Average Error: 0.1 → 0.1
Time: 2.5s
Precision: binary64
\[\left(x \cdot 3\right) \cdot y - z \]
↓
\[3 \cdot \left(y \cdot x\right) - z \]
(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))
↓
(FPCore (x y z) :precision binary64 (- (* 3.0 (* y x)) z))
double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}
↓
double code(double x, double y, double z) {
	return (3.0 * (y * x)) - 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 * 3.0d0) * 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 = (3.0d0 * (y * x)) - z
end function

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}
↓
public static double code(double x, double y, double z) {
	return (3.0 * (y * x)) - z;
}

def code(x, y, z):
	return ((x * 3.0) * y) - z
↓
def code(x, y, z):
	return (3.0 * (y * x)) - z

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end
↓
function code(x, y, z)
	return Float64(Float64(3.0 * Float64(y * x)) - z)
end

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end
↓
function tmp = code(x, y, z)
	tmp = (3.0 * (y * x)) - z;
end

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]
↓
code[x_, y_, z_] := N[(N[(3.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

\left(x \cdot 3\right) \cdot y - z
↓
3 \cdot \left(y \cdot x\right) - z

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z \]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot 3\right) \cdot y - z \]

  2. Taylor expanded in x around 0 0.1

    \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} - z \]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \left(y \cdot x\right) - z \]

Reproduce

herbie shell --seed 2022134 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))