Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Average Error: 11.7 → 3.1

Time: 6.2s

Precision: 64

Math

\[\frac{x \cdot \left(y - z\right)}{y}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -7.326181763082673 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 2.6779333906407255 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{1}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r13727296 = x;
        double r13727297 = y;
        double r13727298 = z;
        double r13727299 = r13727297 - r13727298;
        double r13727300 = r13727296 * r13727299;
        double r13727301 = r13727300 / r13727297;
        return r13727301;
}

↓

double f(double x, double y, double z) {
        double r13727302 = y;
        double r13727303 = -7.326181763082673e-13;
        bool r13727304 = r13727302 <= r13727303;
        double r13727305 = x;
        double r13727306 = z;
        double r13727307 = r13727302 - r13727306;
        double r13727308 = r13727307 / r13727302;
        double r13727309 = r13727305 * r13727308;
        double r13727310 = 2.6779333906407255e-232;
        bool r13727311 = r13727302 <= r13727310;
        double r13727312 = r13727305 / r13727302;
        double r13727313 = 1.0;
        double r13727314 = r13727313 / r13727307;
        double r13727315 = r13727312 / r13727314;
        double r13727316 = r13727302 / r13727307;
        double r13727317 = r13727305 / r13727316;
        double r13727318 = r13727311 ? r13727315 : r13727317;
        double r13727319 = r13727304 ? r13727309 : r13727318;
        return r13727319;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	11.7
Target	3.2
Herbie	3.1

\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if y < -7.326181763082673e-13

   1. Initial program 14.4

      \[\frac{x \cdot \left(y - z\right)}{y}\]
   2. Using strategy rm

   3. Applied *-un-lft-identity 14.4

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot y}}\]

   4. Applied times-frac 0.1

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

   5. Simplified 0.1

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

   if -7.326181763082673e-13 < y < 2.6779333906407255e-232

   1. Initial program 8.1

      \[\frac{x \cdot \left(y - z\right)}{y}\]
   2. Using strategy rm

   3. Applied associate-/l* 8.6

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

   5. Applied div-inv 8.7

      \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{y - z}}}\]

   6. Applied associate-/r* 8.9

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{\frac{1}{y - z}}}\]

   if 2.6779333906407255e-232 < y

   1. Initial program 11.9

      \[\frac{x \cdot \left(y - z\right)}{y}\]
   2. Using strategy rm

   3. Applied associate-/l* 1.9

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

4. Final simplification 3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.326181763082673 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 2.6779333906407255 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{1}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))