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

Average Error: 15.1 → 0.9

Time: 3.8m

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.884682577215762039880854428140955206399 \cdot 10^{200}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.847656812384934442156413516898082202275 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.740047883140276970193031087160782955638 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.072656266341375744037857515166265409716 \cdot 10^{86}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r135818561 = x;
        double r135818562 = y;
        double r135818563 = z;
        double r135818564 = r135818562 / r135818563;
        double r135818565 = t;
        double r135818566 = r135818564 * r135818565;
        double r135818567 = r135818566 / r135818565;
        double r135818568 = r135818561 * r135818567;
        return r135818568;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r135818569 = y;
        double r135818570 = z;
        double r135818571 = r135818569 / r135818570;
        double r135818572 = -1.884682577215762e+200;
        bool r135818573 = r135818571 <= r135818572;
        double r135818574 = x;
        double r135818575 = r135818574 * r135818569;
        double r135818576 = r135818575 / r135818570;
        double r135818577 = -1.8476568123849344e-240;
        bool r135818578 = r135818571 <= r135818577;
        double r135818579 = r135818574 * r135818571;
        double r135818580 = 2.740047883140277e-240;
        bool r135818581 = r135818571 <= r135818580;
        double r135818582 = 2.0726562663413757e+86;
        bool r135818583 = r135818571 <= r135818582;
        double r135818584 = r135818583 ? r135818579 : r135818576;
        double r135818585 = r135818581 ? r135818576 : r135818584;
        double r135818586 = r135818578 ? r135818579 : r135818585;
        double r135818587 = r135818573 ? r135818576 : r135818586;
        return r135818587;
}

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) < -1.884682577215762e+200 or -1.8476568123849344e-240 < (/ y z) < 2.740047883140277e-240 or 2.0726562663413757e+86 < (/ y z)

   1. Initial program 24.9

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

   2. Simplified 14.6

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

   4. Applied associate-*r/ 1.9

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

   if -1.884682577215762e+200 < (/ y z) < -1.8476568123849344e-240 or 2.740047883140277e-240 < (/ y z) < 2.0726562663413757e+86

   1. Initial program 8.2

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

   2. Simplified 0.2

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.884682577215762039880854428140955206399 \cdot 10^{200}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.847656812384934442156413516898082202275 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.740047883140276970193031087160782955638 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.072656266341375744037857515166265409716 \cdot 10^{86}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))