Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4

Percentage Accurate: 99.9% → 100.0%

Time: 2.4s

Alternatives: 9

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 2, \mathsf{fma}\left(3, x, z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma y 2.0 (fma 3.0 x z)))

C

double code(double x, double y, double z) {
	return fma(y, 2.0, fma(3.0, x, z));
}

Julia

function code(x, y, z)
	return fma(y, 2.0, fma(3.0, x, z))
end

Wolfram

code[x_, y_, z_] := N[(y * 2.0 + N[(3.0 * x + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right)} + x \]

   3. lift-+.f64 N/A

      \[\leadsto \left(\color{blue}{\left(\left(\left(x + y\right) + y\right) + x\right)} + z\right) + x \]

   4. lift-+.f64 N/A

      \[\leadsto \left(\left(\color{blue}{\left(\left(x + y\right) + y\right)} + x\right) + z\right) + x \]

   5. lift-+.f64 N/A

      \[\leadsto \left(\left(\left(\color{blue}{\left(x + y\right)} + y\right) + x\right) + z\right) + x \]

   6. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(\left(\left(x + y\right) + y\right) + x\right) + \left(z + x\right)} \]

   7. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(y + x\right)\right)} + \left(z + x\right) \]

   8. +-commutative N/A

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(x + y\right)}\right) + \left(z + x\right) \]

   9. count-2-rev N/A

      \[\leadsto \color{blue}{2 \cdot \left(x + y\right)} + \left(z + x\right) \]

   10. distribute-lft-out N/A

       \[\leadsto \color{blue}{\left(2 \cdot x + 2 \cdot y\right)} + \left(z + x\right) \]

   11. associate-+r+ N/A

       \[\leadsto \color{blue}{\left(\left(2 \cdot x + 2 \cdot y\right) + z\right) + x} \]

   12. +-commutative N/A

       \[\leadsto \color{blue}{\left(z + \left(2 \cdot x + 2 \cdot y\right)\right)} + x \]

   13. associate-+l+ N/A

       \[\leadsto \color{blue}{z + \left(\left(2 \cdot x + 2 \cdot y\right) + x\right)} \]

   14. +-commutative N/A

       \[\leadsto z + \color{blue}{\left(x + \left(2 \cdot x + 2 \cdot y\right)\right)} \]

   15. associate-+r+ N/A

       \[\leadsto z + \color{blue}{\left(\left(x + 2 \cdot x\right) + 2 \cdot y\right)} \]

   16. distribute-rgt1-in N/A

       \[\leadsto z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + 2 \cdot y\right) \]

   17. metadata-eval N/A

       \[\leadsto z + \left(\color{blue}{3} \cdot x + 2 \cdot y\right) \]

   18. +-commutative N/A

       \[\leadsto z + \color{blue}{\left(2 \cdot y + 3 \cdot x\right)} \]

   19. +-commutative N/A

       \[\leadsto \color{blue}{\left(2 \cdot y + 3 \cdot x\right) + z} \]

   20. associate-+l+ N/A

       \[\leadsto \color{blue}{2 \cdot y + \left(3 \cdot x + z\right)} \]

3. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 2, \mathsf{fma}\left(3, x, z\right)\right)} \]
4. Add Preprocessing

Alternative 2: 86.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(2, y, z\right) + x\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1200000:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (fma 2.0 y z) x)))
   (if (<= y -1.8e+50) t_0 (if (<= y 1200000.0) (fma 3.0 x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(2.0, y, z) + x;
	double tmp;
	if (y <= -1.8e+50) {
		tmp = t_0;
	} else if (y <= 1200000.0) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(2.0, y, z) + x)
	tmp = 0.0
	if (y <= -1.8e+50)
		tmp = t_0;
	elseif (y <= 1200000.0)
		tmp = fma(3.0, x, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 * y + z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.8e+50], t$95$0, If[LessEqual[y, 1200000.0], N[(3.0 * x + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999993e50 or 1.2e6 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(z + 2 \cdot y\right)} + x \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(2 \cdot y + \color{blue}{z}\right) + x \]

      2. lower-fma.f64 83.6

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{y}, z\right) + x \]

   4. Applied rewrites 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} + x \]

   if -1.79999999999999993e50 < y < 1.2e6

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \left(2 \cdot x + \color{blue}{z}\right) \]

      2. associate-+r+ N/A

         \[\leadsto \left(x + 2 \cdot x\right) + \color{blue}{z} \]

      3. distribute-rgt1-in N/A

         \[\leadsto \left(2 + 1\right) \cdot x + z \]

      4. metadata-eval N/A

         \[\leadsto 3 \cdot x + z \]

      5. lower-fma.f64 89.5

         \[\leadsto \mathsf{fma}\left(3, \color{blue}{x}, z\right) \]

