Average Error: 0.2 → 0.0
Time: 2.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r318933 = 1.0;
        double r318934 = 4.0;
        double r318935 = x;
        double r318936 = y;
        double r318937 = 0.75;
        double r318938 = r318936 * r318937;
        double r318939 = r318935 + r318938;
        double r318940 = z;
        double r318941 = r318939 - r318940;
        double r318942 = r318934 * r318941;
        double r318943 = r318942 / r318936;
        double r318944 = r318933 + r318943;
        return r318944;
}
↓
double f(double x, double y, double z) {
        double r318945 = 1.0;
        double r318946 = 0.75;
        double r318947 = 4.0;
        double r318948 = r318946 * r318947;
        double r318949 = r318945 + r318948;
        double r318950 = x;
        double r318951 = z;
        double r318952 = r318950 - r318951;
        double r318953 = y;
        double r318954 = r318952 / r318953;
        double r318955 = r318947 * r318954;
        double r318956 = r318949 + r318955;
        return r318956;
}

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 distribute-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 
(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)))