Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
Cost: 320
\[ \begin{array}{c}[x, y, z] = \mathsf{sort}([x, y, z])\\ \end{array} \]
\[\left(x + y\right) + z \]
↓
\[x + \left(y + z\right) \]
(FPCore (x y z) :precision binary64 (+ (+ x y) z))
↓
(FPCore (x y z) :precision binary64 (+ x (+ y z)))
double code(double x, double y, double z) {
	return (x + y) + z;
}
↓
double code(double x, double y, double z) {
	return x + (y + z);
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) + z
end function
↓
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y + z)
end function

public static double code(double x, double y, double z) {
	return (x + y) + z;
}
↓
public static double code(double x, double y, double z) {
	return x + (y + z);
}

def code(x, y, z):
	return (x + y) + z
↓
def code(x, y, z):
	return x + (y + z)

function code(x, y, z)
	return Float64(Float64(x + y) + z)
end
↓
function code(x, y, z)
	return Float64(x + Float64(y + z))
end

function tmp = code(x, y, z)
	tmp = (x + y) + z;
end
↓
function tmp = code(x, y, z)
	tmp = x + (y + z);
end

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision]
↓
code[x_, y_, z_] := N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision]

\left(x + y\right) + z
↓
x + \left(y + z\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) + z \]

  2. Simplified0.0

    \[\leadsto \color{blue}{x + \left(y + z\right)} \]
    Proof
    (+.f64 x (+.f64 y z)): 0 points increase in error, 0 points decrease in error
    (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 x y) z)): 1 points increase in error, 0 points decrease in error

  3. Final simplification0.0

    \[\leadsto x + \left(y + z\right) \]

Reproduce

herbie shell --seed 2022330 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))