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

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

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

  2. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021015 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))