   4. Applied rewrites 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 28000000000000:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, y + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+50)
   (fma 2.0 y z)
   (if (<= y 28000000000000.0) (fma 3.0 x z) (fma 3.0 x (+ y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+50) {
		tmp = fma(2.0, y, z);
	} else if (y <= 28000000000000.0) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = fma(3.0, x, (y + y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+50)
		tmp = fma(2.0, y, z);
	elseif (y <= 28000000000000.0)
		tmp = fma(3.0, x, z);
	else
		tmp = fma(3.0, x, Float64(y + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e+50], N[(2.0 * y + z), $MachinePrecision], If[LessEqual[y, 28000000000000.0], N[(3.0 * x + z), $MachinePrecision], N[(3.0 * x + N[(y + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999993e50

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot y + \color{blue}{z} \]

      2. lower-fma.f64 82.0

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{y}, z\right) \]

   4. Applied rewrites 82.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]

   if -1.79999999999999993e50 < y < 2.8e13

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \left(2 \cdot x + \color{blue}{z}\right) \]

      2. associate-+r+ N/A

         \[\leadsto \left(x + 2 \cdot x\right) + \color{blue}{z} \]

      3. distribute-rgt1-in N/A

         \[\leadsto \left(2 + 1\right) \cdot x + z \]

      4. metadata-eval N/A

         \[\leadsto 3 \cdot x + z \]

      5. lower-fma.f64 89.3

         \[\leadsto \mathsf{fma}\left(3, \color{blue}{x}, z\right) \]

   4. Applied rewrites 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, z\right)} \]

   if 2.8e13 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(2 \cdot x + 2 \cdot y\right)} \]
   3. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + 2 \cdot x\right) + \color{blue}{2 \cdot y} \]

      2. distribute-rgt1-in N/A

         \[\leadsto \left(2 + 1\right) \cdot x + \color{blue}{2} \cdot y \]

      3. metadata-eval N/A

         \[\leadsto 3 \cdot x + 2 \cdot y \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(3, \color{blue}{x}, 2 \cdot y\right) \]

      5. count-2-rev N/A

         \[\leadsto \mathsf{fma}\left(3, x, y + y\right) \]

      6. lower-+.f64 79.2

         \[\leadsto \mathsf{fma}\left(3, x, y + y\right) \]

   4. Applied rewrites 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, y + y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 2150000:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+50)
   (fma 2.0 y z)
   (if (<= y 2150000.0) (fma 3.0 x z) (fma 2.0 y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+50) {
		tmp = fma(2.0, y, z);
	} else if (y <= 2150000.0) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = fma(2.0, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+50)
		tmp = fma(2.0, y, z);
	elseif (y <= 2150000.0)
		tmp = fma(3.0, x, z);
	else
		tmp = fma(2.0, y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e+50], N[(2.0 * y + z), $MachinePrecision], If[LessEqual[y, 2150000.0], N[(3.0 * x + z), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999993e50 or 2.15e6 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot y + \color{blue}{z} \]

      2. lower-fma.f64 81.1

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{y}, z\right) \]

   4. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]

   if -1.79999999999999993e50 < y < 2.15e6

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \left(2 \cdot x + \color{blue}{z}\right) \]

      2. associate-+r+ N/A

         \[\leadsto \left(x + 2 \cdot x\right) + \color{blue}{z} \]

      3. distribute-rgt1-in N/A

         \[\leadsto \left(2 + 1\right) \cdot x + z \]

      4. metadata-eval N/A

         \[\leadsto 3 \cdot x + z \]

      5. lower-fma.f64 89.5

         \[\leadsto \mathsf{fma}\left(3, \color{blue}{x}, z\right) \]

   4. Applied rewrites 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 78.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+150}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.4e+150) (* 3.0 x) (if (<= x 1.6e+207) (fma 2.0 y z) (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e+150) {
		tmp = 3.0 * x;
	} else if (x <= 1.6e+207) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e+150)
		tmp = Float64(3.0 * x);
	elseif (x <= 1.6e+207)
		tmp = fma(2.0, y, z);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e+150], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, 1.6e+207], N[(2.0 * y + z), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000003e150 or 1.6000000000000001e207 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{3 \cdot x} \]
   3. Step-by-step derivation

      1. lower-*.f64 76.4

         \[\leadsto 3 \cdot \color{blue}{x} \]

   4. Applied rewrites 76.4%

      \[\leadsto \color{blue}{3 \cdot x} \]

   if -2.40000000000000003e150 < x < 1.6000000000000001e207

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot y + \color{blue}{z} \]

      2. lower-fma.f64 78.5

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{y}, z\right) \]

