fabs fraction 2

?

Percentage Accurate: 100.0% → 100.0%
Time: 1.1s
Precision: binary64
Cost: 6720

?

\[\frac{\left|a - b\right|}{2} \]
↓
\[\frac{\left|a - b\right|}{2} \]
(FPCore (a b) :precision binary64 (/ (fabs (- a b)) 2.0))
↓
(FPCore (a b) :precision binary64 (/ (fabs (- a b)) 2.0))
double code(double a, double b) {
	return fabs((a - b)) / 2.0;
}
↓
double code(double a, double b) {
	return fabs((a - b)) / 2.0;
}

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = abs((a - b)) / 2.0d0
end function
↓
real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = abs((a - b)) / 2.0d0
end function

public static double code(double a, double b) {
	return Math.abs((a - b)) / 2.0;
}
↓
public static double code(double a, double b) {
	return Math.abs((a - b)) / 2.0;
}

def code(a, b):
	return math.fabs((a - b)) / 2.0
↓
def code(a, b):
	return math.fabs((a - b)) / 2.0

function code(a, b)
	return Float64(abs(Float64(a - b)) / 2.0)
end
↓
function code(a, b)
	return Float64(abs(Float64(a - b)) / 2.0)
end

function tmp = code(a, b)
	tmp = abs((a - b)) / 2.0;
end
↓
function tmp = code(a, b)
	tmp = abs((a - b)) / 2.0;
end

code[a_, b_] := N[(N[Abs[N[(a - b), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]
↓
code[a_, b_] := N[(N[Abs[N[(a - b), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]

\frac{\left|a - b\right|}{2}
↓
\frac{\left|a - b\right|}{2}

Local Percentage Accuracy?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 100.0%

    \[\frac{\left|a - b\right|}{2} \]

  2. Final simplification100.0%

    \[\leadsto \frac{\left|a - b\right|}{2} \]

Reproduce?

herbie shell --seed 2023161 
(FPCore (a b)
  :name "fabs fraction 2"
  :precision binary64
  (/ (fabs (- a b)) 2.0))