Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A

Average Error: 0.0 → 0

Time: 1.2s

Precision: binary64

Cost: 320

Math

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

↓

\[2 \cdot x + y \]

FPCore

(FPCore (x y) :precision binary64 (+ (+ x y) x))

↓

(FPCore (x y) :precision binary64 (+ (* 2.0 x) y))

C

double code(double x, double y) {
	return (x + y) + x;
}

↓

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

Fortran

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

Java

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;
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0
Herbie	0

\[y + 2 \cdot x \]

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 simplification 0

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

Alternatives

Alternative 1
Error	18.3
Cost	1248

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq -1050000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-61}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-101}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 10^{-11}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+98}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 2
Error	32.1
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022330 
(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))