Average Error: 0.2 → 0.0
Time: 17.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\left(\frac{x}{y} - \frac{z}{y}\right) + 0.75\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\left(\frac{x}{y} - \frac{z}{y}\right) + 0.75\right) + 1
double f(double x, double y, double z) {
        double r228046 = 1.0;
        double r228047 = 4.0;
        double r228048 = x;
        double r228049 = y;
        double r228050 = 0.75;
        double r228051 = r228049 * r228050;
        double r228052 = r228048 + r228051;
        double r228053 = z;
        double r228054 = r228052 - r228053;
        double r228055 = r228047 * r228054;
        double r228056 = r228055 / r228049;
        double r228057 = r228046 + r228056;
        return r228057;
}
↓
double f(double x, double y, double z) {
        double r228058 = 4.0;
        double r228059 = x;
        double r228060 = y;
        double r228061 = r228059 / r228060;
        double r228062 = z;
        double r228063 = r228062 / r228060;
        double r228064 = r228061 - r228063;
        double r228065 = 0.75;
        double r228066 = r228064 + r228065;
        double r228067 = r228058 * r228066;
        double r228068 = 1.0;
        double r228069 = r228067 + r228068;
        return r228069;
}

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 0.2

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(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)))