Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3

Percentage Accurate: 77.7% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))

C

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

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 = x + ((1.0d0 - x) * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))

C

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

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 = x + ((1.0d0 - x) * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, 1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y x (- 1.0 y)))

C

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

Julia

function code(x, y)
	return fma(y, x, Float64(1.0 - y))
end

Wolfram

code[x_, y_] := N[(y * x + N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.5%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 1 - y\right)} \]
6. Add Preprocessing

Alternative 2: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \left(1 - x\right) \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 20000000000\right):\\ \;\;\;\;\left(-1 + x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (* (- 1.0 x) (- 1.0 y)))))
   (if (or (<= t_0 0.0) (not (<= t_0 20000000000.0)))
     (* (+ -1.0 x) y)
     (- 1.0 y))))

C

double code(double x, double y) {
	double t_0 = x + ((1.0 - x) * (1.0 - y));
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 20000000000.0)) {
		tmp = (-1.0 + x) * y;
	} else {
		tmp = 1.0 - 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 = x + ((1.0d0 - x) * (1.0d0 - y))
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 20000000000.0d0))) then
        tmp = ((-1.0d0) + x) * y
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + ((1.0 - x) * (1.0 - y));
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 20000000000.0)) {
		tmp = (-1.0 + x) * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + ((1.0 - x) * (1.0 - y))
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 20000000000.0):
		tmp = (-1.0 + x) * y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 20000000000.0))
		tmp = Float64(Float64(-1.0 + x) * y);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + ((1.0 - x) * (1.0 - y));
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 20000000000.0)))
		tmp = (-1.0 + x) * y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 20000000000.0]], $MachinePrecision]], N[(N[(-1.0 + x), $MachinePrecision] * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 0.0 or 2e10 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y)))

   1. Initial program 68.3%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower-+.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 2e10

   1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{1 - y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(1 - x\right) \cdot \left(1 - y\right) \leq 0 \lor \neg \left(x + \left(1 - x\right) \cdot \left(1 - y\right) \leq 20000000000\right):\\ \;\;\;\;\left(-1 + x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \left(1 - x\right) \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\left(-1 + x\right) \cdot y\\ \mathbf{elif}\;t\_0 \leq 20000000000:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (* (- 1.0 x) (- 1.0 y)))))
   (if (<= t_0 0.0)
     (* (+ -1.0 x) y)
     (if (<= t_0 20000000000.0) (- 1.0 y) (fma y x (- y))))))

C

double code(double x, double y) {
	double t_0 = x + ((1.0 - x) * (1.0 - y));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (-1.0 + x) * y;
	} else if (t_0 <= 20000000000.0) {
		tmp = 1.0 - y;
	} else {
		tmp = fma(y, x, -y);
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(-1.0 + x) * y);
	elseif (t_0 <= 20000000000.0)
		tmp = Float64(1.0 - y);
	else
		tmp = fma(y, x, Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(-1.0 + x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$0, 20000000000.0], N[(1.0 - y), $MachinePrecision], N[(y * x + (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 51.3%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower-+.f64 77.6

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

   5. Applied rewrites 77.6%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 2e10

   1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if 2e10 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y)))

   1. Initial program 98.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. distribute-lft-neg-out N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-rgt1-in N/A

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

      12. mul-1-neg N/A

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

      13. fp-cancel-sub-sign-inv N/A

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

      14. *-commutative N/A

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

      15. metadata-eval N/A

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. associate--r- N/A

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

      19. metadata-eval N/A

          \[\leadsto \left(\color{blue}{0} + y\right) \cdot x \]

      20. +-lft-identity N/A

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

      21. lower-*.f64 49.4

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

   5. Applied rewrites 49.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 100.0%

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

Alternative 4: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+18} \lor \neg \left(x \leq 2600\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.2e+18) (not (<= x 2600.0))) (* y x) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.2e+18) || !(x <= 2600.0)) {
		tmp = y * x;
	} else {
		tmp = 1.0 - 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) :: tmp
    if ((x <= (-2.2d+18)) .or. (.not. (x <= 2600.0d0))) then
        tmp = y * x
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.2e+18) || !(x <= 2600.0)) {
		tmp = y * x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.2e+18) or not (x <= 2600.0):
		tmp = y * x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.2e+18) || !(x <= 2600.0))
		tmp = Float64(y * x);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.2e+18) || ~((x <= 2600.0)))
		tmp = y * x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.2e+18], N[Not[LessEqual[x, 2600.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2e18 or 2600 < x

