Average Error: 0.1 → 0.0
Time: 11.0s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r13074994 = 1.0;
        double r13074995 = 4.0;
        double r13074996 = x;
        double r13074997 = y;
        double r13074998 = 0.25;
        double r13074999 = r13074997 * r13074998;
        double r13075000 = r13074996 + r13074999;
        double r13075001 = z;
        double r13075002 = r13075000 - r13075001;
        double r13075003 = r13074995 * r13075002;
        double r13075004 = r13075003 / r13074997;
        double r13075005 = r13074994 + r13075004;
        return r13075005;
}
↓
double f(double x, double y, double z) {
        double r13075006 = 2.0;
        double r13075007 = 4.0;
        double r13075008 = x;
        double r13075009 = y;
        double r13075010 = r13075008 / r13075009;
        double r13075011 = z;
        double r13075012 = r13075011 / r13075009;
        double r13075013 = r13075010 - r13075012;
        double r13075014 = r13075007 * r13075013;
        double r13075015 = r13075006 + r13075014;
        return r13075015;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.25 - \frac{z - x}{y}\right) + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 2.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 2.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))