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

Average Error: 0.1 → 0.1

Time: 8.8s

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	28.3
Cost	6852

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-220}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5 + x \cdot 0.75\\ \end{array} \]

Alternative 2
Error	19.3
Cost	6852

\[\begin{array}{l} \mathbf{if}\;y \leq -3.28 \cdot 10^{-7}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, 0.5, x\right)\\ \end{array} \]

Alternative 3
Error	41.3
Cost	448

\[y \cdot 0.5 + x \cdot 0.75 \]

Alternative 4
Error	56.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))