Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.8%

Time: 5.2s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - 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 - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - 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 - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x - (log(y) * (y - -0.5))) + (y - 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 - (log(y) * (y - (-0.5d0)))) + (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift--.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. associate--l+ N/A

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

   8. lower-+.f64 N/A

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

4. Applied rewrites 99.8%

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

Alternative 2: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - \left(y + 0.5\right) \cdot \log y\right) + y\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+189}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y\\ \mathbf{elif}\;t\_0 \leq -2 \cdot 10^{+25} \lor \neg \left(t\_0 \leq 500\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log y, 0.5, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- x (* (+ y 0.5) (log y))) y)))
   (if (<= t_0 -4e+189)
     (* (- 1.0 (log y)) y)
     (if (or (<= t_0 -2e+25) (not (<= t_0 500.0)))
       (- x z)
       (- (fma (log y) 0.5 z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - ((y + 0.5) * log(y))) + y;
	double tmp;
	if (t_0 <= -4e+189) {
		tmp = (1.0 - log(y)) * y;
	} else if ((t_0 <= -2e+25) || !(t_0 <= 500.0)) {
		tmp = x - z;
	} else {
		tmp = -fma(log(y), 0.5, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y)
	tmp = 0.0
	if (t_0 <= -4e+189)
		tmp = Float64(Float64(1.0 - log(y)) * y);
	elseif ((t_0 <= -2e+25) || !(t_0 <= 500.0))
		tmp = Float64(x - z);
	else
		tmp = Float64(-fma(log(y), 0.5, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+189], N[(N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[t$95$0, -2e+25], N[Not[LessEqual[t$95$0, 500.0]], $MachinePrecision]], N[(x - z), $MachinePrecision], (-N[(N[Log[y], $MachinePrecision] * 0.5 + z), $MachinePrecision])]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) < -4.0000000000000001e189

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(1 - -1 \cdot \log \left(\frac{1}{y}\right)\right) \cdot y \]

      4. log-pow-rev N/A

         \[\leadsto \left(1 - \log \left({\left(\frac{1}{y}\right)}^{-1}\right)\right) \cdot y \]

      5. inv-pow N/A

         \[\leadsto \left(1 - \log \left({\left({y}^{-1}\right)}^{-1}\right)\right) \cdot y \]

      6. pow-pow N/A

         \[\leadsto \left(1 - \log \left({y}^{\left(-1 \cdot -1\right)}\right)\right) \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \left(1 - \log \left({y}^{1}\right)\right) \cdot y \]

      8. log-pow-rev N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      9. lower-*.f64 N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      10. lift-log.f64 65.4

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

   5. Applied rewrites 65.4%

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

      1. lift-*.f64 N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      2. lift-log.f64 N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      3. *-lft-identity N/A

         \[\leadsto \left(1 - \log y\right) \cdot y \]

      4. lift-log.f64 65.4

         \[\leadsto \left(1 - \log y\right) \cdot y \]

   7. Applied rewrites 65.4%

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

   if -4.0000000000000001e189 < (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) < -2.00000000000000018e25 or 500 < (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 74.4%

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

   if -2.00000000000000018e25 < (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) < 500

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 95.1

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

   5. Applied rewrites 95.1%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(z + \frac{1}{2} \cdot \log y\right)\right) \]

