Average Error: 0.1 → 0.0
Time: 3.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}
double f(double x, double y, double z) {
        double r147995 = 1.0;
        double r147996 = 4.0;
        double r147997 = x;
        double r147998 = y;
        double r147999 = 0.25;
        double r148000 = r147998 * r147999;
        double r148001 = r147997 + r148000;
        double r148002 = z;
        double r148003 = r148001 - r148002;
        double r148004 = r147996 * r148003;
        double r148005 = r148004 / r147998;
        double r148006 = r147995 + r148005;
        return r148006;
}
↓
double f(double x, double y, double z) {
        double r148007 = 4.0;
        double r148008 = x;
        double r148009 = y;
        double r148010 = r148008 / r148009;
        double r148011 = r148007 * r148010;
        double r148012 = 2.0;
        double r148013 = r148011 + r148012;
        double r148014 = z;
        double r148015 = r148014 / r148009;
        double r148016 = r148007 * r148015;
        double r148017 = r148013 - r148016;
        return r148017;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  3. Final simplification0.0

    \[\leadsto \left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}\]

Reproduce

herbie shell --seed 2020003 
(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)))