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

Average Error: 11.3 → 1.7

Time: 3.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -2.49472440264539668 \cdot 10^{76} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 4.7703587704786577 \cdot 10^{284}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t - z}{x \cdot \left(y - z\right)}}\\ \end{array}\]

C

double code(double x, double y, double z, double t) {
	return ((x * (y - z)) / (t - z));
}

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((((x * (y - z)) / (t - z)) <= -2.4947244026453967e+76) || !(((x * (y - z)) / (t - z)) <= 4.770358770478658e+284))) {
		VAR = (x / ((t - z) / (y - z)));
	} else {
		VAR = (1.0 / ((t - z) / (x * (y - z))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.3
Target	2.0
Herbie	1.7

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

Derivation

1. Split input into 2 regimes

2. if (/ (* x (- y z)) (- t z)) < -2.4947244026453967e+76 or 4.770358770478658e+284 < (/ (* x (- y z)) (- t z))

   1. Initial program 41.3

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

   3. Applied associate-/l* 1.8

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

   if -2.4947244026453967e+76 < (/ (* x (- y z)) (- t z)) < 4.770358770478658e+284

   1. Initial program 1.3

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

   3. Applied clear-num 1.7

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

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -2.49472440264539668 \cdot 10^{76} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \le 4.7703587704786577 \cdot 10^{284}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t - z}{x \cdot \left(y - z\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(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)))