Average Error: 0.2 → 0.0
Time: 9.3s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\mathsf{fma}\left(4, 0.75 + \frac{x - z}{y}, 1\right)
double f(double x, double y, double z) {
        double r281368 = 1.0;
        double r281369 = 4.0;
        double r281370 = x;
        double r281371 = y;
        double r281372 = 0.75;
        double r281373 = r281371 * r281372;
        double r281374 = r281370 + r281373;
        double r281375 = z;
        double r281376 = r281374 - r281375;
        double r281377 = r281369 * r281376;
        double r281378 = r281377 / r281371;
        double r281379 = r281368 + r281378;
        return r281379;
}
↓
double f(double x, double y, double z) {
        double r281380 = 4.0;
        double r281381 = 0.75;
        double r281382 = x;
        double r281383 = z;
        double r281384 = r281382 - r281383;
        double r281385 = y;
        double r281386 = r281384 / r281385;
        double r281387 = r281381 + r281386;
        double r281388 = 1.0;
        double r281389 = fma(r281380, r281387, r281388);
        return r281389;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +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)))