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

Average Error: 14.8 → 2.0

Time: 19.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.83026178989142014305978763319490962789 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.596958462099602498549530904168498131342 \cdot 10^{273}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r5060856 = x;
        double r5060857 = y;
        double r5060858 = z;
        double r5060859 = r5060857 / r5060858;
        double r5060860 = t;
        double r5060861 = r5060859 * r5060860;
        double r5060862 = r5060861 / r5060860;
        double r5060863 = r5060856 * r5060862;
        return r5060863;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r5060864 = y;
        double r5060865 = z;
        double r5060866 = r5060864 / r5060865;
        double r5060867 = -1.83026178989142e-172;
        bool r5060868 = r5060866 <= r5060867;
        double r5060869 = x;
        double r5060870 = r5060865 / r5060864;
        double r5060871 = r5060869 / r5060870;
        double r5060872 = 0.0;
        bool r5060873 = r5060866 <= r5060872;
        double r5060874 = r5060869 * r5060864;
        double r5060875 = r5060874 / r5060865;
        double r5060876 = 2.5969584620996025e+273;
        bool r5060877 = r5060866 <= r5060876;
        double r5060878 = r5060877 ? r5060871 : r5060875;
        double r5060879 = r5060873 ? r5060875 : r5060878;
        double r5060880 = r5060868 ? r5060871 : r5060879;
        return r5060880;
}

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) < -1.83026178989142e-172 or 0.0 < (/ y z) < 2.5969584620996025e+273

   1. Initial program 12.3

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

   2. Simplified 8.1

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

   4. Applied associate-/l* 2.4

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

   if -1.83026178989142e-172 < (/ y z) < 0.0 or 2.5969584620996025e+273 < (/ y z)

   1. Initial program 21.9

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

   2. Simplified 0.8

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

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.83026178989142014305978763319490962789 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.596958462099602498549530904168498131342 \cdot 10^{273}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))