System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Percentage Accurate: 99.9% → 99.9%

Time: 4.6s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(z)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(z)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(\log z + 1\right) - z, y, 0.5 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- (+ (log z) 1.0) z) y (* 0.5 x)))

C

double code(double x, double y, double z) {
	return fma(((log(z) + 1.0) - z), y, (0.5 * x));
}

Julia

function code(x, y, z)
	return fma(Float64(Float64(log(z) + 1.0) - z), y, Float64(0.5 * x))
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[Log[z], $MachinePrecision] + 1.0), $MachinePrecision] - z), $MachinePrecision] * y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 99.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(1 - z\right) + \log z, y, x \cdot 0.5\right)} \]

   6. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(1 - z\right) + \log z}, y, x \cdot \frac{1}{2}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\log z + \left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

   8. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\log z + \color{blue}{\left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

   9. associate-+r- N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

   10. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

   11. lower-+.f64 99.9

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right)} - z, y, x \cdot 0.5\right) \]

   12. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{x \cdot \frac{1}{2}}\right) \]

   13. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]

   14. lower-*.f64 99.9

       \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{0.5 \cdot x}\right) \]

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\log z + 1\right) - z, y, 0.5 \cdot x\right)} \]
5. Add Preprocessing

Alternative 2: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) + \log z\\ \mathbf{if}\;t\_0 \leq -492 \lor \neg \left(t\_0 \leq -330 \lor \neg \left(t\_0 \leq -90.2\right)\right):\\ \;\;\;\;\mathsf{fma}\left(-z, y, 0.5 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log z, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- 1.0 z) (log z))))
   (if (or (<= t_0 -492.0) (not (or (<= t_0 -330.0) (not (<= t_0 -90.2)))))
     (fma (- z) y (* 0.5 x))
     (fma (log z) y y))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - z) + log(z);
	double tmp;
	if ((t_0 <= -492.0) || !((t_0 <= -330.0) || !(t_0 <= -90.2))) {
		tmp = fma(-z, y, (0.5 * x));
	} else {
		tmp = fma(log(z), y, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - z) + log(z))
	tmp = 0.0
	if ((t_0 <= -492.0) || !((t_0 <= -330.0) || !(t_0 <= -90.2)))
		tmp = fma(Float64(-z), y, Float64(0.5 * x));
	else
		tmp = fma(log(z), y, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -492.0], N[Not[Or[LessEqual[t$95$0, -330.0], N[Not[LessEqual[t$95$0, -90.2]], $MachinePrecision]]], $MachinePrecision]], N[((-z) * y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision], N[(N[Log[z], $MachinePrecision] * y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -492 or -330 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -90.2000000000000028

   1. Initial program 99.9%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(1 - z\right) + \log z, y, x \cdot 0.5\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(1 - z\right) + \log z}, y, x \cdot \frac{1}{2}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log z + \left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log z + \color{blue}{\left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

      9. associate-+r- N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

      11. lower-+.f64 99.9

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right)} - z, y, x \cdot 0.5\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{x \cdot \frac{1}{2}}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]

      14. lower-*.f64 99.9

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{0.5 \cdot x}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\log z + 1\right) - z, y, 0.5 \cdot x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot z}, y, \frac{1}{2} \cdot x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 84.2%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, y, 0.5 \cdot x\right) \]

   if -492 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -330 or -90.2000000000000028 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))

   1. Initial program 99.7%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x + y \cdot \left(1 + \log z\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z, y, y\right)\right)} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -492 \lor \neg \left(\left(1 - z\right) + \log z \leq -330 \lor \neg \left(\left(1 - z\right) + \log z \leq -90.2\right)\right):\\ \;\;\;\;\mathsf{fma}\left(-z, y, 0.5 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log z, y, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+37} \lor \neg \left(t\_0 \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ (- 1.0 z) (log z)))))
   (if (or (<= t_0 -5e+37) (not (<= t_0 2e+113))) (* (- y) z) (* 0.5 x))))

