Average Error: 0.2 → 0.0
Time: 17.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r256407 = 1.0;
        double r256408 = 4.0;
        double r256409 = x;
        double r256410 = y;
        double r256411 = 0.75;
        double r256412 = r256410 * r256411;
        double r256413 = r256409 + r256412;
        double r256414 = z;
        double r256415 = r256413 - r256414;
        double r256416 = r256408 * r256415;
        double r256417 = r256416 / r256410;
        double r256418 = r256407 + r256417;
        return r256418;
}
↓
double f(double x, double y, double z) {
        double r256419 = 4.0;
        double r256420 = x;
        double r256421 = y;
        double r256422 = r256420 / r256421;
        double r256423 = z;
        double r256424 = r256423 / r256421;
        double r256425 = r256422 - r256424;
        double r256426 = r256425 * r256419;
        double r256427 = r256419 + r256426;
        return r256427;
}

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 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + \left(\frac{x - z}{y} + 0.75\right) \cdot 4}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 1 + \left(\color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)} + 0.75\right) \cdot 4\]

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))