Average Error: 0.1 → 0.0
Time: 8.3s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1
double f(double x, double y, double z) {
        double r158444 = 1.0;
        double r158445 = 4.0;
        double r158446 = x;
        double r158447 = y;
        double r158448 = 0.25;
        double r158449 = r158447 * r158448;
        double r158450 = r158446 + r158449;
        double r158451 = z;
        double r158452 = r158450 - r158451;
        double r158453 = r158445 * r158452;
        double r158454 = r158453 / r158447;
        double r158455 = r158444 + r158454;
        return r158455;
}
↓
double f(double x, double y, double z) {
        double r158456 = 4.0;
        double r158457 = 0.25;
        double r158458 = x;
        double r158459 = y;
        double r158460 = r158458 / r158459;
        double r158461 = z;
        double r158462 = r158461 / r158459;
        double r158463 = r158460 - r158462;
        double r158464 = r158457 + r158463;
        double r158465 = r158456 * r158464;
        double r158466 = 1.0;
        double r158467 = r158465 + r158466;
        return r158467;
}

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 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.25 + \frac{x - z}{y}\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.25 + 4 \cdot \frac{x - z}{y}\right)}\]

  5. Applied associate-+r+0.0

    \[\leadsto \color{blue}{\left(1 + 4 \cdot 0.25\right) + 4 \cdot \frac{x - z}{y}}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{\left(1 + 0.25 \cdot 4\right)} + 4 \cdot \frac{x - z}{y}\]
  7. Using strategy rm

  8. Applied div-sub0.0

    \[\leadsto \left(1 + 0.25 \cdot 4\right) + 4 \cdot \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)}\]

  9. Final simplification0.0

    \[\leadsto 4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))