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

Average Error: 11.5 → 1.1

Time: 4.1s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -inf.0:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -4.02155928931499 \cdot 10^{-311}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

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) (t - z)) / ((double) (y - z))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z)))) <= -4.021559289315e-311)) {
			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	11.5
Target	2.2
Herbie	1.1

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

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. Using strategy rm

   3. Applied associate-/l* 0.1

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

   if -inf.0 < (/ (* x (- y z)) (- t z)) < -4.02155928931499e-311

   1. Initial program 0.3

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

   if -4.02155928931499e-311 < (/ (* x (- y z)) (- t z))

   1. Initial program 11.1

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

   3. Applied *-un-lft-identity 11.1

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

   4. Applied times-frac 1.8

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

   5. Simplified 1.8

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} = -inf.0:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -4.02155928931499 \cdot 10^{-311}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(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)))