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

Average Accuracy: 99.9% → 99.9%

Time: 6.7s

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 99.9%

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

2. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	79.3%
Cost	7512

\[\begin{array}{l} t_0 := 0.5 \cdot \left(x + y\right)\\ t_1 := \left|y - x\right| \cdot 0.5\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -0.11:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-203}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 12500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t_0\\ \end{array} \]

Alternative 2
Accuracy	68.9%
Cost	977

\[\begin{array}{l} t_0 := 0.5 \cdot \left(x + y\right)\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{-45}:\\ \;\;\;\;\frac{-0.25}{\frac{0.5}{y}}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-260} \lor \neg \left(y \leq 4.7 \cdot 10^{-261}\right) \land y \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;x + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	43.3%
Cost	589

\[\begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-215} \lor \neg \left(y \leq 5.8 \cdot 10^{-120}\right) \land y \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 4
Accuracy	69.6%
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-174}:\\ \;\;\;\;\frac{-0.25}{\frac{0.5}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]

Alternative 5
Accuracy	31.4%
Cost	324

\[\begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 6
Accuracy	55.2%
Cost	320

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

Alternative 7
Accuracy	11.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))