Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 65.9% → 99.5%

Time: 8.0s

Alternatives: 10

Speedup: 1.1×

Specification

Math

\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

FPCore

(FPCore (x y)
  :precision binary64
  (- 1 (/ (* (- 1 x) y) (+ y 1))))

C

double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

Python

def code(x, y):
	return 1.0 - (((1.0 - x) * y) / (y + 1.0))

Julia

function code(x, y)
	return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
end

Wolfram

code[x_, y_] := N[(1 - N[(N[(N[(1 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 65.9% accurate, 1.0× speedup

Math

\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

FPCore

(FPCore (x y)
  :precision binary64
  (- 1 (/ (* (- 1 x) y) (+ y 1))))

C

double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

Python

def code(x, y):
	return 1.0 - (((1.0 - x) * y) / (y + 1.0))

Julia

function code(x, y)
	return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
end

Wolfram

code[x_, y_] := N[(1 - N[(N[(N[(1 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -132000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 60000:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (+ x (/ 1 y))))
  (if (<= y -132000000000000)
    t_0
    (if (<= y 60000) (- 1 (/ (* (- 1 x) y) (+ y 1))) t_0))))

C

double code(double x, double y) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (y <= -1.32e+14) {
		tmp = t_0;
	} else if (y <= 60000.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (1.0d0 / y)
    if (y <= (-1.32d+14)) then
        tmp = t_0
    else if (y <= 60000.0d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (y <= -1.32e+14) {
		tmp = t_0;
	} else if (y <= 60000.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + (1.0 / y)
	tmp = 0
	if y <= -1.32e+14:
		tmp = t_0
	elif y <= 60000.0:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(1.0 / y))
	tmp = 0.0
	if (y <= -1.32e+14)
		tmp = t_0;
	elseif (y <= 60000.0)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + (1.0 / y);
	tmp = 0.0;
	if (y <= -1.32e+14)
		tmp = t_0;
	elseif (y <= 60000.0)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(1 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -132000000000000], t$95$0, If[LessEqual[y, 60000], N[(1 - N[(N[(N[(1 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.32e14 or 6e4 < y

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]

   8. Taylor expanded in x around 0

      \[\leadsto x + \frac{1}{\color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 50.2%

         \[\leadsto x + \frac{1}{y} \]

   10. Applied rewrites 50.2%

       \[\leadsto x + \frac{1}{\color{blue}{y}} \]

   if -1.32e14 < y < 6e4

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := x - \frac{x - 1}{y}\\ \mathbf{if}\;y \leq -21:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 + y \cdot \left(x - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- x (/ (- x 1) y))))
  (if (<= y -21) t_0 (if (<= y 1) (+ 1 (* y (- x 1))) t_0))))

C

double code(double x, double y) {
	double t_0 = x - ((x - 1.0) / y);
	double tmp;
	if (y <= -21.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = 1.0 + (y * (x - 1.0));
	} 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - ((x - 1.0d0) / y)
    if (y <= (-21.0d0)) then
        tmp = t_0
    else if (y <= 1.0d0) then
        tmp = 1.0d0 + (y * (x - 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - ((x - 1.0) / y);
	double tmp;
	if (y <= -21.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = 1.0 + (y * (x - 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - ((x - 1.0) / y)
	tmp = 0
	if y <= -21.0:
		tmp = t_0
	elif y <= 1.0:
		tmp = 1.0 + (y * (x - 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(Float64(x - 1.0) / y))
	tmp = 0.0
	if (y <= -21.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = Float64(1.0 + Float64(y * Float64(x - 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - ((x - 1.0) / y);
	tmp = 0.0;
	if (y <= -21.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = 1.0 + (y * (x - 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(N[(x - 1), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -21], t$95$0, If[LessEqual[y, 1], N[(1 + N[(y * N[(x - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -21 or 1 < y

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      6. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{x - 1}{\mathsf{neg}\left(y\right)}\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto x - \frac{\mathsf{neg}\left(\left(x - 1\right)\right)}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

