Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\left(x + y \cdot x\right) + z \cdot y\]
x + y \cdot \left(z + x\right)
↓
\left(x + y \cdot x\right) + z \cdot y
double code(double x, double y, double z) {
	return (x + (y * (z + x)));
}
↓
double code(double x, double y, double z) {
	return ((x + (y * x)) + (z * y));
}

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. Using strategy rm

  3. Applied +-commutative0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020066 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))