Average Error: 0.3 → 0.0
Time: 10.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.75 + \frac{x - z}{y}\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(0.75 + \frac{x - z}{y}\right) + 1
double f(double x, double y, double z) {
        double r202829 = 1.0;
        double r202830 = 4.0;
        double r202831 = x;
        double r202832 = y;
        double r202833 = 0.75;
        double r202834 = r202832 * r202833;
        double r202835 = r202831 + r202834;
        double r202836 = z;
        double r202837 = r202835 - r202836;
        double r202838 = r202830 * r202837;
        double r202839 = r202838 / r202832;
        double r202840 = r202829 + r202839;
        return r202840;
}
↓
double f(double x, double y, double z) {
        double r202841 = 4.0;
        double r202842 = 0.75;
        double r202843 = x;
        double r202844 = z;
        double r202845 = r202843 - r202844;
        double r202846 = y;
        double r202847 = r202845 / r202846;
        double r202848 = r202842 + r202847;
        double r202849 = r202841 * r202848;
        double r202850 = 1.0;
        double r202851 = r202849 + r202850;
        return r202851;
}

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 0.3

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

  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

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

Reproduce

herbie shell --seed 2019298 
(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)))