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

Average Error: 12.0 → 1.3

Time: 3.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.503045921817015 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.503823389807409 \cdot 10^{+304}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x * ((double) (y - z)))) / ((double) (t - z))) <= 1.503045921817015e-229)) {
		VAR = ((double) (x * (((double) (y - z)) / ((double) (t - z)))));
	} else {
		double VAR_1;
		if (((((double) (x * ((double) (y - z)))) / ((double) (t - z))) <= 1.503823389807409e+304)) {
			VAR_1 = (((double) (x * ((double) (y - z)))) / ((double) (t - z)));
		} else {
			VAR_1 = (x / (((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	12.0
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)) < 1.5030459218170149e-229

   1. Initial program 10.6

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

   2. Simplified 2.0

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

   if 1.5030459218170149e-229 < (/ (* x (- y z)) (- t z)) < 1.5038233898074091e304

   1. Initial program 0.3

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

   if 1.5038233898074091e304 < (/ (* x (- y z)) (- t z))

   1. Initial program 63.7

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

   2. Simplified 0.2

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

   4. Applied clear-num 0.2

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}}\]
   5. Using strategy rm

   6. Applied un-div-inv 0.2

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.503045921817015 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 1.503823389807409 \cdot 10^{+304}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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)))