Average Error: 0.1 → 0.1
Time: 14.6s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2.0 + \frac{\left(x - z\right) \cdot 4.0}{y}\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2.0 + \frac{\left(x - z\right) \cdot 4.0}{y}
double f(double x, double y, double z) {
        double r13175010 = 1.0;
        double r13175011 = 4.0;
        double r13175012 = x;
        double r13175013 = y;
        double r13175014 = 0.25;
        double r13175015 = r13175013 * r13175014;
        double r13175016 = r13175012 + r13175015;
        double r13175017 = z;
        double r13175018 = r13175016 - r13175017;
        double r13175019 = r13175011 * r13175018;
        double r13175020 = r13175019 / r13175013;
        double r13175021 = r13175010 + r13175020;
        return r13175021;
}
↓
double f(double x, double y, double z) {
        double r13175022 = 2.0;
        double r13175023 = x;
        double r13175024 = z;
        double r13175025 = r13175023 - r13175024;
        double r13175026 = 4.0;
        double r13175027 = r13175025 * r13175026;
        double r13175028 = y;
        double r13175029 = r13175027 / r13175028;
        double r13175030 = r13175022 + r13175029;
        return r13175030;
}

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

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +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)))