Average Error: 0.1 → 0.2
Time: 2.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\frac{4}{y} \cdot \left(x - z\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\frac{4}{y} \cdot \left(x - z\right) + 2
double f(double x, double y, double z) {
        double r209107 = 1.0;
        double r209108 = 4.0;
        double r209109 = x;
        double r209110 = y;
        double r209111 = 0.25;
        double r209112 = r209110 * r209111;
        double r209113 = r209109 + r209112;
        double r209114 = z;
        double r209115 = r209113 - r209114;
        double r209116 = r209108 * r209115;
        double r209117 = r209116 / r209110;
        double r209118 = r209107 + r209117;
        return r209118;
}
↓
double f(double x, double y, double z) {
        double r209119 = 4.0;
        double r209120 = y;
        double r209121 = r209119 / r209120;
        double r209122 = x;
        double r209123 = z;
        double r209124 = r209122 - r209123;
        double r209125 = r209121 * r209124;
        double r209126 = 2.0;
        double r209127 = r209125 + r209126;
        return r209127;
}

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

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

  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

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019308 
(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)))