Average Error: 0.1 → 0.0
Time: 9.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 2
double f(double x, double y, double z) {
        double r15535221 = 1.0;
        double r15535222 = 4.0;
        double r15535223 = x;
        double r15535224 = y;
        double r15535225 = 0.25;
        double r15535226 = r15535224 * r15535225;
        double r15535227 = r15535223 + r15535226;
        double r15535228 = z;
        double r15535229 = r15535227 - r15535228;
        double r15535230 = r15535222 * r15535229;
        double r15535231 = r15535230 / r15535224;
        double r15535232 = r15535221 + r15535231;
        return r15535232;
}
↓
double f(double x, double y, double z) {
        double r15535233 = 4.0;
        double r15535234 = x;
        double r15535235 = y;
        double r15535236 = r15535234 / r15535235;
        double r15535237 = z;
        double r15535238 = r15535237 / r15535235;
        double r15535239 = r15535236 - r15535238;
        double r15535240 = r15535233 * r15535239;
        double r15535241 = 2.0;
        double r15535242 = r15535240 + r15535241;
        return r15535242;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(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)))