Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + \left(0.5 + y\right) \cdot x\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + \left(0.5 + y\right) \cdot x
double f(double x, double y, double z) {
        double r12881530 = x;
        double r12881531 = 2.0;
        double r12881532 = r12881530 / r12881531;
        double r12881533 = y;
        double r12881534 = r12881533 * r12881530;
        double r12881535 = r12881532 + r12881534;
        double r12881536 = z;
        double r12881537 = r12881535 + r12881536;
        return r12881537;
}
↓
double f(double x, double y, double z) {
        double r12881538 = z;
        double r12881539 = 0.5;
        double r12881540 = y;
        double r12881541 = r12881539 + r12881540;
        double r12881542 = x;
        double r12881543 = r12881541 * r12881542;
        double r12881544 = r12881538 + r12881543;
        return r12881544;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))