Average Error: 0.1 → 0.0
Time: 22.9s
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 r206023 = 1.0;
        double r206024 = 4.0;
        double r206025 = x;
        double r206026 = y;
        double r206027 = 0.25;
        double r206028 = r206026 * r206027;
        double r206029 = r206025 + r206028;
        double r206030 = z;
        double r206031 = r206029 - r206030;
        double r206032 = r206024 * r206031;
        double r206033 = r206032 / r206026;
        double r206034 = r206023 + r206033;
        return r206034;
}
↓
double f(double x, double y, double z) {
        double r206035 = 4.0;
        double r206036 = x;
        double r206037 = y;
        double r206038 = r206036 / r206037;
        double r206039 = z;
        double r206040 = r206039 / r206037;
        double r206041 = r206038 - r206040;
        double r206042 = r206035 * r206041;
        double r206043 = 2.0;
        double r206044 = r206042 + r206043;
        return r206044;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))