Average Error: 0.2 → 0.0
Time: 12.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r201997 = 1.0;
        double r201998 = 4.0;
        double r201999 = x;
        double r202000 = y;
        double r202001 = 0.75;
        double r202002 = r202000 * r202001;
        double r202003 = r201999 + r202002;
        double r202004 = z;
        double r202005 = r202003 - r202004;
        double r202006 = r201998 * r202005;
        double r202007 = r202006 / r202000;
        double r202008 = r201997 + r202007;
        return r202008;
}
↓
double f(double x, double y, double z) {
        double r202009 = 4.0;
        double r202010 = 1.0;
        double r202011 = x;
        double r202012 = y;
        double r202013 = r202011 / r202012;
        double r202014 = r202010 + r202013;
        double r202015 = z;
        double r202016 = r202015 / r202012;
        double r202017 = r202014 - r202016;
        double r202018 = r202009 * r202017;
        return r202018;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(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)))