Average Error: 0.1 → 0.0
Time: 1.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r304108 = 1.0;
        double r304109 = 4.0;
        double r304110 = x;
        double r304111 = y;
        double r304112 = 0.25;
        double r304113 = r304111 * r304112;
        double r304114 = r304110 + r304113;
        double r304115 = z;
        double r304116 = r304114 - r304115;
        double r304117 = r304109 * r304116;
        double r304118 = r304117 / r304111;
        double r304119 = r304108 + r304118;
        return r304119;
}
↓
double f(double x, double y, double z) {
        double r304120 = 1.0;
        double r304121 = 0.25;
        double r304122 = 4.0;
        double r304123 = r304121 * r304122;
        double r304124 = r304120 + r304123;
        double r304125 = x;
        double r304126 = z;
        double r304127 = r304125 - r304126;
        double r304128 = y;
        double r304129 = r304127 / r304128;
        double r304130 = r304129 * r304122;
        double r304131 = r304124 + r304130;
        return r304131;
}

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

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(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)))