Average Error: 0.1 → 0.2
Time: 7.4s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 \cdot 2 + \frac{4}{y} \cdot \left(x - z\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 \cdot 2 + \frac{4}{y} \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r191734 = 1.0;
        double r191735 = 4.0;
        double r191736 = x;
        double r191737 = y;
        double r191738 = 0.25;
        double r191739 = r191737 * r191738;
        double r191740 = r191736 + r191739;
        double r191741 = z;
        double r191742 = r191740 - r191741;
        double r191743 = r191735 * r191742;
        double r191744 = r191743 / r191737;
        double r191745 = r191734 + r191744;
        return r191745;
}
↓
double f(double x, double y, double z) {
        double r191746 = 1.0;
        double r191747 = 2.0;
        double r191748 = r191746 * r191747;
        double r191749 = 4.0;
        double r191750 = y;
        double r191751 = r191749 / r191750;
        double r191752 = x;
        double r191753 = z;
        double r191754 = r191752 - r191753;
        double r191755 = r191751 * r191754;
        double r191756 = r191748 + r191755;
        return r191756;
}

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. Final simplification0.2

    \[\leadsto 1 \cdot 2 + \frac{4}{y} \cdot \left(x - z\right)\]

Reproduce

herbie shell --seed 2019303 
(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)))