Average Error: 0.2 → 0.0
Time: 6.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.75 - \left(\frac{z}{y} - \frac{x}{y}\right)\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(0.75 - \left(\frac{z}{y} - \frac{x}{y}\right)\right) + 1
double f(double x, double y, double z) {
        double r367600 = 1.0;
        double r367601 = 4.0;
        double r367602 = x;
        double r367603 = y;
        double r367604 = 0.75;
        double r367605 = r367603 * r367604;
        double r367606 = r367602 + r367605;
        double r367607 = z;
        double r367608 = r367606 - r367607;
        double r367609 = r367601 * r367608;
        double r367610 = r367609 / r367603;
        double r367611 = r367600 + r367610;
        return r367611;
}
↓
double f(double x, double y, double z) {
        double r367612 = 4.0;
        double r367613 = 0.75;
        double r367614 = z;
        double r367615 = y;
        double r367616 = r367614 / r367615;
        double r367617 = x;
        double r367618 = r367617 / r367615;
        double r367619 = r367616 - r367618;
        double r367620 = r367613 - r367619;
        double r367621 = r367612 * r367620;
        double r367622 = 1.0;
        double r367623 = r367621 + r367622;
        return r367623;
}

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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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)))