C

double code(double x, double y, double z) {
	double t_0 = y * ((1.0 - z) + log(z));
	double tmp;
	if ((t_0 <= -5e+37) || !(t_0 <= 2e+113)) {
		tmp = -y * z;
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * ((1.0d0 - z) + log(z))
    if ((t_0 <= (-5d+37)) .or. (.not. (t_0 <= 2d+113))) then
        tmp = -y * z
    else
        tmp = 0.5d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * ((1.0 - z) + Math.log(z));
	double tmp;
	if ((t_0 <= -5e+37) || !(t_0 <= 2e+113)) {
		tmp = -y * z;
	} else {
		tmp = 0.5 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * ((1.0 - z) + math.log(z))
	tmp = 0
	if (t_0 <= -5e+37) or not (t_0 <= 2e+113):
		tmp = -y * z
	else:
		tmp = 0.5 * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(Float64(1.0 - z) + log(z)))
	tmp = 0.0
	if ((t_0 <= -5e+37) || !(t_0 <= 2e+113))
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(0.5 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * ((1.0 - z) + log(z));
	tmp = 0.0;
	if ((t_0 <= -5e+37) || ~((t_0 <= 2e+113)))
		tmp = -y * z;
	else
		tmp = 0.5 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e+37], N[Not[LessEqual[t$95$0, 2e+113]], $MachinePrecision]], N[((-y) * z), $MachinePrecision], N[(0.5 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))) < -4.99999999999999989e37 or 2e113 < (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)))

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 61.6%

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

   if -4.99999999999999989e37 < (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))) < 2e113

   1. Initial program 99.9%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
   4. Step-by-step derivation

   5. Applied rewrites 67.0%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(\left(1 - z\right) + \log z\right) \leq -5 \cdot 10^{+37} \lor \neg \left(y \cdot \left(\left(1 - z\right) + \log z\right) \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+17} \lor \neg \left(x \leq 17500000000\right):\\ \;\;\;\;\mathsf{fma}\left(-z, y, 0.5 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log z - z, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+17) (not (<= x 17500000000.0)))
   (fma (- z) y (* 0.5 x))
   (fma (- (log z) z) y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+17) || !(x <= 17500000000.0)) {
		tmp = fma(-z, y, (0.5 * x));
	} else {
		tmp = fma((log(z) - z), y, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+17) || !(x <= 17500000000.0))
		tmp = fma(Float64(-z), y, Float64(0.5 * x));
	else
		tmp = fma(Float64(log(z) - z), y, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+17], N[Not[LessEqual[x, 17500000000.0]], $MachinePrecision]], N[((-z) * y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] * y + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4e17 or 1.75e10 < x

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(1 - z\right) + \log z, y, x \cdot 0.5\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(1 - z\right) + \log z}, y, x \cdot \frac{1}{2}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log z + \left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log z + \color{blue}{\left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

      9. associate-+r- N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

      11. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right)} - z, y, x \cdot 0.5\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{x \cdot \frac{1}{2}}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]

      14. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{0.5 \cdot x}\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\log z + 1\right) - z, y, 0.5 \cdot x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot z}, y, \frac{1}{2} \cdot x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 92.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, y, 0.5 \cdot x\right) \]

   if -4e17 < x < 1.75e10

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+17} \lor \neg \left(x \leq 17500000000\right):\\ \;\;\;\;\mathsf{fma}\left(-z, y, 0.5 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log z - z, y, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.32:\\ \;\;\;\;\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z, y, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log z - z, y, x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.32)
   (fma 0.5 x (fma (log z) y y))
   (fma (- (log z) z) y (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.32) {
		tmp = fma(0.5, x, fma(log(z), y, y));
	} else {
		tmp = fma((log(z) - z), y, (x * 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.32)
		tmp = fma(0.5, x, fma(log(z), y, y));
	else
		tmp = fma(Float64(log(z) - z), y, Float64(x * 0.5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.32], N[(0.5 * x + N[(N[Log[z], $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] * y + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.320000000000000007

   1. Initial program 99.7%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x + y \cdot \left(1 + \log z\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z, y, y\right)\right)} \]

   if 0.320000000000000007 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(1 - z\right) + \log z, y, x \cdot 0.5\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(1 - z\right) + \log z}, y, x \cdot \frac{1}{2}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log z + \left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log z + \color{blue}{\left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

      9. associate-+r- N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

      11. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right)} - z, y, x \cdot 0.5\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{x \cdot \frac{1}{2}}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]

      14. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{0.5 \cdot x}\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\log z + 1\right) - z, y, 0.5 \cdot x\right)} \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log z - z, y, \mathsf{fma}\left(0.5, x, y\right)\right)} \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\log z - z, y, \frac{1}{2} \cdot x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.7%

       \[\leadsto \mathsf{fma}\left(\log z - z, y, x \cdot 0.5\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.32:\\ \;\;\;\;\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z, y, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log z - z, y, x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.56:\\ \;\;\;\;\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z, y, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, 0.5 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.56) (fma 0.5 x (fma (log z) y y)) (fma (- 1.0 z) y (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.56) {
		tmp = fma(0.5, x, fma(log(z), y, y));
	} else {
		tmp = fma((1.0 - z), y, (0.5 * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.56)
		tmp = fma(0.5, x, fma(log(z), y, y));
	else
		tmp = fma(Float64(1.0 - z), y, Float64(0.5 * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.56], N[(0.5 * x + N[(N[Log[z], $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.56000000000000005

