Average Error: 0.1 → 0.0
Time: 12.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r237043 = 1.0;
        double r237044 = 4.0;
        double r237045 = x;
        double r237046 = y;
        double r237047 = 0.25;
        double r237048 = r237046 * r237047;
        double r237049 = r237045 + r237048;
        double r237050 = z;
        double r237051 = r237049 - r237050;
        double r237052 = r237044 * r237051;
        double r237053 = r237052 / r237046;
        double r237054 = r237043 + r237053;
        return r237054;
}
↓
double f(double x, double y, double z) {
        double r237055 = 2.0;
        double r237056 = 4.0;
        double r237057 = x;
        double r237058 = y;
        double r237059 = r237057 / r237058;
        double r237060 = z;
        double r237061 = r237060 / r237058;
        double r237062 = r237059 - r237061;
        double r237063 = r237056 * r237062;
        double r237064 = r237055 + r237063;
        return r237064;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(0.25 - \frac{z - x}{y}\right) \cdot 4 + 1}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))