Average Error: 0.1 → 0.0
Time: 10.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r271164 = 1.0;
        double r271165 = 4.0;
        double r271166 = x;
        double r271167 = y;
        double r271168 = 0.25;
        double r271169 = r271167 * r271168;
        double r271170 = r271166 + r271169;
        double r271171 = z;
        double r271172 = r271170 - r271171;
        double r271173 = r271165 * r271172;
        double r271174 = r271173 / r271167;
        double r271175 = r271164 + r271174;
        return r271175;
}
↓
double f(double x, double y, double z) {
        double r271176 = 2.0;
        double r271177 = x;
        double r271178 = y;
        double r271179 = r271177 / r271178;
        double r271180 = z;
        double r271181 = r271180 / r271178;
        double r271182 = r271179 - r271181;
        double r271183 = 4.0;
        double r271184 = r271182 * r271183;
        double r271185 = r271176 + r271184;
        return r271185;
}

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

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

  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

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

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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)))