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

Average Error: 12.0 → 2.6

Time: 7.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -2.5026958423490979 \cdot 10^{-124} \lor \neg \left(x \le -1.9079591839021169 \cdot 10^{-291}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{x \cdot z}{y}\right)\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r882705 = x;
        double r882706 = y;
        double r882707 = z;
        double r882708 = r882706 - r882707;
        double r882709 = r882705 * r882708;
        double r882710 = r882709 / r882706;
        return r882710;
}

↓

double f(double x, double y, double z) {
        double r882711 = x;
        double r882712 = -2.502695842349098e-124;
        bool r882713 = r882711 <= r882712;
        double r882714 = -1.907959183902117e-291;
        bool r882715 = r882711 <= r882714;
        double r882716 = !r882715;
        bool r882717 = r882713 || r882716;
        double r882718 = y;
        double r882719 = z;
        double r882720 = r882718 - r882719;
        double r882721 = r882718 / r882720;
        double r882722 = r882711 / r882721;
        double r882723 = r882711 * r882719;
        double r882724 = r882723 / r882718;
        double r882725 = -r882724;
        double r882726 = r882711 + r882725;
        double r882727 = r882717 ? r882722 : r882726;
        return r882727;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.0
Target	3.3
Herbie	2.6

\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if x < -2.502695842349098e-124 or -1.907959183902117e-291 < x

   1. Initial program 12.9

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

   3. Applied associate-/l* 2.4

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

   if -2.502695842349098e-124 < x < -1.907959183902117e-291

   1. Initial program 6.9

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

   3. Applied *-un-lft-identity 6.9

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

   4. Applied times-frac 7.9

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

   5. Simplified 7.9

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

   6. Simplified 7.9

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{y}\right)}\]
   7. Using strategy rm

   8. Applied sub-neg 7.9

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

   9. Applied distribute-lft-in 7.9

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

   10. Simplified 7.9

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

   11. Simplified 3.7

       \[\leadsto x + \color{blue}{\left(-\frac{x \cdot z}{y}\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification 2.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.5026958423490979 \cdot 10^{-124} \lor \neg \left(x \le -1.9079591839021169 \cdot 10^{-291}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{x \cdot z}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :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))