Average Error: 0.1 → 0.0
Time: 11.2s
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 r248139 = 1.0;
        double r248140 = 4.0;
        double r248141 = x;
        double r248142 = y;
        double r248143 = 0.25;
        double r248144 = r248142 * r248143;
        double r248145 = r248141 + r248144;
        double r248146 = z;
        double r248147 = r248145 - r248146;
        double r248148 = r248140 * r248147;
        double r248149 = r248148 / r248142;
        double r248150 = r248139 + r248149;
        return r248150;
}
↓
double f(double x, double y, double z) {
        double r248151 = 2.0;
        double r248152 = 4.0;
        double r248153 = x;
        double r248154 = y;
        double r248155 = r248153 / r248154;
        double r248156 = z;
        double r248157 = r248156 / r248154;
        double r248158 = r248155 - r248157;
        double r248159 = r248152 * r248158;
        double r248160 = r248151 + r248159;
        return r248160;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Simplified0.0

    \[\leadsto \color{blue}{\left(0.25 - \frac{z - x}{y}\right) \cdot 4 + 1}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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)))