Average Error: 0.1 → 0.2
Time: 2.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\frac{4}{y} \cdot \left(x - z\right) + 2\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\frac{4}{y} \cdot \left(x - z\right) + 2
double f(double x, double y, double z) {
        double r144449 = 1.0;
        double r144450 = 4.0;
        double r144451 = x;
        double r144452 = y;
        double r144453 = 0.25;
        double r144454 = r144452 * r144453;
        double r144455 = r144451 + r144454;
        double r144456 = z;
        double r144457 = r144455 - r144456;
        double r144458 = r144450 * r144457;
        double r144459 = r144458 / r144452;
        double r144460 = r144449 + r144459;
        return r144460;
}
↓
double f(double x, double y, double z) {
        double r144461 = 4.0;
        double r144462 = y;
        double r144463 = r144461 / r144462;
        double r144464 = x;
        double r144465 = z;
        double r144466 = r144464 - r144465;
        double r144467 = r144463 * r144466;
        double r144468 = 2.0;
        double r144469 = r144467 + r144468;
        return r144469;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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

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

  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 simplification0.2

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))