Average Error: 0.0 → 0
Time: 1.4s
Precision: binary64
Cost: 320
\[\left(x + y\right) + x \]
↓
\[2 \cdot x + y \]
(FPCore (x y) :precision binary64 (+ (+ x y) x))
↓
(FPCore (x y) :precision binary64 (+ (* 2.0 x) y))
double code(double x, double y) {
	return (x + y) + x;
}
↓
double code(double x, double y) {
	return (2.0 * x) + y;
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) + x
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 * x) + y
end function

public static double code(double x, double y) {
	return (x + y) + x;
}
↓
public static double code(double x, double y) {
	return (2.0 * x) + y;
}

def code(x, y):
	return (x + y) + x
↓
def code(x, y):
	return (2.0 * x) + y

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

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

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

\left(x + y\right) + x
↓
2 \cdot x + y

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0
Herbie0
\[y + 2 \cdot x \]

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0

    \[\leadsto \color{blue}{2 \cdot x + y} \]

  3. Final simplification0

    \[\leadsto 2 \cdot x + y \]

Alternatives

Alternative 1
Error16.7
Cost984
\[\begin{array}{l} \mathbf{if}\;x \leq -7.176237375628102 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -1.202078793674945 \cdot 10^{-19}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.4908963476635665 \cdot 10^{-76}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq 1.183802484300788 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.0053429597226521 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq 2.5602251346167025 \cdot 10^{+43}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
Alternative 2
Error31.2
Cost64
\[y \]

Error

Reproduce

herbie shell --seed 2022318 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ y (* 2.0 x))

  (+ (+ x y) x))