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

Percentage Accurate: 99.9% → 99.9%

Time: 12.2s

Alternatives: 7

Speedup: 1.1×

Specification

Math

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

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

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

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: 99.9% accurate, 1.1× speedup

Math

\[\left(z + x\right) - -2 \cdot \left(y + x\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  (- (+ z x) (* -2 (+ y x))))

C

double code(double x, double y, double z) {
	return (z + x) - (-2.0 * (y + 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 = (z + x) - ((-2.0d0) * (y + x))
end function

Java

public static double code(double x, double y, double z) {
	return (z + x) - (-2.0 * (y + x));
}

Python

def code(x, y, z):
	return (z + x) - (-2.0 * (y + x))

Julia

function code(x, y, z)
	return Float64(Float64(z + x) - Float64(-2.0 * Float64(y + x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (z + x) - (-2.0 * (y + x));
end

Wolfram

code[x_, y_, z_] := N[(N[(z + x), $MachinePrecision] - N[(-2 * N[(y + x), $MachinePrecision]), $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. +-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-+r+ N/A

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

   6. add-flip N/A

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

   7. lower--.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lift-+.f64 N/A

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

   11. lift-+.f64 N/A

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

   12. associate-+l+ N/A

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

   13. +-commutative N/A

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

   14. lift-+.f64 N/A

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

   15. count-2 N/A

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

   16. distribute-lft-neg-in N/A

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

   17. lower-*.f64 N/A

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

   18. metadata-eval 99.9%

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

   19. lift-+.f64 N/A

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

   20. +-commutative N/A

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

   21. lower-+.f64 99.9%

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

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\left(z + x\right) - -2 \cdot \left(y + x\right)} \]
4. Add Preprocessing

Alternative 2: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(\left(y + y\right) + x\right) + z\right) + x\\ \mathbf{if}\;y \leq -299999999999999997114318848:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5299999999999999786239590985776899293184:\\ \;\;\;\;\left(\left(x + x\right) + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (+ (+ (+ y y) x) z) x)))
  (if (<= y -299999999999999997114318848)
    t_0
    (if (<= y 5299999999999999786239590985776899293184)
      (+ (+ (+ x x) z) x)
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + y) + x) + z) + x;
	double tmp;
	if (y <= -3e+26) {
		tmp = t_0;
	} else if (y <= 5.3e+39) {
		tmp = ((x + x) + z) + x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (((y + y) + x) + z) + x
    if (y <= (-3d+26)) then
        tmp = t_0
    else if (y <= 5.3d+39) then
        tmp = ((x + x) + z) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + y) + x) + z) + x;
	double tmp;
	if (y <= -3e+26) {
		tmp = t_0;
	} else if (y <= 5.3e+39) {
		tmp = ((x + x) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + y) + x) + z) + x
	tmp = 0
	if y <= -3e+26:
		tmp = t_0
	elif y <= 5.3e+39:
		tmp = ((x + x) + z) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + y) + x) + z) + x)
	tmp = 0.0
	if (y <= -3e+26)
		tmp = t_0;
	elseif (y <= 5.3e+39)
		tmp = Float64(Float64(Float64(x + x) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + y) + x) + z) + x;
	tmp = 0.0;
	if (y <= -3e+26)
		tmp = t_0;
	elseif (y <= 5.3e+39)
		tmp = ((x + x) + z) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + y), $MachinePrecision] + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -299999999999999997114318848], t$95$0, If[LessEqual[y, 5299999999999999786239590985776899293184], N[(N[(N[(x + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e26 or 5.2999999999999998e39 < 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

