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

Average Error: 12.5 → 0.8

Time: 2.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.03190189492080534 \cdot 10^{98} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.6608708735287544 \cdot 10^{-84} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 4.93193268925708101 \cdot 10^{238}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r761245 = x;
        double r761246 = y;
        double r761247 = z;
        double r761248 = r761246 - r761247;
        double r761249 = r761245 * r761248;
        double r761250 = r761249 / r761246;
        return r761250;
}

↓

double f(double x, double y, double z) {
        double r761251 = x;
        double r761252 = y;
        double r761253 = z;
        double r761254 = r761252 - r761253;
        double r761255 = r761251 * r761254;
        double r761256 = r761255 / r761252;
        double r761257 = -inf.0;
        bool r761258 = r761256 <= r761257;
        double r761259 = -2.0319018949208053e+98;
        bool r761260 = r761256 <= r761259;
        double r761261 = 3.6608708735287544e-84;
        bool r761262 = r761256 <= r761261;
        double r761263 = 4.931932689257081e+238;
        bool r761264 = r761256 <= r761263;
        double r761265 = !r761264;
        bool r761266 = r761262 || r761265;
        double r761267 = !r761266;
        bool r761268 = r761260 || r761267;
        double r761269 = !r761268;
        bool r761270 = r761258 || r761269;
        double r761271 = r761252 / r761254;
        double r761272 = r761251 / r761271;
        double r761273 = r761270 ? r761272 : r761256;
        return r761273;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	12.5
Target	3.4
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (- y z)) y) < -inf.0 or -2.0319018949208053e+98 < (/ (* x (- y z)) y) < 3.6608708735287544e-84 or 4.931932689257081e+238 < (/ (* x (- y z)) y)

   1. Initial program 19.6

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

   3. Applied associate-/l* 1.1

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

   if -inf.0 < (/ (* x (- y z)) y) < -2.0319018949208053e+98 or 3.6608708735287544e-84 < (/ (* x (- y z)) y) < 4.931932689257081e+238

   1. Initial program 0.3

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.03190189492080534 \cdot 10^{98} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.6608708735287544 \cdot 10^{-84} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 4.93193268925708101 \cdot 10^{238}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 +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))