Average Error: 0.2 → 0.0
Time: 8.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r322595 = 1.0;
        double r322596 = 4.0;
        double r322597 = x;
        double r322598 = y;
        double r322599 = 0.75;
        double r322600 = r322598 * r322599;
        double r322601 = r322597 + r322600;
        double r322602 = z;
        double r322603 = r322601 - r322602;
        double r322604 = r322596 * r322603;
        double r322605 = r322604 / r322598;
        double r322606 = r322595 + r322605;
        return r322606;
}
↓
double f(double x, double y, double z) {
        double r322607 = 4.0;
        double r322608 = x;
        double r322609 = z;
        double r322610 = r322608 - r322609;
        double r322611 = y;
        double r322612 = r322610 / r322611;
        double r322613 = r322612 * r322607;
        double r322614 = r322607 + r322613;
        return r322614;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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)))