Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A

Average Error: 0.3 → 0.0

Time: 2.9s

Precision: 64

Math

\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

↓

\[\left(1 + 0.75 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]

C

double code(double x, double y, double z) {
	return ((double) (1.0 + ((double) (((double) (4.0 * ((double) (((double) (x + ((double) (y * 0.75)))) - z)))) / y))));
}

↓

double code(double x, double y, double z) {
	return ((double) (((double) (1.0 + ((double) (0.75 * 4.0)))) + ((double) (((double) (((double) (x / y)) - ((double) (z / y)))) * 4.0))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.3

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

2. Simplified 0.0

   \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)}\]
3. Using strategy rm

4. Applied div-sub 0.0

   \[\leadsto 1 + 4 \cdot \left(0.75 + \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)}\right)\]

5. Applied associate-+r- 0.0

   \[\leadsto 1 + 4 \cdot \color{blue}{\left(\left(0.75 + \frac{x}{y}\right) - \frac{z}{y}\right)}\]
6. Using strategy rm

7. Applied associate--l+ 0.0

   \[\leadsto 1 + 4 \cdot \color{blue}{\left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)}\]

8. Applied distribute-rgt-in 0.0

   \[\leadsto 1 + \color{blue}{\left(0.75 \cdot 4 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\right)}\]

9. Applied associate-+r+ 0.0

   \[\leadsto \color{blue}{\left(1 + 0.75 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4}\]

10. Final simplification 0.0

    \[\leadsto \left(1 + 0.75 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]

Reproduce

herbie shell --seed 2020114 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))