Average Error: 0.1 → 0.1
Time: 27.6s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2.0 + \frac{4.0 \cdot \left(x - z\right)}{y}\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2.0 + \frac{4.0 \cdot \left(x - z\right)}{y}
double f(double x, double y, double z) {
        double r15013791 = 1.0;
        double r15013792 = 4.0;
        double r15013793 = x;
        double r15013794 = y;
        double r15013795 = 0.25;
        double r15013796 = r15013794 * r15013795;
        double r15013797 = r15013793 + r15013796;
        double r15013798 = z;
        double r15013799 = r15013797 - r15013798;
        double r15013800 = r15013792 * r15013799;
        double r15013801 = r15013800 / r15013794;
        double r15013802 = r15013791 + r15013801;
        return r15013802;
}
↓
double f(double x, double y, double z) {
        double r15013803 = 2.0;
        double r15013804 = 4.0;
        double r15013805 = x;
        double r15013806 = z;
        double r15013807 = r15013805 - r15013806;
        double r15013808 = r15013804 * r15013807;
        double r15013809 = y;
        double r15013810 = r15013808 / r15013809;
        double r15013811 = r15013803 + r15013810;
        return r15013811;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.25 + \frac{x - z}{y}, 4.0, 1.0\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{2.0 + \frac{4.0 \cdot \left(x - z\right)}{y}}\]

  5. Final simplification0.1

    \[\leadsto 2.0 + \frac{4.0 \cdot \left(x - z\right)}{y}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))