Average Error: 0.0 → 0.0
Time: 944.0ms
Precision: binary64
\[\frac{x \cdot y}{2} \]
↓
\[x \cdot \frac{y}{2} \]
\frac{x \cdot y}{2}
↓
x \cdot \frac{y}{2}

(FPCore (x y) :precision binary64 (/ (* x y) 2.0))
↓
(FPCore (x y) :precision binary64 (* x (/ y 2.0)))
double code(double x, double y) {
	return (x * y) / 2.0;
}
↓
double code(double x, double y) {
	return x * (y / 2.0);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2} \]

  2. Applied *-un-lft-identity_binary640.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}} \]

  3. Applied times-frac_binary640.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}} \]

  4. Simplified0.0

    \[\leadsto \color{blue}{x} \cdot \frac{y}{2} \]

  5. Final simplification0.0

    \[\leadsto x \cdot \frac{y}{2} \]

Reproduce

herbie shell --seed 2022076 
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2.0))