      9. frac-2neg N/A

         \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

      10. lift-/.f64 50.0%

          \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

   9. Applied rewrites 50.0%

      \[\leadsto x - \color{blue}{\frac{x - 1}{y}} \]

   if -21 < y < 1

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.2%

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

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq \frac{-7032821178101767}{576460752303423488}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq \frac{5224175567749775}{36028797018963968}:\\ \;\;\;\;1 + y \cdot \left(x - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (+ x (/ 1 y))))
  (if (<= y -7032821178101767/576460752303423488)
    t_0
    (if (<= y 5224175567749775/36028797018963968)
      (+ 1 (* y (- x 1)))
      t_0))))

C

double code(double x, double y) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (y <= -0.0122) {
		tmp = t_0;
	} else if (y <= 0.145) {
		tmp = 1.0 + (y * (x - 1.0));
	} 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (1.0d0 / y)
    if (y <= (-0.0122d0)) then
        tmp = t_0
    else if (y <= 0.145d0) then
        tmp = 1.0d0 + (y * (x - 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (y <= -0.0122) {
		tmp = t_0;
	} else if (y <= 0.145) {
		tmp = 1.0 + (y * (x - 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + (1.0 / y)
	tmp = 0
	if y <= -0.0122:
		tmp = t_0
	elif y <= 0.145:
		tmp = 1.0 + (y * (x - 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(1.0 / y))
	tmp = 0.0
	if (y <= -0.0122)
		tmp = t_0;
	elseif (y <= 0.145)
		tmp = Float64(1.0 + Float64(y * Float64(x - 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + (1.0 / y);
	tmp = 0.0;
	if (y <= -0.0122)
		tmp = t_0;
	elseif (y <= 0.145)
		tmp = 1.0 + (y * (x - 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(1 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7032821178101767/576460752303423488], t$95$0, If[LessEqual[y, 5224175567749775/36028797018963968], N[(1 + N[(y * N[(x - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.012200000000000001 or 0.14499999999999999 < y

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]

   8. Taylor expanded in x around 0

      \[\leadsto x + \frac{1}{\color{blue}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 50.2%

         \[\leadsto x + \frac{1}{y} \]

   10. Applied rewrites 50.2%

       \[\leadsto x + \frac{1}{\color{blue}{y}} \]

   if -0.012200000000000001 < y < 0.14499999999999999

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.2%

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

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{y + 1}\\ t_1 := 1 - \left(1 - x\right)\\ \mathbf{if}\;t\_0 \leq -2000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq \frac{3602879701896397}{18014398509481984}:\\ \;\;\;\;1 + y \cdot -1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;t\_0 \leq 100000000000000003284156248920492607898701256635961169551231342625874700689878799554400131562772741268394950478432243557864849063421149184:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 49999999999999998477451758974159751046482403622374605607421237630054847441436856676344327287652542857018591204612420567252946440591689353040126624759541451965054047394820266694175773042474003475163007869396334450282260856832:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - \left(-x\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (/ (* (- 1 x) y) (+ y 1))) (t_1 (- 1 (- 1 x))))
  (if (<= t_0 -2000000)
    t_1
    (if (<= t_0 3602879701896397/18014398509481984)
      (+ 1 (* y -1))
      (if (<= t_0 2)
        (/ 1 y)
        (if (<=
             t_0
             100000000000000003284156248920492607898701256635961169551231342625874700689878799554400131562772741268394950478432243557864849063421149184)
          t_1
          (if (<=
               t_0
               49999999999999998477451758974159751046482403622374605607421237630054847441436856676344327287652542857018591204612420567252946440591689353040126624759541451965054047394820266694175773042474003475163007869396334450282260856832)
            (* x y)
            (- 1 (- x)))))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (y + 1.0);
	double t_1 = 1.0 - (1.0 - x);
	double tmp;
	if (t_0 <= -2000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.2) {
		tmp = 1.0 + (y * -1.0);
	} else if (t_0 <= 2.0) {
		tmp = 1.0 / y;
	} else if (t_0 <= 1e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+223) {
		tmp = x * y;
	} else {
		tmp = 1.0 - -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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (y + 1.0d0)
    t_1 = 1.0d0 - (1.0d0 - x)
    if (t_0 <= (-2000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.2d0) then
        tmp = 1.0d0 + (y * (-1.0d0))
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0 / y
    else if (t_0 <= 1d+137) then
        tmp = t_1
    else if (t_0 <= 5d+223) then
        tmp = x * y
    else
        tmp = 1.0d0 - -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (y + 1.0);
	double t_1 = 1.0 - (1.0 - x);
	double tmp;
	if (t_0 <= -2000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.2) {
		tmp = 1.0 + (y * -1.0);
	} else if (t_0 <= 2.0) {
		tmp = 1.0 / y;
	} else if (t_0 <= 1e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+223) {
		tmp = x * y;
	} else {
		tmp = 1.0 - -x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (y + 1.0)
	t_1 = 1.0 - (1.0 - x)
	tmp = 0
	if t_0 <= -2000000.0:
		tmp = t_1
	elif t_0 <= 0.2:
		tmp = 1.0 + (y * -1.0)
	elif t_0 <= 2.0:
		tmp = 1.0 / y
	elif t_0 <= 1e+137:
		tmp = t_1
	elif t_0 <= 5e+223:
		tmp = x * y
	else:
		tmp = 1.0 - -x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))
	t_1 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (t_0 <= -2000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.2)
		tmp = Float64(1.0 + Float64(y * -1.0));
	elseif (t_0 <= 2.0)
		tmp = Float64(1.0 / y);
	elseif (t_0 <= 1e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+223)
		tmp = Float64(x * y);
	else
		tmp = Float64(1.0 - Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (y + 1.0);
	t_1 = 1.0 - (1.0 - x);
	tmp = 0.0;
	if (t_0 <= -2000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.2)
		tmp = 1.0 + (y * -1.0);
	elseif (t_0 <= 2.0)
		tmp = 1.0 / y;
	elseif (t_0 <= 1e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+223)
		tmp = x * y;
	else
		tmp = 1.0 - -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1 - N[(1 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2000000], t$95$1, If[LessEqual[t$95$0, 3602879701896397/18014398509481984], N[(1 + N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2], N[(1 / y), $MachinePrecision], If[LessEqual[t$95$0, 100000000000000003284156248920492607898701256635961169551231342625874700689878799554400131562772741268394950478432243557864849063421149184], t$95$1, If[LessEqual[t$95$0, 49999999999999998477451758974159751046482403622374605607421237630054847441436856676344327287652542857018591204612420567252946440591689353040126624759541451965054047394820266694175773042474003475163007869396334450282260856832], N[(x * y), $MachinePrecision], N[(1 - (-x)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < -2e6 or 2 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1e137

