Average Error: 0.1 → 0.0
Time: 3.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.25 + \frac{x - z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.25 + \frac{x - z}{y}\right)
double f(double x, double y, double z) {
        double r297387 = 1.0;
        double r297388 = 4.0;
        double r297389 = x;
        double r297390 = y;
        double r297391 = 0.25;
        double r297392 = r297390 * r297391;
        double r297393 = r297389 + r297392;
        double r297394 = z;
        double r297395 = r297393 - r297394;
        double r297396 = r297388 * r297395;
        double r297397 = r297396 / r297390;
        double r297398 = r297387 + r297397;
        return r297398;
}
↓
double f(double x, double y, double z) {
        double r297399 = 1.0;
        double r297400 = 4.0;
        double r297401 = 0.25;
        double r297402 = x;
        double r297403 = z;
        double r297404 = r297402 - r297403;
        double r297405 = y;
        double r297406 = r297404 / r297405;
        double r297407 = r297401 + r297406;
        double r297408 = r297400 * r297407;
        double r297409 = r297399 + r297408;
        return r297409;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(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)))