Average Error: 0.1 → 0.0
Time: 13.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(4, 0.25 - \frac{z - x}{y}, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\mathsf{fma}\left(4, 0.25 - \frac{z - x}{y}, 1\right)
double f(double x, double y, double z) {
        double r164243 = 1.0;
        double r164244 = 4.0;
        double r164245 = x;
        double r164246 = y;
        double r164247 = 0.25;
        double r164248 = r164246 * r164247;
        double r164249 = r164245 + r164248;
        double r164250 = z;
        double r164251 = r164249 - r164250;
        double r164252 = r164244 * r164251;
        double r164253 = r164252 / r164246;
        double r164254 = r164243 + r164253;
        return r164254;
}
↓
double f(double x, double y, double z) {
        double r164255 = 4.0;
        double r164256 = 0.25;
        double r164257 = z;
        double r164258 = x;
        double r164259 = r164257 - r164258;
        double r164260 = y;
        double r164261 = r164259 / r164260;
        double r164262 = r164256 - r164261;
        double r164263 = 1.0;
        double r164264 = fma(r164255, r164262, r164263);
        return r164264;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.25 - \frac{z - x}{y}, 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(4, 0.25 - \frac{z - x}{y}, 1\right)\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))