Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[x \cdot \left(0.5 + y\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
x \cdot \left(0.5 + y\right) + z
double f(double x, double y, double z) {
        double r788999 = x;
        double r789000 = 2.0;
        double r789001 = r788999 / r789000;
        double r789002 = y;
        double r789003 = r789002 * r788999;
        double r789004 = r789001 + r789003;
        double r789005 = z;
        double r789006 = r789004 + r789005;
        return r789006;
}
↓
double f(double x, double y, double z) {
        double r789007 = x;
        double r789008 = 0.5;
        double r789009 = y;
        double r789010 = r789008 + r789009;
        double r789011 = r789007 * r789010;
        double r789012 = z;
        double r789013 = r789011 + r789012;
        return r789013;
}

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 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot x + x \cdot y\right)} + z\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(0.5 + y\right)} + z\]

  4. Final simplification0.0

    \[\leadsto x \cdot \left(0.5 + y\right) + z\]

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))