Average Error: 0.1 → 0.0
Time: 11.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r168595 = 1.0;
        double r168596 = 4.0;
        double r168597 = x;
        double r168598 = y;
        double r168599 = 0.25;
        double r168600 = r168598 * r168599;
        double r168601 = r168597 + r168600;
        double r168602 = z;
        double r168603 = r168601 - r168602;
        double r168604 = r168596 * r168603;
        double r168605 = r168604 / r168598;
        double r168606 = r168595 + r168605;
        return r168606;
}
↓
double f(double x, double y, double z) {
        double r168607 = 2.0;
        double r168608 = 4.0;
        double r168609 = x;
        double r168610 = z;
        double r168611 = r168609 - r168610;
        double r168612 = y;
        double r168613 = r168611 / r168612;
        double r168614 = r168608 * r168613;
        double r168615 = r168607 + r168614;
        return r168615;
}

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 0.1

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

  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

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

  5. Final simplification0.0

    \[\leadsto 2 + 4 \cdot \frac{x - z}{y}\]

Reproduce

herbie shell --seed 2019322 
(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)))