Average Error: 0.0 → 0.0
Time: 5.1s
Precision: binary64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + x \cdot \left(y + 0.5\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + x \cdot \left(y + 0.5\right)
(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))
↓
(FPCore (x y z) :precision binary64 (+ z (* x (+ y 0.5))))
double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}
↓
double code(double x, double y, double z) {
	return z + (x * (y + 0.5));
}

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

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))