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

Average Error: 11.6 → 1.7

Time: 3.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -4.0798383452349713 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.21143 \cdot 10^{-322}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)\\ \end{array}\]

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)) <= -4.079838345234971e+97)) {
		VAR = (x / ((t - z) / (y - z)));
	} else {
		double VAR_1;
		if ((((x * (y - z)) / (t - z)) <= -3.2114266979681e-322)) {
			VAR_1 = ((x * (y - z)) / (t - z));
		} else {
			VAR_1 = (x * ((y / (t - z)) - (z / (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	11.6
Target	2.3
Herbie	1.7

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) (- t z)) < -4.079838345234971e+97

   1. Initial program 32.7

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

   3. Applied associate-/l* 2.7

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

   if -4.079838345234971e+97 < (/ (* x (- y z)) (- t z)) < -3.2114266979681e-322

   1. Initial program 0.3

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

   if -3.2114266979681e-322 < (/ (* x (- y z)) (- t z))

   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 2.2

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

   5. Simplified 2.2

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

   7. Applied div-sub 2.2

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

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -4.0798383452349713 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le -3.21143 \cdot 10^{-322}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020103 
(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)))