Average Error: 0.1 → 0.0
Time: 9.2s
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 r271195 = 1.0;
        double r271196 = 4.0;
        double r271197 = x;
        double r271198 = y;
        double r271199 = 0.25;
        double r271200 = r271198 * r271199;
        double r271201 = r271197 + r271200;
        double r271202 = z;
        double r271203 = r271201 - r271202;
        double r271204 = r271196 * r271203;
        double r271205 = r271204 / r271198;
        double r271206 = r271195 + r271205;
        return r271206;
}
↓
double f(double x, double y, double z) {
        double r271207 = 2.0;
        double r271208 = 4.0;
        double r271209 = x;
        double r271210 = y;
        double r271211 = r271209 / r271210;
        double r271212 = z;
        double r271213 = r271212 / r271210;
        double r271214 = r271211 - r271213;
        double r271215 = r271208 * r271214;
        double r271216 = r271207 + r271215;
        return r271216;
}

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 2019174 
(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)))