Average Error: 0.2 → 0.0
Time: 1.3s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r342980 = 1.0;
        double r342981 = 4.0;
        double r342982 = x;
        double r342983 = y;
        double r342984 = 0.75;
        double r342985 = r342983 * r342984;
        double r342986 = r342982 + r342985;
        double r342987 = z;
        double r342988 = r342986 - r342987;
        double r342989 = r342981 * r342988;
        double r342990 = r342989 / r342983;
        double r342991 = r342980 + r342990;
        return r342991;
}
↓
double f(double x, double y, double z) {
        double r342992 = 1.0;
        double r342993 = 0.75;
        double r342994 = 4.0;
        double r342995 = r342993 * r342994;
        double r342996 = r342992 + r342995;
        double r342997 = x;
        double r342998 = z;
        double r342999 = r342997 - r342998;
        double r343000 = y;
        double r343001 = r342999 / r343000;
        double r343002 = r343001 * r342994;
        double r343003 = r342996 + r343002;
        return r343003;
}

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-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 
(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)))