Average Error: 0.2 → 0.0
Time: 13.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r18464440 = 1.0;
        double r18464441 = 4.0;
        double r18464442 = x;
        double r18464443 = y;
        double r18464444 = 0.75;
        double r18464445 = r18464443 * r18464444;
        double r18464446 = r18464442 + r18464445;
        double r18464447 = z;
        double r18464448 = r18464446 - r18464447;
        double r18464449 = r18464441 * r18464448;
        double r18464450 = r18464449 / r18464443;
        double r18464451 = r18464440 + r18464450;
        return r18464451;
}
↓
double f(double x, double y, double z) {
        double r18464452 = 4.0;
        double r18464453 = x;
        double r18464454 = y;
        double r18464455 = r18464453 / r18464454;
        double r18464456 = z;
        double r18464457 = r18464456 / r18464454;
        double r18464458 = r18464455 - r18464457;
        double r18464459 = r18464452 * r18464458;
        double r18464460 = r18464452 + r18464459;
        return r18464460;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))