   4. Applied rewrites 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 56.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+108}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-292}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2100000:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9e+108)
   (+ y y)
   (if (<= y -7.8e-292) (+ z x) (if (<= y 2100000.0) (* 3.0 x) (+ y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+108) {
		tmp = y + y;
	} else if (y <= -7.8e-292) {
		tmp = z + x;
	} else if (y <= 2100000.0) {
		tmp = 3.0 * x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.9d+108)) then
        tmp = y + y
    else if (y <= (-7.8d-292)) then
        tmp = z + x
    else if (y <= 2100000.0d0) then
        tmp = 3.0d0 * x
    else
        tmp = y + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+108) {
		tmp = y + y;
	} else if (y <= -7.8e-292) {
		tmp = z + x;
	} else if (y <= 2100000.0) {
		tmp = 3.0 * x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9e+108:
		tmp = y + y
	elif y <= -7.8e-292:
		tmp = z + x
	elif y <= 2100000.0:
		tmp = 3.0 * x
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9e+108)
		tmp = Float64(y + y);
	elseif (y <= -7.8e-292)
		tmp = Float64(z + x);
	elseif (y <= 2100000.0)
		tmp = Float64(3.0 * x);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.9e+108)
		tmp = y + y;
	elseif (y <= -7.8e-292)
		tmp = z + x;
	elseif (y <= 2100000.0)
		tmp = 3.0 * x;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9e+108], N[(y + y), $MachinePrecision], If[LessEqual[y, -7.8e-292], N[(z + x), $MachinePrecision], If[LessEqual[y, 2100000.0], N[(3.0 * x), $MachinePrecision], N[(y + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.89999999999999985e108 or 2.1e6 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot y} \]
   3. Step-by-step derivation

      1. count-2-rev N/A

         \[\leadsto y + \color{blue}{y} \]

      2. lower-+.f64 64.4

         \[\leadsto y + \color{blue}{y} \]

   4. Applied rewrites 64.4%

      \[\leadsto \color{blue}{y + y} \]

   if -3.89999999999999985e108 < y < -7.8e-292

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} + x \]
   3. Step-by-step derivation

   4. Applied rewrites 48.0%

      \[\leadsto \color{blue}{z} + x \]

   if -7.8e-292 < y < 2.1e6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{3 \cdot x} \]
   3. Step-by-step derivation

      1. lower-*.f64 46.4

         \[\leadsto 3 \cdot \color{blue}{x} \]

   4. Applied rewrites 46.4%

      \[\leadsto \color{blue}{3 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 54.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+108}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 28000000000000:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9e+108) (+ y y) (if (<= y 28000000000000.0) (+ z x) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+108) {
		tmp = y + y;
	} else if (y <= 28000000000000.0) {
		tmp = z + x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.9d+108)) then
        tmp = y + y
    else if (y <= 28000000000000.0d0) then
        tmp = z + x
    else
        tmp = y + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+108) {
		tmp = y + y;
	} else if (y <= 28000000000000.0) {
		tmp = z + x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9e+108:
		tmp = y + y
	elif y <= 28000000000000.0:
		tmp = z + x
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9e+108)
		tmp = Float64(y + y);
	elseif (y <= 28000000000000.0)
		tmp = Float64(z + x);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.9e+108)
		tmp = y + y;
	elseif (y <= 28000000000000.0)
		tmp = z + x;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9e+108], N[(y + y), $MachinePrecision], If[LessEqual[y, 28000000000000.0], N[(z + x), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.89999999999999985e108 or 2.8e13 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot y} \]
   3. Step-by-step derivation

      1. count-2-rev N/A

         \[\leadsto y + \color{blue}{y} \]

      2. lower-+.f64 64.9

         \[\leadsto y + \color{blue}{y} \]

   4. Applied rewrites 64.9%

      \[\leadsto \color{blue}{y + y} \]

   if -3.89999999999999985e108 < y < 2.8e13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} + x \]
   3. Step-by-step derivation

   4. Applied rewrites 50.4%

      \[\leadsto \color{blue}{z} + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 52.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+108}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 28000000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+108) (+ y y) (if (<= y 28000000000000.0) z (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+108) {
		tmp = y + y;
	} else if (y <= 28000000000000.0) {
		tmp = z;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.1d+108)) then
        tmp = y + y
    else if (y <= 28000000000000.0d0) then
        tmp = z
    else
        tmp = y + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+108) {
		tmp = y + y;
	} else if (y <= 28000000000000.0) {
		tmp = z;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e+108:
		tmp = y + y
	elif y <= 28000000000000.0:
		tmp = z
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+108)
		tmp = Float64(y + y);
	elseif (y <= 28000000000000.0)
		tmp = z;
	else
		tmp = Float64(y + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e+108)
		tmp = y + y;
	elseif (y <= 28000000000000.0)
		tmp = z;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+108], N[(y + y), $MachinePrecision], If[LessEqual[y, 28000000000000.0], z, N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1000000000000001e108 or 2.8e13 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot y} \]
   3. Step-by-step derivation

      1. count-2-rev N/A

         \[\leadsto y + \color{blue}{y} \]

      2. lower-+.f64 64.9

         \[\leadsto y + \color{blue}{y} \]

   4. Applied rewrites 64.9%

      \[\leadsto \color{blue}{y + y} \]

   if -3.1000000000000001e108 < y < 2.8e13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 43.9%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 33.9% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{z} \]
3. Step-by-step derivation

4. Applied rewrites 33.9%

   \[\leadsto \color{blue}{z} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025106 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))