Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[x \cdot \left(y + 0.5\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
x \cdot \left(y + 0.5\right) + z
double f(double x, double y, double z) {
        double r349411 = x;
        double r349412 = 2.0;
        double r349413 = r349411 / r349412;
        double r349414 = y;
        double r349415 = r349414 * r349411;
        double r349416 = r349413 + r349415;
        double r349417 = z;
        double r349418 = r349416 + r349417;
        return r349418;
}
↓
double f(double x, double y, double z) {
        double r349419 = x;
        double r349420 = y;
        double r349421 = 0.5;
        double r349422 = r349420 + r349421;
        double r349423 = r349419 * r349422;
        double r349424 = z;
        double r349425 = r349423 + r349424;
        return r349425;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))