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

Average Error: 11.8 → 1.4

Time: 3.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -inf.0:\\ \;\;\;\;x \cdot \left(\left(y - z\right) \cdot \frac{1}{t - z}\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 5.6149602498395192 \cdot 10^{218}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z)))) <= -inf.0)) {
		VAR = ((double) (x * ((double) (((double) (y - z)) * ((double) (1.0 / ((double) (t - z))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z)))) <= 5.614960249839519e+218)) {
			VAR_1 = ((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z))));
		} else {
			VAR_1 = ((double) (x * ((double) (((double) (y - z)) / ((double) (t - z))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.8
Target	2.2
Herbie	1.4

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) (- t z)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 0.1

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

   4. Applied div-inv 0.2

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

   if -inf.0 < (/ (* x (- y z)) (- t z)) < 5.6149602498395192e218

   1. Initial program 1.4

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

   if 5.6149602498395192e218 < (/ (* x (- y z)) (- t z))

   1. Initial program 50.1

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

   2. Simplified 2.2

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}}\]
3. Recombined 3 regimes into one program.

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -inf.0:\\ \;\;\;\;x \cdot \left(\left(y - z\right) \cdot \frac{1}{t - z}\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 5.6149602498395192 \cdot 10^{218}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))