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

Average Error: 15.1 → 0.9

Time: 5.1m

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 r411367878 = x;
        double r411367879 = y;
        double r411367880 = z;
        double r411367881 = r411367879 / r411367880;
        double r411367882 = t;
        double r411367883 = r411367881 * r411367882;
        double r411367884 = r411367883 / r411367882;
        double r411367885 = r411367878 * r411367884;
        return r411367885;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r411367886 = y;
        double r411367887 = z;
        double r411367888 = r411367886 / r411367887;
        double r411367889 = -1.884682577215762e+200;
        bool r411367890 = r411367888 <= r411367889;
        double r411367891 = x;
        double r411367892 = r411367891 * r411367886;
        double r411367893 = r411367892 / r411367887;
        double r411367894 = -1.8476568123849344e-240;
        bool r411367895 = r411367888 <= r411367894;
        double r411367896 = r411367891 * r411367888;
        double r411367897 = 2.740047883140277e-240;
        bool r411367898 = r411367888 <= r411367897;
        double r411367899 = 2.0726562663413757e+86;
        bool r411367900 = r411367888 <= r411367899;
        double r411367901 = r411367900 ? r411367896 : r411367893;
        double r411367902 = r411367898 ? r411367893 : r411367901;
        double r411367903 = r411367895 ? r411367896 : r411367902;
        double r411367904 = r411367890 ? r411367893 : r411367903;
        return r411367904;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	15.1
Target	1.6
Herbie	0.9

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

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, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))