Average Error: 0.2 → 0.0
Time: 3.9s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r5358773 = 1.0;
        double r5358774 = 4.0;
        double r5358775 = x;
        double r5358776 = y;
        double r5358777 = 0.75;
        double r5358778 = r5358776 * r5358777;
        double r5358779 = r5358775 + r5358778;
        double r5358780 = z;
        double r5358781 = r5358779 - r5358780;
        double r5358782 = r5358774 * r5358781;
        double r5358783 = r5358782 / r5358776;
        double r5358784 = r5358773 + r5358783;
        return r5358784;
}
↓
double f(double x, double y, double z) {
        double r5358785 = 4.0;
        double r5358786 = x;
        double r5358787 = y;
        double r5358788 = r5358786 / r5358787;
        double r5358789 = z;
        double r5358790 = r5358789 / r5358787;
        double r5358791 = r5358788 - r5358790;
        double r5358792 = r5358785 * r5358791;
        double r5358793 = r5358785 + r5358792;
        return r5358793;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1.0 - 4.0 \cdot \left(\frac{z - x}{y} - 0.75\right)}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))