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   if -2e6 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.20000000000000001

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.2%

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

   4. Applied rewrites 51.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto 1 + y \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 38.8%

      \[\leadsto 1 + y \cdot -1 \]

   if 0.20000000000000001 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      6. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{x - 1}{\mathsf{neg}\left(y\right)}\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto x - \frac{\mathsf{neg}\left(\left(x - 1\right)\right)}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

      9. frac-2neg N/A

         \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

      10. lift-/.f64 50.0%

          \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

   9. Applied rewrites 50.0%

      \[\leadsto x - \color{blue}{\frac{x - 1}{y}} \]

   10. Taylor expanded in x around 0

       \[\leadsto \frac{1}{\color{blue}{y}} \]
   11. Step-by-step derivation

       1. lower-/.f64 13.9%

          \[\leadsto \frac{1}{y} \]

   12. Applied rewrites 13.9%

       \[\leadsto \frac{1}{\color{blue}{y}} \]

   if 1e137 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 4.9999999999999998e223

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. lower-+.f64 38.9%

         \[\leadsto \frac{x \cdot y}{1 + \color{blue}{y}} \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{y}{1 + y}} \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{1 + \color{blue}{y}} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      9. lower-/.f64 51.0%

         \[\leadsto \frac{y}{y + 1} \cdot x \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{y}{y + 1} \cdot x \]

      11. add-flip N/A

          \[\leadsto \frac{y}{y - \left(\mathsf{neg}\left(1\right)\right)} \cdot x \]

      12. metadata-eval N/A

          \[\leadsto \frac{y}{y - -1} \cdot x \]

      13. lift--.f64 51.0%

          \[\leadsto \frac{y}{y - -1} \cdot x \]

   6. Applied rewrites 51.0%

      \[\leadsto \frac{y}{y - -1} \cdot \color{blue}{x} \]

   7. Taylor expanded in y around 0

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

      1. lower-*.f64 14.9%

         \[\leadsto x \cdot y \]

   9. Applied rewrites 14.9%

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

   if 4.9999999999999998e223 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto 1 - -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 50.3%

         \[\leadsto 1 - -1 \cdot x \]

