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

Average Error: 14.7 → 0.4

Time: 30.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -7.261896673005644 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 9.1254418852524 \cdot 10^{-319}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.0418244881514054 \cdot 10^{+300}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r19399656 = x;
        double r19399657 = y;
        double r19399658 = z;
        double r19399659 = r19399657 / r19399658;
        double r19399660 = t;
        double r19399661 = r19399659 * r19399660;
        double r19399662 = r19399661 / r19399660;
        double r19399663 = r19399656 * r19399662;
        return r19399663;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r19399664 = y;
        double r19399665 = z;
        double r19399666 = r19399664 / r19399665;
        double r19399667 = -inf.0;
        bool r19399668 = r19399666 <= r19399667;
        double r19399669 = x;
        double r19399670 = r19399669 * r19399664;
        double r19399671 = r19399670 / r19399665;
        double r19399672 = -7.261896673005644e-233;
        bool r19399673 = r19399666 <= r19399672;
        double r19399674 = r19399665 / r19399664;
        double r19399675 = r19399669 / r19399674;
        double r19399676 = 9.1254418852524e-319;
        bool r19399677 = r19399666 <= r19399676;
        double r19399678 = 5.0418244881514054e+300;
        bool r19399679 = r19399666 <= r19399678;
        double r19399680 = r19399679 ? r19399675 : r19399671;
        double r19399681 = r19399677 ? r19399671 : r19399680;
        double r19399682 = r19399673 ? r19399675 : r19399681;
        double r19399683 = r19399668 ? r19399671 : r19399682;
        return r19399683;
}

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) < -inf.0 or -7.261896673005644e-233 < (/ y z) < 9.1254418852524e-319 or 5.0418244881514054e+300 < (/ y z)

   1. Initial program 28.0

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

   2. Simplified 0.2

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

   if -inf.0 < (/ y z) < -7.261896673005644e-233 or 9.1254418852524e-319 < (/ y z) < 5.0418244881514054e+300

   1. Initial program 10.6

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

   2. Simplified 7.7

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

   4. Applied associate-/l* 0.4

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -7.261896673005644 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 9.1254418852524 \cdot 10^{-319}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.0418244881514054 \cdot 10^{+300}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))