Average Error: 0.1 → 0.0
Time: 1.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r293493 = 1.0;
        double r293494 = 4.0;
        double r293495 = x;
        double r293496 = y;
        double r293497 = 0.25;
        double r293498 = r293496 * r293497;
        double r293499 = r293495 + r293498;
        double r293500 = z;
        double r293501 = r293499 - r293500;
        double r293502 = r293494 * r293501;
        double r293503 = r293502 / r293496;
        double r293504 = r293493 + r293503;
        return r293504;
}
↓
double f(double x, double y, double z) {
        double r293505 = 2.0;
        double r293506 = 4.0;
        double r293507 = x;
        double r293508 = z;
        double r293509 = r293507 - r293508;
        double r293510 = y;
        double r293511 = r293509 / r293510;
        double r293512 = r293506 * r293511;
        double r293513 = r293505 + r293512;
        return r293513;
}

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

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

  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

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

  5. Final simplification0.0

    \[\leadsto 2 + 4 \cdot \frac{x - z}{y}\]

Reproduce

herbie shell --seed 2020056 
(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)))