   7. Applied rewrites 50.3%

      \[\leadsto 1 - -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 1 - -1 \cdot x \]

      2. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(x\right)\right) \]

      3. lower-neg.f64 50.3%

         \[\leadsto 1 - \left(-x\right) \]

   9. Applied rewrites 50.3%

      \[\leadsto 1 - \left(-x\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 73.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := 1 - \left(1 - x\right)\\ \mathbf{if}\;y \leq \frac{-7032821178101767}{576460752303423488}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq \frac{5224175567749775}{36028797018963968}:\\ \;\;\;\;1 + y \cdot \left(x - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- 1 (- 1 x))))
  (if (<= y -7032821178101767/576460752303423488)
    t_0
    (if (<= y 5224175567749775/36028797018963968)
      (+ 1 (* y (- x 1)))
      t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (1.0 - x);
	double tmp;
	if (y <= -0.0122) {
		tmp = t_0;
	} else if (y <= 0.145) {
		tmp = 1.0 + (y * (x - 1.0));
	} 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (1.0d0 - x)
    if (y <= (-0.0122d0)) then
        tmp = t_0
    else if (y <= 0.145d0) then
        tmp = 1.0d0 + (y * (x - 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (1.0 - x);
	double tmp;
	if (y <= -0.0122) {
		tmp = t_0;
	} else if (y <= 0.145) {
		tmp = 1.0 + (y * (x - 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (1.0 - x)
	tmp = 0
	if y <= -0.0122:
		tmp = t_0
	elif y <= 0.145:
		tmp = 1.0 + (y * (x - 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (y <= -0.0122)
		tmp = t_0;
	elseif (y <= 0.145)
		tmp = Float64(1.0 + Float64(y * Float64(x - 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (1.0 - x);
	tmp = 0.0;
	if (y <= -0.0122)
		tmp = t_0;
	elseif (y <= 0.145)
		tmp = 1.0 + (y * (x - 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1 - N[(1 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7032821178101767/576460752303423488], t$95$0, If[LessEqual[y, 5224175567749775/36028797018963968], N[(1 + N[(y * N[(x - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.012200000000000001 or 0.14499999999999999 < y

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   if -0.012200000000000001 < y < 0.14499999999999999

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.2%

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

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{y + 1}\\ t_1 := 1 - \left(1 - x\right)\\ \mathbf{if}\;t\_0 \leq -2000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq \frac{3602879701896397}{18014398509481984}:\\ \;\;\;\;1 + y \cdot -1\\ \mathbf{elif}\;t\_0 \leq 100000000000000003284156248920492607898701256635961169551231342625874700689878799554400131562772741268394950478432243557864849063421149184:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 49999999999999998477451758974159751046482403622374605607421237630054847441436856676344327287652542857018591204612420567252946440591689353040126624759541451965054047394820266694175773042474003475163007869396334450282260856832:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - \left(-x\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (/ (* (- 1 x) y) (+ y 1))) (t_1 (- 1 (- 1 x))))
  (if (<= t_0 -2000000)
    t_1
    (if (<= t_0 3602879701896397/18014398509481984)
      (+ 1 (* y -1))
      (if (<=
           t_0
           100000000000000003284156248920492607898701256635961169551231342625874700689878799554400131562772741268394950478432243557864849063421149184)
        t_1
        (if (<=
             t_0
             49999999999999998477451758974159751046482403622374605607421237630054847441436856676344327287652542857018591204612420567252946440591689353040126624759541451965054047394820266694175773042474003475163007869396334450282260856832)
          (* x y)
          (- 1 (- x))))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (y + 1.0);
	double t_1 = 1.0 - (1.0 - x);
	double tmp;
	if (t_0 <= -2000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.2) {
		tmp = 1.0 + (y * -1.0);
	} else if (t_0 <= 1e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+223) {
		tmp = x * y;
	} else {
		tmp = 1.0 - -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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (y + 1.0d0)
    t_1 = 1.0d0 - (1.0d0 - x)
    if (t_0 <= (-2000000.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.2d0) then
        tmp = 1.0d0 + (y * (-1.0d0))
    else if (t_0 <= 1d+137) then
        tmp = t_1
    else if (t_0 <= 5d+223) then
        tmp = x * y
    else
        tmp = 1.0d0 - -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (y + 1.0);
	double t_1 = 1.0 - (1.0 - x);
	double tmp;
	if (t_0 <= -2000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.2) {
		tmp = 1.0 + (y * -1.0);
	} else if (t_0 <= 1e+137) {
		tmp = t_1;
	} else if (t_0 <= 5e+223) {
		tmp = x * y;
	} else {
		tmp = 1.0 - -x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (y + 1.0)
	t_1 = 1.0 - (1.0 - x)
	tmp = 0
	if t_0 <= -2000000.0:
		tmp = t_1
	elif t_0 <= 0.2:
		tmp = 1.0 + (y * -1.0)
	elif t_0 <= 1e+137:
		tmp = t_1
	elif t_0 <= 5e+223:
		tmp = x * y
	else:
		tmp = 1.0 - -x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))
	t_1 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (t_0 <= -2000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.2)
		tmp = Float64(1.0 + Float64(y * -1.0));
	elseif (t_0 <= 1e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+223)
		tmp = Float64(x * y);
	else
		tmp = Float64(1.0 - Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (y + 1.0);
	t_1 = 1.0 - (1.0 - x);
	tmp = 0.0;
	if (t_0 <= -2000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.2)
		tmp = 1.0 + (y * -1.0);
	elseif (t_0 <= 1e+137)
		tmp = t_1;
	elseif (t_0 <= 5e+223)
		tmp = x * y;
	else
		tmp = 1.0 - -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1 - N[(1 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2000000], t$95$1, If[LessEqual[t$95$0, 3602879701896397/18014398509481984], N[(1 + N[(y * -1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 100000000000000003284156248920492607898701256635961169551231342625874700689878799554400131562772741268394950478432243557864849063421149184], t$95$1, If[LessEqual[t$95$0, 49999999999999998477451758974159751046482403622374605607421237630054847441436856676344327287652542857018591204612420567252946440591689353040126624759541451965054047394820266694175773042474003475163007869396334450282260856832], N[(x * y), $MachinePrecision], N[(1 - (-x)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < -2e6 or 0.20000000000000001 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1e137

