Average Error: 0.0 → 0.0
Time: 3.5s
Precision: binary64
\[\left(x + y\right) \cdot z \]
↓
\[y \cdot z + z \cdot x \]
\left(x + y\right) \cdot z
↓
y \cdot z + z \cdot x

(FPCore (x y z) :precision binary64 (* (+ x y) z))
↓
(FPCore (x y z) :precision binary64 (+ (* y z) (* z x)))
double code(double x, double y, double z) {
	return (x + y) * z;
}
↓
double code(double x, double y, double z) {
	return (y * z) + (z * x);
}

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

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

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{y \cdot z + z \cdot x} \]

  3. Final simplification0.0

    \[\leadsto y \cdot z + z \cdot x \]

Reproduce

herbie shell --seed 2022077 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))