Average Error: 0.1 → 0.0
Time: 1.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}
double f(double x, double y, double z) {
        double r300128 = 1.0;
        double r300129 = 4.0;
        double r300130 = x;
        double r300131 = y;
        double r300132 = 0.25;
        double r300133 = r300131 * r300132;
        double r300134 = r300130 + r300133;
        double r300135 = z;
        double r300136 = r300134 - r300135;
        double r300137 = r300129 * r300136;
        double r300138 = r300137 / r300131;
        double r300139 = r300128 + r300138;
        return r300139;
}
↓
double f(double x, double y, double z) {
        double r300140 = 4.0;
        double r300141 = x;
        double r300142 = y;
        double r300143 = r300141 / r300142;
        double r300144 = r300140 * r300143;
        double r300145 = 2.0;
        double r300146 = r300144 + r300145;
        double r300147 = z;
        double r300148 = r300147 / r300142;
        double r300149 = r300140 * r300148;
        double r300150 = r300146 - r300149;
        return r300150;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(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)))