Average Error: 0.1 → 0.1
Time: 3.6s
Precision: binary64
\[\left(x \cdot y + z\right) \cdot y + t \]
↓
\[y \cdot \left(x \cdot y + z\right) + t \]
(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))
↓
(FPCore (x y z t) :precision binary64 (+ (* y (+ (* x y) z)) t))
double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}
↓
double code(double x, double y, double z, double t) {
	return (y * ((x * y) + z)) + t;
}

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

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

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

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

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2022130 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))