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

Average Error: 11.5 → 2.0

Time: 14.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r31336492 = x;
        double r31336493 = y;
        double r31336494 = z;
        double r31336495 = r31336493 - r31336494;
        double r31336496 = r31336492 * r31336495;
        double r31336497 = t;
        double r31336498 = r31336497 - r31336494;
        double r31336499 = r31336496 / r31336498;
        return r31336499;
}

↓

double f(double x, double y, double z, double t) {
        double r31336500 = z;
        double r31336501 = -1.5211504248577889e-190;
        bool r31336502 = r31336500 <= r31336501;
        double r31336503 = x;
        double r31336504 = t;
        double r31336505 = y;
        double r31336506 = r31336505 - r31336500;
        double r31336507 = r31336504 / r31336506;
        double r31336508 = r31336500 / r31336506;
        double r31336509 = r31336507 - r31336508;
        double r31336510 = r31336503 / r31336509;
        double r31336511 = 4.5513352917512905e-204;
        bool r31336512 = r31336500 <= r31336511;
        double r31336513 = r31336503 * r31336506;
        double r31336514 = r31336504 - r31336500;
        double r31336515 = r31336513 / r31336514;
        double r31336516 = r31336512 ? r31336515 : r31336510;
        double r31336517 = r31336502 ? r31336510 : r31336516;
        return r31336517;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.5
Target	2.0
Herbie	2.0

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

Derivation

1. Split input into 2 regimes

2. if z < -1.5211504248577889e-190 or 4.5513352917512905e-204 < z

   1. Initial program 12.6

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

   3. Applied associate-/l* 1.3

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

   5. Applied div-sub 1.3

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

   if -1.5211504248577889e-190 < z < 4.5513352917512905e-204

   1. Initial program 5.8

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

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.521150424857788861649339444118342642553 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \mathbf{elif}\;z \le 4.55133529175129052669496720638249750795 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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