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

   4. Applied rewrites 72.2%

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

   if -3e26 < y < 5.2999999999999998e39

   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

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

      1. lower-*.f64 66.1%

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

   4. Applied rewrites 66.1%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lower-+.f64 66.1%

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

   6. Applied rewrites 66.1%

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

Alternative 3: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(z + 2 \cdot y\right) + x\\ \mathbf{if}\;y \leq -299999999999999997114318848:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5299999999999999786239590985776899293184:\\ \;\;\;\;\left(\left(x + x\right) + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (+ z (* 2 y)) x)))
  (if (<= y -299999999999999997114318848)
    t_0
    (if (<= y 5299999999999999786239590985776899293184)
      (+ (+ (+ x x) z) x)
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + (2.0 * y)) + x;
	double tmp;
	if (y <= -3e+26) {
		tmp = t_0;
	} else if (y <= 5.3e+39) {
		tmp = ((x + x) + z) + x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (z + (2.0d0 * y)) + x
    if (y <= (-3d+26)) then
        tmp = t_0
    else if (y <= 5.3d+39) then
        tmp = ((x + x) + z) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z + (2.0 * y)) + x;
	double tmp;
	if (y <= -3e+26) {
		tmp = t_0;
	} else if (y <= 5.3e+39) {
		tmp = ((x + x) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z + (2.0 * y)) + x
	tmp = 0
	if y <= -3e+26:
		tmp = t_0
	elif y <= 5.3e+39:
		tmp = ((x + x) + z) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z + Float64(2.0 * y)) + x)
	tmp = 0.0
	if (y <= -3e+26)
		tmp = t_0;
	elseif (y <= 5.3e+39)
		tmp = Float64(Float64(Float64(x + x) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z + (2.0 * y)) + x;
	tmp = 0.0;
	if (y <= -3e+26)
		tmp = t_0;
	elseif (y <= 5.3e+39)
		tmp = ((x + x) + z) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z + N[(2 * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -299999999999999997114318848], t$95$0, If[LessEqual[y, 5299999999999999786239590985776899293184], N[(N[(N[(x + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e26 or 5.2999999999999998e39 < 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. lower-+.f64 N/A

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

      2. lower-*.f64 71.4%

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

   4. Applied rewrites 71.4%

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

   if -3e26 < y < 5.2999999999999998e39

   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

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

      1. lower-*.f64 66.1%

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

   4. Applied rewrites 66.1%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lower-+.f64 66.1%

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

   6. Applied rewrites 66.1%

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

Alternative 4: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(y + y\right) + z\\ \mathbf{if}\;y \leq -73999999999999997971165888386204294016634191872:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5299999999999999786239590985776899293184:\\ \;\;\;\;\left(\left(x + x\right) + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (+ y y) z)))
  (if (<= y -73999999999999997971165888386204294016634191872)
    t_0
    (if (<= y 5299999999999999786239590985776899293184)
      (+ (+ (+ x x) z) x)
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y + y) + z;
	double tmp;
	if (y <= -7.4e+46) {
		tmp = t_0;
	} else if (y <= 5.3e+39) {
		tmp = ((x + x) + z) + x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (y + y) + z
    if (y <= (-7.4d+46)) then
        tmp = t_0
    else if (y <= 5.3d+39) then
        tmp = ((x + x) + z) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y + y) + z;
	double tmp;
	if (y <= -7.4e+46) {
		tmp = t_0;
	} else if (y <= 5.3e+39) {
		tmp = ((x + x) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + y) + z
	tmp = 0
	if y <= -7.4e+46:
		tmp = t_0
	elif y <= 5.3e+39:
		tmp = ((x + x) + z) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + y) + z)
	tmp = 0.0
	if (y <= -7.4e+46)
		tmp = t_0;
	elseif (y <= 5.3e+39)
		tmp = Float64(Float64(Float64(x + x) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + y) + z;
	tmp = 0.0;
	if (y <= -7.4e+46)
		tmp = t_0;
	elseif (y <= 5.3e+39)
		tmp = ((x + x) + z) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + y), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[y, -73999999999999997971165888386204294016634191872], t$95$0, If[LessEqual[y, 5299999999999999786239590985776899293184], N[(N[(N[(x + x), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999998e46 or 5.2999999999999998e39 < y

   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. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. add-flip N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. lift-+.f64 N/A