   1. Initial program 99.7%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x + y \cdot \left(1 + \log z\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z, y, y\right)\right)} \]

   if 0.56000000000000005 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-+l+ N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 - z, y, \log z \cdot y + x \cdot \frac{1}{2}\right)} \]

      8. lower-fma.f64 100.0

         \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{\mathsf{fma}\left(\log z, y, x \cdot 0.5\right)}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - z, y, \mathsf{fma}\left(\log z, y, \color{blue}{x \cdot \frac{1}{2}}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - z, y, \mathsf{fma}\left(\log z, y, \color{blue}{\frac{1}{2} \cdot x}\right)\right) \]

      11. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(1 - z, y, \mathsf{fma}\left(\log z, y, \color{blue}{0.5 \cdot x}\right)\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - z, y, \mathsf{fma}\left(\log z, y, 0.5 \cdot x\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 98.3%

      \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{0.5 \cdot x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z - z, y, y\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma 0.5 x (fma (- (log z) z) y y)))

C

double code(double x, double y, double z) {
	return fma(0.5, x, fma((log(z) - z), y, y));
}

Julia

function code(x, y, z)
	return fma(0.5, x, fma(Float64(log(z) - z), y, y))
end

Wolfram

code[x_, y_, z_] := N[(0.5 * x + N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{2} \cdot x + y \cdot \left(\left(1 + \log z\right) - z\right)} \]
4. Step-by-step derivation

5. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, \mathsf{fma}\left(\log z - z, y, y\right)\right)} \]
6. Add Preprocessing

Alternative 8: 75.1% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-z, y, 0.5 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- z) y (* 0.5 x)))

C

double code(double x, double y, double z) {
	return fma(-z, y, (0.5 * x));
}

Julia

function code(x, y, z)
	return fma(Float64(-z), y, Float64(0.5 * x))
end

Wolfram

code[x_, y_, z_] := N[((-z) * y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 99.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(1 - z\right) + \log z, y, x \cdot 0.5\right)} \]

   6. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(1 - z\right) + \log z}, y, x \cdot \frac{1}{2}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\log z + \left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

   8. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\log z + \color{blue}{\left(1 - z\right)}, y, x \cdot \frac{1}{2}\right) \]

   9. associate-+r- N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

   10. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right) - z}, y, x \cdot \frac{1}{2}\right) \]

   11. lower-+.f64 99.9

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\log z + 1\right)} - z, y, x \cdot 0.5\right) \]

   12. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{x \cdot \frac{1}{2}}\right) \]

   13. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]

   14. lower-*.f64 99.9

       \[\leadsto \mathsf{fma}\left(\left(\log z + 1\right) - z, y, \color{blue}{0.5 \cdot x}\right) \]

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\log z + 1\right) - z, y, 0.5 \cdot x\right)} \]

5. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot z}, y, \frac{1}{2} \cdot x\right) \]
6. Step-by-step derivation

7. Applied rewrites 75.5%

   \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, y, 0.5 \cdot x\right) \]
8. Add Preprocessing

Alternative 9: 40.8% accurate, 20.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.5 x))

C

double code(double x, double y, double z) {
	return 0.5 * x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.5d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 0.5 * x;
}

Python

def code(x, y, z):
	return 0.5 * x

Julia

function code(x, y, z)
	return Float64(0.5 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.5 * x;
end

Wolfram

code[x_, y_, z_] := N[(0.5 * x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
4. Step-by-step derivation

5. Applied rewrites 39.5%

   \[\leadsto \color{blue}{0.5 \cdot x} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ y (* 0.5 x)) (* y (- z (log z)))))

C

double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - log(z)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y + (0.5d0 * x)) - (y * (z - log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - Math.log(z)));
}

Python

def code(x, y, z):
	return (y + (0.5 * x)) - (y * (z - math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(y + Float64(0.5 * x)) - Float64(y * Float64(z - log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y + (0.5 * x)) - (y * (z - log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision] - N[(y * N[(z - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025022 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (* 1/2 x)) (* y (- z (log z)))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))