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

Percentage Accurate: 100.0% → 100.0%

Time: 1.5s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x + y) + x
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x + y) + x
END code

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\mathsf{fma}\left(2, x, y\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (fma 2.0 x y))

C

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

Julia

function code(x, y)
	return fma(2.0, x, y)
end

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((2) * x) + y
END code

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + x \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(2, x, y\right) \]
4. Add Preprocessing

Alternative 2: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1623226477154053 \cdot 10^{-26}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 2.426229654520916 \cdot 10^{+48}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= y -1.1623226477154053e-26)
  (+ y x)
  (if (<= y 2.426229654520916e+48) (+ x x) (+ y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1623226477154053e-26) {
		tmp = y + x;
	} else if (y <= 2.426229654520916e+48) {
		tmp = x + x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.1623226477154053d-26)) then
        tmp = y + x
    else if (y <= 2.426229654520916d+48) then
        tmp = x + x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.1623226477154053e-26) {
		tmp = y + x;
	} else if (y <= 2.426229654520916e+48) {
		tmp = x + x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1623226477154053e-26:
		tmp = y + x
	elif y <= 2.426229654520916e+48:
		tmp = x + x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1623226477154053e-26)
		tmp = Float64(y + x);
	elseif (y <= 2.426229654520916e+48)
		tmp = Float64(x + x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.1623226477154053e-26)
		tmp = y + x;
	elseif (y <= 2.426229654520916e+48)
		tmp = x + x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1623226477154053e-26], N[(y + x), $MachinePrecision], If[LessEqual[y, 2.426229654520916e+48], N[(x + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (y <= (2426229654520915891643607200729785382101422440448)) THEN (x + x) ELSE (y + x) ENDIF IN
	LET tmp = IF (y <= (-11623226477154053309672337016807098596194572553602347814800057447127815991871901957210866385139524936676025390625e-138)) THEN (y + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.1623226477154053e-26 or 2.4262296545209159e48 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto y + x \]
   3. Step-by-step derivation

   4. Applied rewrites 58.0%

      \[\leadsto y + x \]

   if -1.1623226477154053e-26 < y < 2.4262296545209159e48

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto 2 \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto 2 \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 51.3%

      \[\leadsto x + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -3.7736488112764267 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.426229654520916 \cdot 10^{+48}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= y -3.7736488112764267e+33)
  y
  (if (<= y 2.426229654520916e+48) (+ x x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.7736488112764267e+33) {
		tmp = y;
	} else if (y <= 2.426229654520916e+48) {
		tmp = x + x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.7736488112764267d+33)) then
        tmp = y
    else if (y <= 2.426229654520916d+48) then
        tmp = x + x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.7736488112764267e+33) {
		tmp = y;
	} else if (y <= 2.426229654520916e+48) {
		tmp = x + x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.7736488112764267e+33:
		tmp = y
	elif y <= 2.426229654520916e+48:
		tmp = x + x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.7736488112764267e+33)
		tmp = y;
	elseif (y <= 2.426229654520916e+48)
		tmp = Float64(x + x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.7736488112764267e+33)
		tmp = y;
	elseif (y <= 2.426229654520916e+48)
		tmp = x + x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.7736488112764267e+33], y, If[LessEqual[y, 2.426229654520916e+48], N[(x + x), $MachinePrecision], y]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF (y <= (2426229654520915891643607200729785382101422440448)) THEN (x + x) ELSE y ENDIF IN
	LET tmp = IF (y <= (-3773648811276426676203284156383232)) THEN y ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -3.7736488112764267e33 or 2.4262296545209159e48 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto 2 \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto 2 \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 51.3%

      \[\leadsto x + x \]

   7. Taylor expanded in x around 0

      \[\leadsto y \]
   8. Step-by-step derivation

   9. Applied rewrites 50.2%

      \[\leadsto y \]

   if -3.7736488112764267e33 < y < 2.4262296545209159e48

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto 2 \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto 2 \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 51.3%

      \[\leadsto x + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.2% accurate, 6.2× speedup

Math

\[y \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  y)

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y
end function

Java

public static double code(double x, double y) {
	return y;
}

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	y
END code

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf

   \[\leadsto 2 \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 51.3%

   \[\leadsto 2 \cdot x \]
5. Step-by-step derivation

6. Applied rewrites 51.3%

   \[\leadsto x + x \]

7. Taylor expanded in x around 0

   \[\leadsto y \]
8. Step-by-step derivation

9. Applied rewrites 50.2%

   \[\leadsto y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64
  (+ (+ x y) x))