Average Error: 0.2 → 0.0
Time: 10.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r238883 = 1.0;
        double r238884 = 4.0;
        double r238885 = x;
        double r238886 = y;
        double r238887 = 0.75;
        double r238888 = r238886 * r238887;
        double r238889 = r238885 + r238888;
        double r238890 = z;
        double r238891 = r238889 - r238890;
        double r238892 = r238884 * r238891;
        double r238893 = r238892 / r238886;
        double r238894 = r238883 + r238893;
        return r238894;
}
↓
double f(double x, double y, double z) {
        double r238895 = 4.0;
        double r238896 = 1.0;
        double r238897 = x;
        double r238898 = y;
        double r238899 = r238897 / r238898;
        double r238900 = r238896 + r238899;
        double r238901 = z;
        double r238902 = r238901 / r238898;
        double r238903 = r238900 - r238902;
        double r238904 = r238895 * r238903;
        return r238904;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))