Average Error: 0.2 → 0.0
Time: 2.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(\frac{x - z}{y} + 1\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(\frac{x - z}{y} + 1\right) \cdot 4
double f(double x, double y, double z) {
        double r249743 = 1.0;
        double r249744 = 4.0;
        double r249745 = x;
        double r249746 = y;
        double r249747 = 0.75;
        double r249748 = r249746 * r249747;
        double r249749 = r249745 + r249748;
        double r249750 = z;
        double r249751 = r249749 - r249750;
        double r249752 = r249744 * r249751;
        double r249753 = r249752 / r249746;
        double r249754 = r249743 + r249753;
        return r249754;
}
↓
double f(double x, double y, double z) {
        double r249755 = x;
        double r249756 = z;
        double r249757 = r249755 - r249756;
        double r249758 = y;
        double r249759 = r249757 / r249758;
        double r249760 = 1.0;
        double r249761 = r249759 + r249760;
        double r249762 = 4.0;
        double r249763 = r249761 * r249762;
        return r249763;
}

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 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{3 + \left(\frac{4}{y} \cdot \left(x - z\right) + 1\right)}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))