Average Error: 0.2 → 0.0
Time: 9.3s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0
double f(double x, double y, double z) {
        double r14896130 = 1.0;
        double r14896131 = 4.0;
        double r14896132 = x;
        double r14896133 = y;
        double r14896134 = 0.75;
        double r14896135 = r14896133 * r14896134;
        double r14896136 = r14896132 + r14896135;
        double r14896137 = z;
        double r14896138 = r14896136 - r14896137;
        double r14896139 = r14896131 * r14896138;
        double r14896140 = r14896139 / r14896133;
        double r14896141 = r14896130 + r14896140;
        return r14896141;
}
↓
double f(double x, double y, double z) {
        double r14896142 = 0.75;
        double r14896143 = z;
        double r14896144 = x;
        double r14896145 = r14896143 - r14896144;
        double r14896146 = y;
        double r14896147 = r14896145 / r14896146;
        double r14896148 = r14896142 - r14896147;
        double r14896149 = 4.0;
        double r14896150 = r14896148 * r14896149;
        double r14896151 = 1.0;
        double r14896152 = r14896150 + r14896151;
        return r14896152;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0}\]

  3. Final simplification0.0

    \[\leadsto \left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0\]

Reproduce

herbie shell --seed 2019163 
(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)))