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   if -2e6 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.20000000000000001

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + y \cdot \left(x - 1\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.2%

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

   4. Applied rewrites 51.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto 1 + y \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 38.8%

      \[\leadsto 1 + y \cdot -1 \]

   if 1e137 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 4.9999999999999998e223

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. lower-+.f64 38.9%

         \[\leadsto \frac{x \cdot y}{1 + \color{blue}{y}} \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{y}{1 + y}} \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{1 + \color{blue}{y}} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      9. lower-/.f64 51.0%

         \[\leadsto \frac{y}{y + 1} \cdot x \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{y}{y + 1} \cdot x \]

      11. add-flip N/A

          \[\leadsto \frac{y}{y - \left(\mathsf{neg}\left(1\right)\right)} \cdot x \]

      12. metadata-eval N/A

          \[\leadsto \frac{y}{y - -1} \cdot x \]

      13. lift--.f64 51.0%

          \[\leadsto \frac{y}{y - -1} \cdot x \]

   6. Applied rewrites 51.0%

      \[\leadsto \frac{y}{y - -1} \cdot \color{blue}{x} \]

   7. Taylor expanded in y around 0

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

      1. lower-*.f64 14.9%

         \[\leadsto x \cdot y \]

   9. Applied rewrites 14.9%

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

   if 4.9999999999999998e223 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto 1 - -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 50.3%

         \[\leadsto 1 - -1 \cdot x \]

   7. Applied rewrites 50.3%

      \[\leadsto 1 - -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 1 - -1 \cdot x \]

      2. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(x\right)\right) \]

      3. lower-neg.f64 50.3%

         \[\leadsto 1 - \left(-x\right) \]

