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

Average Error: 0.2 → 0.0

Time: 13.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r22386 = 1.0;
        double r22387 = 4.0;
        double r22388 = x;
        double r22389 = y;
        double r22390 = 0.75;
        double r22391 = r22389 * r22390;
        double r22392 = r22388 + r22391;
        double r22393 = z;
        double r22394 = r22392 - r22393;
        double r22395 = r22387 * r22394;
        double r22396 = r22395 / r22389;
        double r22397 = r22386 + r22396;
        return r22397;
}

↓

double f(double x, double y, double z) {
        double r22398 = 1.0;
        double r22399 = x;
        double r22400 = y;
        double r22401 = r22399 / r22400;
        double r22402 = z;
        double r22403 = r22402 / r22400;
        double r22404 = r22401 - r22403;
        double r22405 = 0.75;
        double r22406 = r22404 + r22405;
        double r22407 = 4.0;
        double r22408 = r22406 * r22407;
        double r22409 = r22398 + r22408;
        return r22409;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.2

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

2. Simplified 0.0

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

4. Applied div-sub 0.0

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

5. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019310 
(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)))