Average Error: 0.0 → 0.0
Time: 5.3s
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 r280375 = x;
        double r280376 = 2.0;
        double r280377 = r280375 / r280376;
        double r280378 = y;
        double r280379 = r280378 * r280375;
        double r280380 = r280377 + r280379;
        double r280381 = z;
        double r280382 = r280380 + r280381;
        return r280382;
}
↓
double f(double x, double y, double z) {
        double r280383 = x;
        double r280384 = 0.5;
        double r280385 = y;
        double r280386 = r280384 + r280385;
        double r280387 = r280383 * r280386;
        double r280388 = z;
        double r280389 = r280387 + r280388;
        return r280389;
}

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 2020047 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))