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

Average Error: 14.2 → 0.9

Time: 36.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.029723206596843 \cdot 10^{+176}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.8469932729033145 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 5.578817110085708 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.3970034463555168 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r3558435 = x;
        double r3558436 = y;
        double r3558437 = z;
        double r3558438 = r3558436 / r3558437;
        double r3558439 = t;
        double r3558440 = r3558438 * r3558439;
        double r3558441 = r3558440 / r3558439;
        double r3558442 = r3558435 * r3558441;
        return r3558442;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r3558443 = y;
        double r3558444 = z;
        double r3558445 = r3558443 / r3558444;
        double r3558446 = -2.029723206596843e+176;
        bool r3558447 = r3558445 <= r3558446;
        double r3558448 = x;
        double r3558449 = r3558448 * r3558443;
        double r3558450 = r3558449 / r3558444;
        double r3558451 = -1.8469932729033145e-146;
        bool r3558452 = r3558445 <= r3558451;
        double r3558453 = r3558444 / r3558443;
        double r3558454 = r3558448 / r3558453;
        double r3558455 = 5.578817110085708e-247;
        bool r3558456 = r3558445 <= r3558455;
        double r3558457 = 1.3970034463555168e+102;
        bool r3558458 = r3558445 <= r3558457;
        double r3558459 = r3558458 ? r3558454 : r3558450;
        double r3558460 = r3558456 ? r3558450 : r3558459;
        double r3558461 = r3558452 ? r3558454 : r3558460;
        double r3558462 = r3558447 ? r3558450 : r3558461;
        return r3558462;
}

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) < -2.029723206596843e+176 or -1.8469932729033145e-146 < (/ y z) < 5.578817110085708e-247 or 1.3970034463555168e+102 < (/ y z)

   1. Initial program 22.2

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

   2. Simplified 1.8

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

   4. Applied associate-*l/ 1.6

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

   if -2.029723206596843e+176 < (/ y z) < -1.8469932729033145e-146 or 5.578817110085708e-247 < (/ y z) < 1.3970034463555168e+102

   1. Initial program 7.1

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

   2. Simplified 10.3

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

   4. Applied associate-*l/ 9.4

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

   6. Applied associate-/l* 0.2

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.029723206596843 \cdot 10^{+176}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.8469932729033145 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 5.578817110085708 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.3970034463555168 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019142 +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)))