Average Error: 0.2 → 0.0
Time: 20.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 4
double f(double x, double y, double z) {
        double r145743 = 1.0;
        double r145744 = 4.0;
        double r145745 = x;
        double r145746 = y;
        double r145747 = 0.75;
        double r145748 = r145746 * r145747;
        double r145749 = r145745 + r145748;
        double r145750 = z;
        double r145751 = r145749 - r145750;
        double r145752 = r145744 * r145751;
        double r145753 = r145752 / r145746;
        double r145754 = r145743 + r145753;
        return r145754;
}
↓
double f(double x, double y, double z) {
        double r145755 = 4.0;
        double r145756 = x;
        double r145757 = y;
        double r145758 = r145756 / r145757;
        double r145759 = z;
        double r145760 = r145759 / r145757;
        double r145761 = r145758 - r145760;
        double r145762 = r145755 * r145761;
        double r145763 = r145762 + r145755;
        return r145763;
}

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

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

  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

    \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 4}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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)))