Average Error: 0.1 → 0.0
Time: 1.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)
double f(double x, double y, double z) {
        double r294903 = 1.0;
        double r294904 = 4.0;
        double r294905 = x;
        double r294906 = y;
        double r294907 = 0.75;
        double r294908 = r294906 * r294907;
        double r294909 = r294905 + r294908;
        double r294910 = z;
        double r294911 = r294909 - r294910;
        double r294912 = r294904 * r294911;
        double r294913 = r294912 / r294906;
        double r294914 = r294903 + r294913;
        return r294914;
}
↓
double f(double x, double y, double z) {
        double r294915 = 1.0;
        double r294916 = 4.0;
        double r294917 = 0.75;
        double r294918 = x;
        double r294919 = z;
        double r294920 = r294918 - r294919;
        double r294921 = y;
        double r294922 = r294920 / r294921;
        double r294923 = r294917 + r294922;
        double r294924 = r294916 * r294923;
        double r294925 = r294915 + r294924;
        return r294925;
}

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 0.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(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)))