Average Error: 0.1 → 0.0
Time: 17.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r175133 = 1.0;
        double r175134 = 4.0;
        double r175135 = x;
        double r175136 = y;
        double r175137 = 0.25;
        double r175138 = r175136 * r175137;
        double r175139 = r175135 + r175138;
        double r175140 = z;
        double r175141 = r175139 - r175140;
        double r175142 = r175134 * r175141;
        double r175143 = r175142 / r175136;
        double r175144 = r175133 + r175143;
        return r175144;
}
↓
double f(double x, double y, double z) {
        double r175145 = 2.0;
        double r175146 = 4.0;
        double r175147 = x;
        double r175148 = y;
        double r175149 = r175147 / r175148;
        double r175150 = z;
        double r175151 = r175150 / r175148;
        double r175152 = r175149 - r175151;
        double r175153 = r175146 * r175152;
        double r175154 = r175145 + r175153;
        return r175154;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  4. Final simplification0.0

    \[\leadsto 2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019323 
(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)))