Average Error: 0.2 → 0.1
Time: 27.3s
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 r9546117 = 1.0;
        double r9546118 = 4.0;
        double r9546119 = x;
        double r9546120 = y;
        double r9546121 = 0.75;
        double r9546122 = r9546120 * r9546121;
        double r9546123 = r9546119 + r9546122;
        double r9546124 = z;
        double r9546125 = r9546123 - r9546124;
        double r9546126 = r9546118 * r9546125;
        double r9546127 = r9546126 / r9546120;
        double r9546128 = r9546117 + r9546127;
        return r9546128;
}
↓
double f(double x, double y, double z) {
        double r9546129 = 4.0;
        double r9546130 = x;
        double r9546131 = z;
        double r9546132 = r9546130 - r9546131;
        double r9546133 = r9546132 * r9546129;
        double r9546134 = y;
        double r9546135 = r9546133 / r9546134;
        double r9546136 = r9546129 + r9546135;
        return r9546136;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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)))