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

      15. count-2 N/A

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

      16. distribute-lft-neg-in N/A

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

      17. lower-*.f64 N/A

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

      18. metadata-eval 99.9%

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

      19. lift-+.f64 N/A

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

      20. +-commutative N/A

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

      21. lower-+.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 66.6%

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

   6. Applied rewrites 66.6%

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

   8. Applied rewrites 66.6%

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

   if -7.3999999999999998e46 < y < 5.2999999999999998e39

   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

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

      1. lower-*.f64 66.1%

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

   4. Applied rewrites 66.1%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lower-+.f64 66.1%

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

   6. Applied rewrites 66.1%

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

Alternative 5: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -240000000000000004852530990517427277258263117571445857873066445489920961199559434246087478607872:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 102000000000000002923230082887857256260896210505761714049709740517660113588191232:\\ \;\;\;\;\left(y + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<=
     x
     -240000000000000004852530990517427277258263117571445857873066445489920961199559434246087478607872)
  (* 3 x)
  (if (<=
       x
       102000000000000002923230082887857256260896210505761714049709740517660113588191232)
    (+ (+ y y) z)
    (* 3 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e+95) {
		tmp = 3.0 * x;
	} else if (x <= 1.02e+80) {
		tmp = (y + y) + z;
	} else {
		tmp = 3.0 * x;
	}
	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 (x <= (-2.4d+95)) then
        tmp = 3.0d0 * x
    else if (x <= 1.02d+80) then
        tmp = (y + y) + z
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e+95) {
		tmp = 3.0 * x;
	} else if (x <= 1.02e+80) {
		tmp = (y + y) + z;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e+95:
		tmp = 3.0 * x
	elif x <= 1.02e+80:
		tmp = (y + y) + z
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e+95)
		tmp = Float64(3.0 * x);
	elseif (x <= 1.02e+80)
		tmp = Float64(Float64(y + y) + z);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e+95)
		tmp = 3.0 * x;
	elseif (x <= 1.02e+80)
		tmp = (y + y) + z;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -240000000000000004852530990517427277258263117571445857873066445489920961199559434246087478607872], N[(3 * x), $MachinePrecision], If[LessEqual[x, 102000000000000002923230082887857256260896210505761714049709740517660113588191232], N[(N[(y + y), $MachinePrecision] + z), $MachinePrecision], N[(3 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e95 or 1.02e80 < x

   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 34.5%

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

   4. Applied rewrites 34.5%

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

   if -2.4e95 < x < 1.02e80

   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. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. add-flip N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. lift-+.f64 N/A

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

      15. count-2 N/A

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

      16. distribute-lft-neg-in N/A

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

      17. lower-*.f64 N/A

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

      18. metadata-eval 99.9%

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

      19. lift-+.f64 N/A

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

      20. +-commutative N/A

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

      21. lower-+.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 66.6%

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

   6. Applied rewrites 66.6%

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

   8. Applied rewrites 66.6%

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

Alternative 6: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq \frac{-3530822107858469}{144115188075855872}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 16000000000000000718171402849214668568788992:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x -3530822107858469/144115188075855872)
  (* 3 x)
  (if (<= x 16000000000000000718171402849214668568788992) z (* 3 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0245) {
		tmp = 3.0 * x;
	} else if (x <= 1.6e+43) {
		tmp = z;
	} else {
		tmp = 3.0 * x;
	}
	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 (x <= (-0.0245d0)) then
        tmp = 3.0d0 * x
    else if (x <= 1.6d+43) then
        tmp = z
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0245) {
		tmp = 3.0 * x;
	} else if (x <= 1.6e+43) {
		tmp = z;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0245:
		tmp = 3.0 * x
	elif x <= 1.6e+43:
		tmp = z
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0245)
		tmp = Float64(3.0 * x);
	elseif (x <= 1.6e+43)
		tmp = z;
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0245)
		tmp = 3.0 * x;
	elseif (x <= 1.6e+43)
		tmp = z;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3530822107858469/144115188075855872], N[(3 * x), $MachinePrecision], If[LessEqual[x, 16000000000000000718171402849214668568788992], z, N[(3 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.024500000000000001 or 1.6000000000000001e43 < x

   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 34.5%

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

   4. Applied rewrites 34.5%

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

   if -0.024500000000000001 < x < 1.6000000000000001e43

   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. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. add-flip N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. lift-+.f64 N/A

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

      15. count-2 N/A

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

      16. distribute-lft-neg-in N/A

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

      17. lower-*.f64 N/A

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

      18. metadata-eval 99.9%

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

      19. lift-+.f64 N/A

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

      20. +-commutative N/A

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

      21. lower-+.f64 99.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 66.6%

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

   6. Applied rewrites 66.6%

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

   8. Applied rewrites 66.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto z \]
   10. Step-by-step derivation

   11. Applied rewrites 33.5%

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

Alternative 7: 33.5% accurate, 16.0× speedup

Math

\[z \]

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. 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. +-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-+r+ N/A

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

   6. add-flip N/A

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

   7. lower--.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lift-+.f64 N/A

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

   11. lift-+.f64 N/A

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

   12. associate-+l+ N/A

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

   13. +-commutative N/A

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

   14. lift-+.f64 N/A

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

   15. count-2 N/A

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

   16. distribute-lft-neg-in N/A

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

   17. lower-*.f64 N/A

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

   18. metadata-eval 99.9%

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

   19. lift-+.f64 N/A

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

   20. +-commutative N/A

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

   21. lower-+.f64 99.9%

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

3. Applied rewrites 99.9%

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

4. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

   2. lower-*.f64 66.6%

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

6. Applied rewrites 66.6%

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

8. Applied rewrites 66.6%

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

9. Taylor expanded in y around 0

   \[\leadsto z \]
10. Step-by-step derivation

11. Applied rewrites 33.5%

    \[\leadsto z \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(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))