Average Error: 0.1 → 0.0
Time: 21.4s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r16384059 = 1.0;
        double r16384060 = 4.0;
        double r16384061 = x;
        double r16384062 = y;
        double r16384063 = 0.25;
        double r16384064 = r16384062 * r16384063;
        double r16384065 = r16384061 + r16384064;
        double r16384066 = z;
        double r16384067 = r16384065 - r16384066;
        double r16384068 = r16384060 * r16384067;
        double r16384069 = r16384068 / r16384062;
        double r16384070 = r16384059 + r16384069;
        return r16384070;
}
↓
double f(double x, double y, double z) {
        double r16384071 = 2.0;
        double r16384072 = 4.0;
        double r16384073 = x;
        double r16384074 = y;
        double r16384075 = r16384073 / r16384074;
        double r16384076 = z;
        double r16384077 = r16384076 / r16384074;
        double r16384078 = r16384075 - r16384077;
        double r16384079 = r16384072 * r16384078;
        double r16384080 = r16384071 + r16384079;
        return r16384080;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))