Average Error: 0.1 → 0.0
Time: 2.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 0.25 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 0.25 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r349255 = 1.0;
        double r349256 = 4.0;
        double r349257 = x;
        double r349258 = y;
        double r349259 = 0.25;
        double r349260 = r349258 * r349259;
        double r349261 = r349257 + r349260;
        double r349262 = z;
        double r349263 = r349261 - r349262;
        double r349264 = r349256 * r349263;
        double r349265 = r349264 / r349258;
        double r349266 = r349255 + r349265;
        return r349266;
}
↓
double f(double x, double y, double z) {
        double r349267 = 1.0;
        double r349268 = 0.25;
        double r349269 = 4.0;
        double r349270 = r349268 * r349269;
        double r349271 = r349267 + r349270;
        double r349272 = x;
        double r349273 = y;
        double r349274 = r349272 / r349273;
        double r349275 = z;
        double r349276 = r349275 / r349273;
        double r349277 = r349274 - r349276;
        double r349278 = r349277 * r349269;
        double r349279 = r349271 + r349278;
        return r349279;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Using strategy rm

  7. Applied div-sub0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(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)))