Average Error: 0.0 → 0.0
Time: 4.0s
Precision: binary64
\[x + y \cdot \left(z + x\right)\]
↓
\[x \cdot y + \left(x + y \cdot z\right)\]
x + y \cdot \left(z + x\right)
↓
x \cdot y + \left(x + y \cdot z\right)
(FPCore (x y z) :precision binary64 (+ x (* y (+ z x))))
↓
(FPCore (x y z) :precision binary64 (+ (* x y) (+ x (* 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 * y) + (x + (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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021024 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))