   9. Applied rewrites 50.3%

      \[\leadsto 1 - \left(-x\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := 1 - \left(1 - x\right)\\ \mathbf{if}\;y \leq \frac{-7378697629483821}{9223372036854775808}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq \frac{-6224982717398119}{29642774844752946028434172162224104410437116074403984394101141506025761187823616}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq \frac{6530219459687219}{2251799813685248}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- 1 (- 1 x))))
  (if (<= y -7378697629483821/9223372036854775808)
    t_0
    (if (<=
         y
         -6224982717398119/29642774844752946028434172162224104410437116074403984394101141506025761187823616)
      (* x y)
      (if (<= y 6530219459687219/2251799813685248) 1 t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (1.0 - x);
	double tmp;
	if (y <= -0.0008) {
		tmp = t_0;
	} else if (y <= -2.1e-64) {
		tmp = x * y;
	} else if (y <= 2.9) {
		tmp = 1.0;
	} 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (1.0d0 - x)
    if (y <= (-0.0008d0)) then
        tmp = t_0
    else if (y <= (-2.1d-64)) then
        tmp = x * y
    else if (y <= 2.9d0) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (1.0 - x);
	double tmp;
	if (y <= -0.0008) {
		tmp = t_0;
	} else if (y <= -2.1e-64) {
		tmp = x * y;
	} else if (y <= 2.9) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (1.0 - x)
	tmp = 0
	if y <= -0.0008:
		tmp = t_0
	elif y <= -2.1e-64:
		tmp = x * y
	elif y <= 2.9:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (y <= -0.0008)
		tmp = t_0;
	elseif (y <= -2.1e-64)
		tmp = Float64(x * y);
	elseif (y <= 2.9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (1.0 - x);
	tmp = 0.0;
	if (y <= -0.0008)
		tmp = t_0;
	elseif (y <= -2.1e-64)
		tmp = x * y;
	elseif (y <= 2.9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1 - N[(1 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7378697629483821/9223372036854775808], t$95$0, If[LessEqual[y, -6224982717398119/29642774844752946028434172162224104410437116074403984394101141506025761187823616], N[(x * y), $MachinePrecision], If[LessEqual[y, 6530219459687219/2251799813685248], 1, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000004e-4 or 2.8999999999999999 < y

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   if -8.0000000000000004e-4 < y < -2.1000000000000001e-64

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. lower-+.f64 38.9%

         \[\leadsto \frac{x \cdot y}{1 + \color{blue}{y}} \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{y}{1 + y}} \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{1 + \color{blue}{y}} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      9. lower-/.f64 51.0%

         \[\leadsto \frac{y}{y + 1} \cdot x \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{y}{y + 1} \cdot x \]

      11. add-flip N/A

          \[\leadsto \frac{y}{y - \left(\mathsf{neg}\left(1\right)\right)} \cdot x \]

      12. metadata-eval N/A

          \[\leadsto \frac{y}{y - -1} \cdot x \]

      13. lift--.f64 51.0%

          \[\leadsto \frac{y}{y - -1} \cdot x \]

   6. Applied rewrites 51.0%

      \[\leadsto \frac{y}{y - -1} \cdot \color{blue}{x} \]

   7. Taylor expanded in y around 0

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

      1. lower-*.f64 14.9%

         \[\leadsto x \cdot y \]

   9. Applied rewrites 14.9%

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

   if -2.1000000000000001e-64 < y < 2.8999999999999999

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      6. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{x - 1}{\mathsf{neg}\left(y\right)}\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto x - \frac{\mathsf{neg}\left(\left(x - 1\right)\right)}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

      9. frac-2neg N/A

         \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

      10. lift-/.f64 50.0%

          \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

   9. Applied rewrites 50.0%

      \[\leadsto x - \color{blue}{\frac{x - 1}{y}} \]