   1. Initial program 51.8%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. distribute-lft-neg-out N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-rgt1-in N/A

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

      12. mul-1-neg N/A

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

      13. fp-cancel-sub-sign-inv N/A

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

      14. *-commutative N/A

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

      15. metadata-eval N/A

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. associate--r- N/A

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

      19. metadata-eval N/A

          \[\leadsto \left(\color{blue}{0} + y\right) \cdot x \]

      20. +-lft-identity N/A

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

      21. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -2.2e18 < x < 2600

   1. Initial program 99.2%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower--.f64 95.8

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

   5. Applied rewrites 95.8%

      \[\leadsto \color{blue}{1 - y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+18} \lor \neg \left(x \leq 2600\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3500 \lor \neg \left(y \leq 55000\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3500.0) (not (<= y 55000.0))) (- y) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3500.0) || !(y <= 55000.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	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) :: tmp
    if ((y <= (-3500.0d0)) .or. (.not. (y <= 55000.0d0))) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3500.0) || !(y <= 55000.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3500.0) or not (y <= 55000.0):
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3500.0) || !(y <= 55000.0))
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3500.0) || ~((y <= 55000.0)))
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3500.0], N[Not[LessEqual[y, 55000.0]], $MachinePrecision]], (-y), 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -3500 or 55000 < y

   1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower-+.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 51.1%

      \[\leadsto -y \]

   if -3500 < y < 55000

   1. Initial program 54.4%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. distribute-lft-neg-out N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

      8. distribute-rgt-neg-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-rgt1-in N/A

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

      12. mul-1-neg N/A

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

      13. fp-cancel-sub-sign-inv N/A

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

      14. *-commutative N/A

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

      15. metadata-eval N/A

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

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

      18. associate--r- N/A

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

      19. metadata-eval N/A

          \[\leadsto \left(\color{blue}{0} + y\right) \cdot x \]

      20. +-lft-identity N/A

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

      21. lower-*.f64 32.1

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

   5. Applied rewrites 32.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3500 \lor \neg \left(y \leq 55000\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 y))

C

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

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 - y
end function

Java

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

Python

def code(x, y):
	return 1.0 - y

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(1.0 - y), $MachinePrecision]

Derivation

1. Initial program 76.5%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. lower--.f64 61.0

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

5. Applied rewrites 61.0%

   \[\leadsto \color{blue}{1 - y} \]
6. Add Preprocessing

Alternative 7: 38.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

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_] := 1.0

Derivation

1. Initial program 76.5%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. remove-double-neg N/A

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

   2. distribute-lft-neg-out N/A

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

   3. mul-1-neg N/A

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

   4. distribute-rgt-neg-in N/A

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

   5. *-commutative N/A

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

   6. associate-*r* N/A

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

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

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

   8. distribute-rgt-neg-in N/A

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

   9. metadata-eval N/A

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

   10. +-commutative N/A

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

   11. distribute-rgt1-in N/A

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

   12. mul-1-neg N/A

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

   13. fp-cancel-sub-sign-inv N/A

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

   14. *-commutative N/A

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

   15. metadata-eval N/A

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

   16. metadata-eval N/A

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

   17. *-lft-identity N/A

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

   18. associate--r- N/A

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

   19. metadata-eval N/A

       \[\leadsto \left(\color{blue}{0} + y\right) \cdot x \]

   20. +-lft-identity N/A

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

   21. lower-*.f64 39.6

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

5. Applied rewrites 39.6%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 36.6%

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

Developer Target 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot x - \left(y - 1\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* y x) (- y 1.0)))

C

double code(double x, double y) {
	return (y * x) - (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 = (y * x) - (y - 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(y * x), $MachinePrecision] - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024359 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* y x) (- y 1)))

  (+ x (* (- 1.0 x) (- 1.0 y))))