Average Error: 0.2 → 0.0
Time: 2.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r272767 = 1.0;
        double r272768 = 4.0;
        double r272769 = x;
        double r272770 = y;
        double r272771 = 0.75;
        double r272772 = r272770 * r272771;
        double r272773 = r272769 + r272772;
        double r272774 = z;
        double r272775 = r272773 - r272774;
        double r272776 = r272768 * r272775;
        double r272777 = r272776 / r272770;
        double r272778 = r272767 + r272777;
        return r272778;
}
↓
double f(double x, double y, double z) {
        double r272779 = 1.0;
        double r272780 = 4.0;
        double r272781 = 0.75;
        double r272782 = x;
        double r272783 = y;
        double r272784 = r272782 / r272783;
        double r272785 = z;
        double r272786 = r272785 / r272783;
        double r272787 = r272784 - r272786;
        double r272788 = r272781 + r272787;
        double r272789 = r272780 * r272788;
        double r272790 = r272779 + r272789;
        return r272790;
}

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. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(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)))