Average Error: 0.2 → 0.0
Time: 9.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)
double f(double x, double y, double z) {
        double r251360 = 1.0;
        double r251361 = 4.0;
        double r251362 = x;
        double r251363 = y;
        double r251364 = 0.75;
        double r251365 = r251363 * r251364;
        double r251366 = r251362 + r251365;
        double r251367 = z;
        double r251368 = r251366 - r251367;
        double r251369 = r251361 * r251368;
        double r251370 = r251369 / r251363;
        double r251371 = r251360 + r251370;
        return r251371;
}
↓
double f(double x, double y, double z) {
        double r251372 = 0.75;
        double r251373 = x;
        double r251374 = z;
        double r251375 = r251373 - r251374;
        double r251376 = y;
        double r251377 = r251375 / r251376;
        double r251378 = r251372 + r251377;
        double r251379 = 4.0;
        double r251380 = 1.0;
        double r251381 = fma(r251378, r251379, r251380);
        return r251381;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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)))