Average Error: 0.1 → 0.0
Time: 18.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r186420 = 1.0;
        double r186421 = 4.0;
        double r186422 = x;
        double r186423 = y;
        double r186424 = 0.25;
        double r186425 = r186423 * r186424;
        double r186426 = r186422 + r186425;
        double r186427 = z;
        double r186428 = r186426 - r186427;
        double r186429 = r186421 * r186428;
        double r186430 = r186429 / r186423;
        double r186431 = r186420 + r186430;
        return r186431;
}
↓
double f(double x, double y, double z) {
        double r186432 = 2.0;
        double r186433 = 4.0;
        double r186434 = x;
        double r186435 = y;
        double r186436 = r186434 / r186435;
        double r186437 = z;
        double r186438 = r186437 / r186435;
        double r186439 = r186436 - r186438;
        double r186440 = r186433 * r186439;
        double r186441 = r186432 + r186440;
        return r186441;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))