Average Error: 0.1 → 0.0
Time: 1.4s
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 r306974 = 1.0;
        double r306975 = 4.0;
        double r306976 = x;
        double r306977 = y;
        double r306978 = 0.25;
        double r306979 = r306977 * r306978;
        double r306980 = r306976 + r306979;
        double r306981 = z;
        double r306982 = r306980 - r306981;
        double r306983 = r306975 * r306982;
        double r306984 = r306983 / r306977;
        double r306985 = r306974 + r306984;
        return r306985;
}
↓
double f(double x, double y, double z) {
        double r306986 = 1.0;
        double r306987 = 0.25;
        double r306988 = 4.0;
        double r306989 = r306987 * r306988;
        double r306990 = r306986 + r306989;
        double r306991 = x;
        double r306992 = y;
        double r306993 = r306991 / r306992;
        double r306994 = z;
        double r306995 = r306994 / r306992;
        double r306996 = r306993 - r306995;
        double r306997 = r306996 * r306988;
        double r306998 = r306990 + r306997;
        return r306998;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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 2020062 
(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)))