Average Error: 0.0 → 0.0
Time: 838.0ms
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 r265400 = x;
        double r265401 = 2.0;
        double r265402 = r265400 / r265401;
        double r265403 = y;
        double r265404 = r265403 * r265400;
        double r265405 = r265402 + r265404;
        double r265406 = z;
        double r265407 = r265405 + r265406;
        return r265407;
}
↓
double f(double x, double y, double z) {
        double r265408 = x;
        double r265409 = y;
        double r265410 = 0.5;
        double r265411 = r265409 + r265410;
        double r265412 = r265408 * r265411;
        double r265413 = z;
        double r265414 = r265412 + r265413;
        return r265414;
}

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 2020036 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))