Average Error: 0.1 → 0.0
Time: 5.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.25 + \frac{x - z}{y}\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(0.25 + \frac{x - z}{y}\right) + 1
double f(double x, double y, double z) {
        double r388857 = 1.0;
        double r388858 = 4.0;
        double r388859 = x;
        double r388860 = y;
        double r388861 = 0.25;
        double r388862 = r388860 * r388861;
        double r388863 = r388859 + r388862;
        double r388864 = z;
        double r388865 = r388863 - r388864;
        double r388866 = r388858 * r388865;
        double r388867 = r388866 / r388860;
        double r388868 = r388857 + r388867;
        return r388868;
}
↓
double f(double x, double y, double z) {
        double r388869 = 4.0;
        double r388870 = 0.25;
        double r388871 = x;
        double r388872 = z;
        double r388873 = r388871 - r388872;
        double r388874 = y;
        double r388875 = r388873 / r388874;
        double r388876 = r388870 + r388875;
        double r388877 = r388869 * r388876;
        double r388878 = 1.0;
        double r388879 = r388877 + r388878;
        return r388879;
}

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

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(0.25 + \frac{x - z}{y}\right) + 1}\]

  3. Final simplification0.0

    \[\leadsto 4 \cdot \left(0.25 + \frac{x - z}{y}\right) + 1\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))