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

Average Error: 13.1 → 1.1

Time: 2.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -9.340475670529612 \cdot 10^{153} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.61774820575826244 \cdot 10^{129} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 8.4362316469862765 \cdot 10^{300}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r720433 = x;
        double r720434 = y;
        double r720435 = z;
        double r720436 = r720434 - r720435;
        double r720437 = r720433 * r720436;
        double r720438 = r720437 / r720434;
        return r720438;
}

↓

double f(double x, double y, double z) {
        double r720439 = x;
        double r720440 = y;
        double r720441 = z;
        double r720442 = r720440 - r720441;
        double r720443 = r720439 * r720442;
        double r720444 = r720443 / r720440;
        double r720445 = -inf.0;
        bool r720446 = r720444 <= r720445;
        double r720447 = -9.340475670529612e+153;
        bool r720448 = r720444 <= r720447;
        double r720449 = 1.6177482057582624e+129;
        bool r720450 = r720444 <= r720449;
        double r720451 = 8.436231646986276e+300;
        bool r720452 = r720444 <= r720451;
        double r720453 = !r720452;
        bool r720454 = r720450 || r720453;
        double r720455 = !r720454;
        bool r720456 = r720448 || r720455;
        double r720457 = !r720456;
        bool r720458 = r720446 || r720457;
        double r720459 = r720442 / r720440;
        double r720460 = r720439 * r720459;
        double r720461 = r720458 ? r720460 : r720444;
        return r720461;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	13.1
Target	3.1
Herbie	1.1

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (- y z)) y) < -inf.0 or -9.340475670529612e+153 < (/ (* x (- y z)) y) < 1.6177482057582624e+129 or 8.436231646986276e+300 < (/ (* x (- y z)) y)

   1. Initial program 16.3

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

   3. Applied *-un-lft-identity 16.3

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

   4. Applied times-frac 1.3

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

   5. Simplified 1.3

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

   if -inf.0 < (/ (* x (- y z)) y) < -9.340475670529612e+153 or 1.6177482057582624e+129 < (/ (* x (- y z)) y) < 8.436231646986276e+300

   1. Initial program 0.2

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -9.340475670529612 \cdot 10^{153} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.61774820575826244 \cdot 10^{129} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 8.4362316469862765 \cdot 10^{300}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 +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))