Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 11.9 → 2.4

Time: 7.6s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r750554 = x;
        double r750555 = y;
        double r750556 = z;
        double r750557 = r750555 - r750556;
        double r750558 = r750554 * r750557;
        double r750559 = t;
        double r750560 = r750559 - r750556;
        double r750561 = r750558 / r750560;
        return r750561;
}

↓

double f(double x, double y, double z, double t) {
        double r750562 = z;
        double r750563 = -9.512737302380148e-222;
        bool r750564 = r750562 <= r750563;
        double r750565 = 5.4381737647266115e-107;
        bool r750566 = r750562 <= r750565;
        double r750567 = !r750566;
        bool r750568 = r750564 || r750567;
        double r750569 = x;
        double r750570 = y;
        double r750571 = r750570 - r750562;
        double r750572 = t;
        double r750573 = r750572 - r750562;
        double r750574 = r750571 / r750573;
        double r750575 = r750569 * r750574;
        double r750576 = r750569 / r750573;
        double r750577 = r750576 * r750571;
        double r750578 = r750568 ? r750575 : r750577;
        return r750578;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.9
Target	2.2
Herbie	2.4

\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

1. Split input into 2 regimes

2. if z < -9.512737302380148e-222 or 5.4381737647266115e-107 < z

   1. Initial program 13.3

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

   3. Applied *-un-lft-identity 13.3

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

   4. Applied times-frac 1.2

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

   5. Simplified 1.2

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

   if -9.512737302380148e-222 < z < 5.4381737647266115e-107

   1. Initial program 6.7

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

   3. Applied *-un-lft-identity 6.7

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

   4. Applied times-frac 5.5

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

   5. Simplified 5.5

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

   7. Applied pow1 5.5

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

   8. Applied pow1 5.5

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

   9. Applied pow-prod-down 5.5

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

   10. Simplified 6.9

       \[\leadsto {\color{blue}{\left(\left(y - z\right) \cdot \frac{x}{t - z}\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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