Average Error: 0.1 → 0.0
Time: 12.9s
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 r15774511 = 1.0;
        double r15774512 = 4.0;
        double r15774513 = x;
        double r15774514 = y;
        double r15774515 = 0.25;
        double r15774516 = r15774514 * r15774515;
        double r15774517 = r15774513 + r15774516;
        double r15774518 = z;
        double r15774519 = r15774517 - r15774518;
        double r15774520 = r15774512 * r15774519;
        double r15774521 = r15774520 / r15774514;
        double r15774522 = r15774511 + r15774521;
        return r15774522;
}
↓
double f(double x, double y, double z) {
        double r15774523 = 2.0;
        double r15774524 = 4.0;
        double r15774525 = x;
        double r15774526 = y;
        double r15774527 = r15774525 / r15774526;
        double r15774528 = z;
        double r15774529 = r15774528 / r15774526;
        double r15774530 = r15774527 - r15774529;
        double r15774531 = r15774524 * r15774530;
        double r15774532 = r15774523 + r15774531;
        return r15774532;
}

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 2019158 
(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)))