Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3

Average Error: 0.1 → 0.1

Time: 4.8s

Precision: binary64

Cost: 6848

Math

\[x + \frac{\left|y - x\right|}{2} \]

↓

\[x + \frac{\left|y - x\right|}{2} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (fabs (- y x)) 2.0)))

↓

(FPCore (x y) :precision binary64 (+ x (/ (fabs (- y x)) 2.0)))

C

double code(double x, double y) {
	return x + (fabs((y - x)) / 2.0);
}

↓

double code(double x, double y) {
	return x + (fabs((y - x)) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (abs((y - x)) / 2.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (abs((y - x)) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (Math.abs((y - x)) / 2.0);
}

↓

public static double code(double x, double y) {
	return x + (Math.abs((y - x)) / 2.0);
}

Python

def code(x, y):
	return x + (math.fabs((y - x)) / 2.0)

↓

def code(x, y):
	return x + (math.fabs((y - x)) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(abs(Float64(y - x)) / 2.0))
end

↓

function code(x, y)
	return Float64(x + Float64(abs(Float64(y - x)) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (abs((y - x)) / 2.0);
end

↓

function tmp = code(x, y)
	tmp = x + (abs((y - x)) / 2.0);
end

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

   \[x + \frac{\left|y - x\right|}{2} \]

2. Final simplification 0.1

   \[\leadsto x + \frac{\left|y - x\right|}{2} \]

Alternatives

Alternative 1
Error	11.5
Cost	6984

\[\begin{array}{l} t_0 := 0.5 \cdot \left(x + y\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-164}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x + t_0\\ \end{array} \]

Alternative 2
Error	16.0
Cost	580

\[\begin{array}{l} t_0 := 0.5 \cdot \left(x + y\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-291}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + t_0\\ \end{array} \]

Alternative 3
Error	19.5
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;\frac{-0.25}{\frac{0.5}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]

Alternative 4
Error	44.9
Cost	324

\[\begin{array}{l} \mathbf{if}\;y \leq 9.2 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 5
Error	34.7
Cost	324

\[\begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 6
Error	28.6
Cost	320

\[0.5 \cdot \left(x + y\right) \]

Alternative 7
Error	56.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022329 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))