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

Average Error: 15.1 → 0.9

Time: 5.4m

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 r219528857 = x;
        double r219528858 = y;
        double r219528859 = z;
        double r219528860 = r219528858 / r219528859;
        double r219528861 = t;
        double r219528862 = r219528860 * r219528861;
        double r219528863 = r219528862 / r219528861;
        double r219528864 = r219528857 * r219528863;
        return r219528864;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r219528865 = y;
        double r219528866 = z;
        double r219528867 = r219528865 / r219528866;
        double r219528868 = -1.884682577215762e+200;
        bool r219528869 = r219528867 <= r219528868;
        double r219528870 = x;
        double r219528871 = r219528870 * r219528865;
        double r219528872 = r219528871 / r219528866;
        double r219528873 = -1.8476568123849344e-240;
        bool r219528874 = r219528867 <= r219528873;
        double r219528875 = r219528870 * r219528867;
        double r219528876 = 2.740047883140277e-240;
        bool r219528877 = r219528867 <= r219528876;
        double r219528878 = 2.0726562663413757e+86;
        bool r219528879 = r219528867 <= r219528878;
        double r219528880 = r219528879 ? r219528875 : r219528872;
        double r219528881 = r219528877 ? r219528872 : r219528880;
        double r219528882 = r219528874 ? r219528875 : r219528881;
        double r219528883 = r219528869 ? r219528872 : r219528882;
        return r219528883;
}

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 +o rules:numerics
(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)))