Average Error: 0.1 → 0.0
Time: 23.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2
double f(double x, double y, double z) {
        double r164981 = 1.0;
        double r164982 = 4.0;
        double r164983 = x;
        double r164984 = y;
        double r164985 = 0.25;
        double r164986 = r164984 * r164985;
        double r164987 = r164983 + r164986;
        double r164988 = z;
        double r164989 = r164987 - r164988;
        double r164990 = r164982 * r164989;
        double r164991 = r164990 / r164984;
        double r164992 = r164981 + r164991;
        return r164992;
}
↓
double f(double x, double y, double z) {
        double r164993 = 4.0;
        double r164994 = x;
        double r164995 = y;
        double r164996 = r164994 / r164995;
        double r164997 = z;
        double r164998 = r164997 / r164995;
        double r164999 = r164996 - r164998;
        double r165000 = r164993 * r164999;
        double r165001 = 2.0;
        double r165002 = r165000 + r165001;
        return r165002;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.25 + \frac{x - z}{y}, 4, 1\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

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

  5. Applied associate-+r-0.0

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

  6. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  7. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2}\]

  8. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2\]

Reproduce

herbie shell --seed 2019325 +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)))