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

Average Error: 0.0 → 0.0

Time: 1.5s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return y * (0.5 * 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 = y * (0.5d0 * 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 y * (0.5 * x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

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

   [Start] 0.0	\[ 0.5 \cdot \left(y \cdot x\right) \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.0	\[ \color{blue}{y \cdot \left(0.5 \cdot x\right)} \]

4. Final simplification 0.0

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

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Numeric.Interval.Internal:scale from intervals-0.7.1, B"
  :precision binary64
  (/ (* x y) 2.0))