   10. Taylor expanded in y around 0

       \[\leadsto \color{blue}{1} \]
   11. Step-by-step derivation

   12. Applied rewrites 39.0%

       \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := 1 - \left(-x\right)\\ \mathbf{if}\;y \leq \frac{-8715097876569077}{79228162514264337593543950336}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq \frac{-6224982717398119}{29642774844752946028434172162224104410437116074403984394101141506025761187823616}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq \frac{5440166188265831}{1208925819614629174706176}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- 1 (- x))))
  (if (<= y -8715097876569077/79228162514264337593543950336)
    t_0
    (if (<=
         y
         -6224982717398119/29642774844752946028434172162224104410437116074403984394101141506025761187823616)
      (* x y)
      (if (<= y 5440166188265831/1208925819614629174706176) 1 t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - -x;
	double tmp;
	if (y <= -1.1e-13) {
		tmp = t_0;
	} else if (y <= -2.1e-64) {
		tmp = x * y;
	} else if (y <= 4.5e-9) {
		tmp = 1.0;
	} 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - -x
    if (y <= (-1.1d-13)) then
        tmp = t_0
    else if (y <= (-2.1d-64)) then
        tmp = x * y
    else if (y <= 4.5d-9) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - -x;
	double tmp;
	if (y <= -1.1e-13) {
		tmp = t_0;
	} else if (y <= -2.1e-64) {
		tmp = x * y;
	} else if (y <= 4.5e-9) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - -x
	tmp = 0
	if y <= -1.1e-13:
		tmp = t_0
	elif y <= -2.1e-64:
		tmp = x * y
	elif y <= 4.5e-9:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(-x))
	tmp = 0.0
	if (y <= -1.1e-13)
		tmp = t_0;
	elseif (y <= -2.1e-64)
		tmp = Float64(x * y);
	elseif (y <= 4.5e-9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - -x;
	tmp = 0.0;
	if (y <= -1.1e-13)
		tmp = t_0;
	elseif (y <= -2.1e-64)
		tmp = x * y;
	elseif (y <= 4.5e-9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1 - (-x)), $MachinePrecision]}, If[LessEqual[y, -8715097876569077/79228162514264337593543950336], t$95$0, If[LessEqual[y, -6224982717398119/29642774844752946028434172162224104410437116074403984394101141506025761187823616], N[(x * y), $MachinePrecision], If[LessEqual[y, 5440166188265831/1208925819614629174706176], 1, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e-13 or 4.4999999999999998e-9 < y

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto 1 - -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 50.3%

         \[\leadsto 1 - -1 \cdot x \]

   7. Applied rewrites 50.3%

      \[\leadsto 1 - -1 \cdot \color{blue}{x} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 1 - -1 \cdot x \]

      2. mul-1-neg N/A

         \[\leadsto 1 - \left(\mathsf{neg}\left(x\right)\right) \]

      3. lower-neg.f64 50.3%

         \[\leadsto 1 - \left(-x\right) \]

   9. Applied rewrites 50.3%

      \[\leadsto 1 - \left(-x\right) \]

   if -1.1e-13 < y < -2.1000000000000001e-64

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. lower-+.f64 38.9%

         \[\leadsto \frac{x \cdot y}{1 + \color{blue}{y}} \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{y}{1 + y}} \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{1 + \color{blue}{y}} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      9. lower-/.f64 51.0%

         \[\leadsto \frac{y}{y + 1} \cdot x \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{y}{y + 1} \cdot x \]

      11. add-flip N/A

          \[\leadsto \frac{y}{y - \left(\mathsf{neg}\left(1\right)\right)} \cdot x \]

      12. metadata-eval N/A

          \[\leadsto \frac{y}{y - -1} \cdot x \]

      13. lift--.f64 51.0%

          \[\leadsto \frac{y}{y - -1} \cdot x \]

   6. Applied rewrites 51.0%

      \[\leadsto \frac{y}{y - -1} \cdot \color{blue}{x} \]

   7. Taylor expanded in y around 0

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

      1. lower-*.f64 14.9%

         \[\leadsto x \cdot y \]

   9. Applied rewrites 14.9%

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

   if -2.1000000000000001e-64 < y < 4.4999999999999998e-9

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      6. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{x - 1}{\mathsf{neg}\left(y\right)}\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto x - \frac{\mathsf{neg}\left(\left(x - 1\right)\right)}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

      9. frac-2neg N/A

         \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

      10. lift-/.f64 50.0%

          \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

   9. Applied rewrites 50.0%

      \[\leadsto x - \color{blue}{\frac{x - 1}{y}} \]

   10. Taylor expanded in y around 0

       \[\leadsto \color{blue}{1} \]
   11. Step-by-step derivation

   12. Applied rewrites 39.0%

       \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := 1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  (let* ((t_0 (- 1 (/ (* (- 1 x) y) (+ y 1)))))
  (if (<= t_0 0) (* x y) (if (<= t_0 2) 1 (* x y)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = x * y;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x * 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    if (t_0 <= 0.0d0) then
        tmp = x * y
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = x * y;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	tmp = 0
	if t_0 <= 0.0:
		tmp = x * y
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(x * y);
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = x * y;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1 - N[(N[(N[(1 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0], N[(x * y), $MachinePrecision], If[LessEqual[t$95$0, 2], 1, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))) < 0.0 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))))

