Average Error: 0.2 → 0.1
Time: 12.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{\left(x - z\right) \cdot 4}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{\left(x - z\right) \cdot 4}{y}
double f(double x, double y, double z) {
        double r14457171 = 1.0;
        double r14457172 = 4.0;
        double r14457173 = x;
        double r14457174 = y;
        double r14457175 = 0.75;
        double r14457176 = r14457174 * r14457175;
        double r14457177 = r14457173 + r14457176;
        double r14457178 = z;
        double r14457179 = r14457177 - r14457178;
        double r14457180 = r14457172 * r14457179;
        double r14457181 = r14457180 / r14457174;
        double r14457182 = r14457171 + r14457181;
        return r14457182;
}
↓
double f(double x, double y, double z) {
        double r14457183 = 4.0;
        double r14457184 = x;
        double r14457185 = z;
        double r14457186 = r14457184 - r14457185;
        double r14457187 = r14457186 * r14457183;
        double r14457188 = y;
        double r14457189 = r14457187 / r14457188;
        double r14457190 = r14457183 + r14457189;
        return r14457190;
}

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 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  6. Applied sub-div0.0

    \[\leadsto 4 + 4 \cdot \color{blue}{\frac{x - z}{y}}\]

  7. Applied associate-*r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))