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

Average Error: 11.7 → 1.3

Time: 18.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -0.0:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 1.44466708885499135 \cdot 10^{284}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]

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)))) <= -0.0)) {
		VAR = ((double) (x * ((double) (((double) (y - z)) / ((double) (t - z))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z)))) <= 1.4446670888549914e+284)) {
			VAR_1 = ((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z))));
		} else {
			VAR_1 = ((double) (x / ((double) (((double) (t - z)) / ((double) (y - 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	11.7
Target	2.1
Herbie	1.3

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) (- t z)) < -0.0

   1. Initial program 11.6

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

   3. Applied *-un-lft-identity 11.6

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

   4. Applied times-frac 2.1

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

   5. Simplified 2.1

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

   if -0.0 < (/ (* x (- y z)) (- t z)) < 1.44466708885499135e284

   1. Initial program 0.4

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

   if 1.44466708885499135e284 < (/ (* x (- y z)) (- t z))

   1. Initial program 60.6

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

   3. Applied associate-/l* 0.5

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -0.0:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 1.44466708885499135 \cdot 10^{284}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(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)))