Average Error: 0.2 → 0.0
Time: 10.9s
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 r164099 = 1.0;
        double r164100 = 4.0;
        double r164101 = x;
        double r164102 = y;
        double r164103 = 0.75;
        double r164104 = r164102 * r164103;
        double r164105 = r164101 + r164104;
        double r164106 = z;
        double r164107 = r164105 - r164106;
        double r164108 = r164100 * r164107;
        double r164109 = r164108 / r164102;
        double r164110 = r164099 + r164109;
        return r164110;
}
↓
double f(double x, double y, double z) {
        double r164111 = 0.75;
        double r164112 = x;
        double r164113 = z;
        double r164114 = r164112 - r164113;
        double r164115 = y;
        double r164116 = r164114 / r164115;
        double r164117 = r164111 + r164116;
        double r164118 = 4.0;
        double r164119 = 1.0;
        double r164120 = fma(r164117, r164118, r164119);
        return r164120;
}

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 2019322 +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)))