Average Error: 0.1 → 0.0
Time: 12.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4 + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4 + 4
double f(double x, double y, double z) {
        double r238010 = 1.0;
        double r238011 = 4.0;
        double r238012 = x;
        double r238013 = y;
        double r238014 = 0.75;
        double r238015 = r238013 * r238014;
        double r238016 = r238012 + r238015;
        double r238017 = z;
        double r238018 = r238016 - r238017;
        double r238019 = r238011 * r238018;
        double r238020 = r238019 / r238013;
        double r238021 = r238010 + r238020;
        return r238021;
}
↓
double f(double x, double y, double z) {
        double r238022 = x;
        double r238023 = y;
        double r238024 = r238022 / r238023;
        double r238025 = z;
        double r238026 = r238025 / r238023;
        double r238027 = r238024 - r238026;
        double r238028 = 4.0;
        double r238029 = r238027 * r238028;
        double r238030 = r238029 + r238028;
        return r238030;
}

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

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))