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

Average Error: 0.0 → 0

Time: 1.1s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (x / 2.0d0) * y
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 (x / 2.0) * y;
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0

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

   [Start] 0.0	\[ \frac{x \cdot y}{2} \]
   associate-*l/ [<=] 0	\[ \color{blue}{\frac{x}{2} \cdot y} \]

3. Final simplification 0

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

Reproduce

herbie shell --seed 2023187 
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2.0))