979716351 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.95252516672997235341255034294577097892 \cdot 10^{-323}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.425467457487989591337114825286942269211 \cdot 10^{307}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019318 
(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)))