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. lower-+.f64 38.9%

         \[\leadsto \frac{x \cdot y}{1 + \color{blue}{y}} \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{1 + y}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1 + y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{\color{blue}{1} + y} \]

      3. associate-/l* N/A

         \[\leadsto x \cdot \color{blue}{\frac{y}{1 + y}} \]

      4. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{1 + \color{blue}{y}} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      6. lift-+.f64 N/A

         \[\leadsto x \cdot \frac{y}{y + \color{blue}{1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{y}{y + 1} \cdot \color{blue}{x} \]

      9. lower-/.f64 51.0%

         \[\leadsto \frac{y}{y + 1} \cdot x \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{y}{y + 1} \cdot x \]

      11. add-flip N/A

          \[\leadsto \frac{y}{y - \left(\mathsf{neg}\left(1\right)\right)} \cdot x \]

      12. metadata-eval N/A

          \[\leadsto \frac{y}{y - -1} \cdot x \]

      13. lift--.f64 51.0%

          \[\leadsto \frac{y}{y - -1} \cdot x \]

   6. Applied rewrites 51.0%

      \[\leadsto \frac{y}{y - -1} \cdot \color{blue}{x} \]

   7. Taylor expanded in y around 0

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

      1. lower-*.f64 14.9%

         \[\leadsto x \cdot y \]

   9. Applied rewrites 14.9%

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

   if 0.0 < (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))) < 2

   1. Initial program 65.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

   2. Taylor expanded in y around inf

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 28.2%

         \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

   4. Applied rewrites 28.2%

      \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   6. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

      4. lower--.f64 50.0%

         \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

   7. Applied rewrites 50.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

      2. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      6. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{x - 1}{\mathsf{neg}\left(y\right)}\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto x - \frac{\mathsf{neg}\left(\left(x - 1\right)\right)}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

      9. frac-2neg N/A

         \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

      10. lift-/.f64 50.0%

          \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

   9. Applied rewrites 50.0%

      \[\leadsto x - \color{blue}{\frac{x - 1}{y}} \]

   10. Taylor expanded in y around 0

       \[\leadsto \color{blue}{1} \]
   11. Step-by-step derivation

   12. Applied rewrites 39.0%

       \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 39.0% accurate, 26.0× speedup

Math

\[1 \]

FPCore

(FPCore (x y)
  :precision binary64
  1)

C

double code(double x, double y) {
	return 1.0;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1

Derivation

1. Initial program 65.9%

   \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

2. Taylor expanded in y around inf

   \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 28.2%

      \[\leadsto 1 - \left(1 - \color{blue}{x}\right) \]

4. Applied rewrites 28.2%

   \[\leadsto 1 - \color{blue}{\left(1 - x\right)} \]

5. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
6. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

   2. lower-*.f64 N/A

      \[\leadsto x + -1 \cdot \color{blue}{\frac{x - 1}{y}} \]

   3. lower-/.f64 N/A

      \[\leadsto x + -1 \cdot \frac{x - 1}{\color{blue}{y}} \]

   4. lower--.f64 50.0%

      \[\leadsto x + -1 \cdot \frac{x - 1}{y} \]

7. Applied rewrites 50.0%

   \[\leadsto \color{blue}{x + -1 \cdot \frac{x - 1}{y}} \]
8. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x - 1}{y}} \]

   2. add-flip N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

   3. lower--.f64 N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto x - \left(\mathsf{neg}\left(-1 \cdot \frac{x - 1}{y}\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

   6. lift-/.f64 N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{x - 1}{y}\right)\right)\right)\right) \]

   7. distribute-neg-frac2 N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{x - 1}{\mathsf{neg}\left(y\right)}\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto x - \frac{\mathsf{neg}\left(\left(x - 1\right)\right)}{\color{blue}{\mathsf{neg}\left(y\right)}} \]

   9. frac-2neg N/A

      \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

   10. lift-/.f64 50.0%

       \[\leadsto x - \frac{x - 1}{\color{blue}{y}} \]

9. Applied rewrites 50.0%

   \[\leadsto x - \color{blue}{\frac{x - 1}{y}} \]

10. Taylor expanded in y around 0

    \[\leadsto \color{blue}{1} \]
11. Step-by-step derivation

12. Applied rewrites 39.0%

    \[\leadsto \color{blue}{1} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64
  (- 1 (/ (* (- 1 x) y) (+ y 1))))