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

Average Error: 14.1 → 2.4

Time: 1.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.00847826157384981 \cdot 10^{150} \lor \neg \left(\frac{y}{z} \le -9.59916746614835709 \cdot 10^{-156} \lor \neg \left(\frac{y}{z} \le 1.38338 \cdot 10^{-322}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r601827 = x;
        double r601828 = y;
        double r601829 = z;
        double r601830 = r601828 / r601829;
        double r601831 = t;
        double r601832 = r601830 * r601831;
        double r601833 = r601832 / r601831;
        double r601834 = r601827 * r601833;
        return r601834;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r601835 = y;
        double r601836 = z;
        double r601837 = r601835 / r601836;
        double r601838 = -3.0084782615738498e+150;
        bool r601839 = r601837 <= r601838;
        double r601840 = -9.599167466148357e-156;
        bool r601841 = r601837 <= r601840;
        double r601842 = 1.3833838083555e-322;
        bool r601843 = r601837 <= r601842;
        double r601844 = !r601843;
        bool r601845 = r601841 || r601844;
        double r601846 = !r601845;
        bool r601847 = r601839 || r601846;
        double r601848 = x;
        double r601849 = r601848 * r601835;
        double r601850 = r601849 / r601836;
        double r601851 = r601836 / r601835;
        double r601852 = r601848 / r601851;
        double r601853 = r601847 ? r601850 : r601852;
        return r601853;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.1
Target	1.4
Herbie	2.4

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -3.0084782615738498e+150 or -9.599167466148357e-156 < (/ y z) < 1.3833838083555e-322

   1. Initial program 21.1

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

   2. Simplified 13.0

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

   4. Applied associate-*r/ 1.3

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

   if -3.0084782615738498e+150 < (/ y z) < -9.599167466148357e-156 or 1.3833838083555e-322 < (/ y z)

   1. Initial program 10.8

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

   2. Simplified 2.9

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

   4. Applied associate-*r/ 8.5

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

   6. Applied associate-/l* 2.9

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

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.00847826157384981 \cdot 10^{150} \lor \neg \left(\frac{y}{z} \le -9.59916746614835709 \cdot 10^{-156} \lor \neg \left(\frac{y}{z} \le 1.38338 \cdot 10^{-322}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :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)))