Average Error: 0.1 → 0.0
Time: 12.4s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r14282451 = 1.0;
        double r14282452 = 4.0;
        double r14282453 = x;
        double r14282454 = y;
        double r14282455 = 0.25;
        double r14282456 = r14282454 * r14282455;
        double r14282457 = r14282453 + r14282456;
        double r14282458 = z;
        double r14282459 = r14282457 - r14282458;
        double r14282460 = r14282452 * r14282459;
        double r14282461 = r14282460 / r14282454;
        double r14282462 = r14282451 + r14282461;
        return r14282462;
}
↓
double f(double x, double y, double z) {
        double r14282463 = 2.0;
        double r14282464 = 4.0;
        double r14282465 = x;
        double r14282466 = y;
        double r14282467 = r14282465 / r14282466;
        double r14282468 = z;
        double r14282469 = r14282468 / r14282466;
        double r14282470 = r14282467 - r14282469;
        double r14282471 = r14282464 * r14282470;
        double r14282472 = r14282463 + r14282471;
        return r14282472;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019162 
(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)))