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

Average Error: 12.7 → 0.4

Time: 3.2s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -588372703331281.625:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.44083856738268095 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.61243343433184086 \cdot 10^{294}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r705911 = x;
        double r705912 = y;
        double r705913 = z;
        double r705914 = r705912 - r705913;
        double r705915 = r705911 * r705914;
        double r705916 = r705915 / r705912;
        return r705916;
}

↓

double f(double x, double y, double z) {
        double r705917 = x;
        double r705918 = y;
        double r705919 = z;
        double r705920 = r705918 - r705919;
        double r705921 = r705917 * r705920;
        double r705922 = r705921 / r705918;
        double r705923 = -inf.0;
        bool r705924 = r705922 <= r705923;
        double r705925 = r705917 / r705918;
        double r705926 = r705925 * r705920;
        double r705927 = -588372703331281.6;
        bool r705928 = r705922 <= r705927;
        double r705929 = 2.440838567382681e+97;
        bool r705930 = r705922 <= r705929;
        double r705931 = r705918 / r705920;
        double r705932 = r705917 / r705931;
        double r705933 = 3.612433434331841e+294;
        bool r705934 = r705922 <= r705933;
        double r705935 = r705934 ? r705922 : r705932;
        double r705936 = r705930 ? r705932 : r705935;
        double r705937 = r705928 ? r705922 : r705936;
        double r705938 = r705924 ? r705926 : r705937;
        return r705938;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.7
Target	3.0
Herbie	0.4

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) y) < -inf.0

   1. Initial program 64.0

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

   3. Applied associate-/l* 0.1

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

   5. Applied associate-/r/ 0.1

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

   if -inf.0 < (/ (* x (- y z)) y) < -588372703331281.6 or 2.440838567382681e+97 < (/ (* x (- y z)) y) < 3.612433434331841e+294

   1. Initial program 0.2

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

   if -588372703331281.6 < (/ (* x (- y z)) y) < 2.440838567382681e+97 or 3.612433434331841e+294 < (/ (* x (- y z)) y)

   1. Initial program 13.2

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

   3. Applied associate-/l* 0.6

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -588372703331281.625:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.44083856738268095 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.61243343433184086 \cdot 10^{294}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(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))