Numeric.Interval.Internal:scale from intervals-0.7.1, B

Average Error: 0.0 → 0.0

Time: 9.6s

Precision: binary64

Cost: 320

Math

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

↓

\[\left(0.5 \cdot y\right) \cdot x \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x y) 2.0))

↓

(FPCore (x y) :precision binary64 (* (* 0.5 y) x))

C

double code(double x, double y) {
	return (x * y) / 2.0;
}

↓

double code(double x, double y) {
	return (0.5 * y) * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) / 2.0d0
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (0.5d0 * y) * x
end function

Java

public static double code(double x, double y) {
	return (x * y) / 2.0;
}

↓

public static double code(double x, double y) {
	return (0.5 * y) * x;
}

Python

def code(x, y):
	return (x * y) / 2.0

↓

def code(x, y):
	return (0.5 * y) * x

Julia

function code(x, y)
	return Float64(Float64(x * y) / 2.0)
end

↓

function code(x, y)
	return Float64(Float64(0.5 * y) * x)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) / 2.0;
end

↓

function tmp = code(x, y)
	tmp = (0.5 * y) * x;
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision]

↓

code[x_, y_] := N[(N[(0.5 * y), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{0.5 \cdot \left(y \cdot x\right)} \]

3. Simplified 0.0

   \[\leadsto \color{blue}{\left(0.5 \cdot y\right) \cdot x} \]
   Proof

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2.0))