Average Error: 0.0 → 0.0
Time: 7.7s
Precision: binary64
\[x + y \cdot \left(z + x\right)\]
↓
\[\left(x + y \cdot z\right) + x \cdot y\]
x + y \cdot \left(z + x\right)
↓
\left(x + y \cdot z\right) + x \cdot y
(FPCore (x y z) :precision binary64 (+ x (* y (+ z x))))
↓
(FPCore (x y z) :precision binary64 (+ (+ x (* y z)) (* x 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 * z)) + (x * 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 distribute-rgt-in_binary64_41200.0

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

  4. Applied associate-+r+_binary64_41020.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021007 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))