Average Error: 0.2 → 0.0
Time: 4.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r271596 = 1.0;
        double r271597 = 4.0;
        double r271598 = x;
        double r271599 = y;
        double r271600 = 0.75;
        double r271601 = r271599 * r271600;
        double r271602 = r271598 + r271601;
        double r271603 = z;
        double r271604 = r271602 - r271603;
        double r271605 = r271597 * r271604;
        double r271606 = r271605 / r271599;
        double r271607 = r271596 + r271606;
        return r271607;
}
↓
double f(double x, double y, double z) {
        double r271608 = 1.0;
        double r271609 = 4.0;
        double r271610 = 0.75;
        double r271611 = x;
        double r271612 = y;
        double r271613 = r271611 / r271612;
        double r271614 = z;
        double r271615 = r271614 / r271612;
        double r271616 = r271613 - r271615;
        double r271617 = r271610 + r271616;
        double r271618 = r271609 * r271617;
        double r271619 = r271608 + r271618;
        return r271619;
}

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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(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)))