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-log.f64 93.3

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

   8. Applied rewrites 93.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \left(y + 0.5\right) \cdot \log y\right) + y \leq -4 \cdot 10^{+189}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y\\ \mathbf{elif}\;\left(x - \left(y + 0.5\right) \cdot \log y\right) + y \leq -2 \cdot 10^{+25} \lor \neg \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y \leq 500\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log y, 0.5, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\\ \mathbf{if}\;t\_0 \leq -1000 \lor \neg \left(t\_0 \leq 500\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (- x (* (+ y 0.5) (log y))) y) z)))
   (if (or (<= t_0 -1000.0) (not (<= t_0 500.0))) (- x z) (* -0.5 (log y)))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - ((y + 0.5) * log(y))) + y) - z;
	double tmp;
	if ((t_0 <= -1000.0) || !(t_0 <= 500.0)) {
		tmp = x - z;
	} else {
		tmp = -0.5 * log(y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x - ((y + 0.5d0) * log(y))) + y) - z
    if ((t_0 <= (-1000.0d0)) .or. (.not. (t_0 <= 500.0d0))) then
        tmp = x - z
    else
        tmp = (-0.5d0) * log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x - ((y + 0.5) * Math.log(y))) + y) - z;
	double tmp;
	if ((t_0 <= -1000.0) || !(t_0 <= 500.0)) {
		tmp = x - z;
	} else {
		tmp = -0.5 * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x - ((y + 0.5) * math.log(y))) + y) - z
	tmp = 0
	if (t_0 <= -1000.0) or not (t_0 <= 500.0):
		tmp = x - z
	else:
		tmp = -0.5 * math.log(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
	tmp = 0.0
	if ((t_0 <= -1000.0) || !(t_0 <= 500.0))
		tmp = Float64(x - z);
	else
		tmp = Float64(-0.5 * log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x - ((y + 0.5) * log(y))) + y) - z;
	tmp = 0.0;
	if ((t_0 <= -1000.0) || ~((t_0 <= 500.0)))
		tmp = x - z;
	else
		tmp = -0.5 * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1000.0], N[Not[LessEqual[t$95$0, 500.0]], $MachinePrecision]], N[(x - z), $MachinePrecision], N[(-0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) z) < -1e3 or 500 < (-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) z)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.8%

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

   if -1e3 < (-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) z) < 500

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 93.4

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(z + \frac{1}{2} \cdot \log y\right)\right) \]

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-log.f64 90.2

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

   8. Applied rewrites 90.2%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{-1}{2} \cdot \log y \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{-1}{2} \cdot \log y \]

       2. lift-log.f64 87.6

          \[\leadsto -0.5 \cdot \log y \]

   11. Applied rewrites 87.6%

       \[\leadsto -0.5 \cdot \log y \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \leq -1000 \lor \neg \left(\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \leq 500\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -230 \lor \neg \left(x \leq 0.0026\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log y, 0.5, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -230.0) (not (<= x 0.0026))) (- x z) (- (fma (log y) 0.5 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -230.0) || !(x <= 0.0026)) {
		tmp = x - z;
	} else {
		tmp = -fma(log(y), 0.5, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -230.0) || !(x <= 0.0026))
		tmp = Float64(x - z);
	else
		tmp = Float64(-fma(log(y), 0.5, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -230.0], N[Not[LessEqual[x, 0.0026]], $MachinePrecision]], N[(x - z), $MachinePrecision], (-N[(N[Log[y], $MachinePrecision] * 0.5 + z), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if x < -230 or 0.0025999999999999999 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 79.8%

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

   if -230 < x < 0.0025999999999999999

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(z + \frac{1}{2} \cdot \log y\right)\right) \]

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-log.f64 56.6

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

   8. Applied rewrites 56.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -230 \lor \neg \left(x \leq 0.0026\right):\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log y, 0.5, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+75}:\\ \;\;\;\;x - \mathsf{fma}\left(\log y, 0.5, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.7e+75) (- x (fma (log y) 0.5 z)) (- (* (- 1.0 (log y)) y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.7e+75) {
		tmp = x - fma(log(y), 0.5, z);
	} else {
		tmp = ((1.0 - log(y)) * y) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.7e+75)
		tmp = Float64(x - fma(log(y), 0.5, z));
	else
		tmp = Float64(Float64(Float64(1.0 - log(y)) * y) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.7e+75], N[(x - N[(N[Log[y], $MachinePrecision] * 0.5 + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.70000000000000006e75

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 93.0

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

   5. Applied rewrites 93.0%

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

   if 1.70000000000000006e75 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

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

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-log.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. lower--.f64 69.9

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

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

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

      3. metadata-eval N/A

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

      4. log-pow-rev N/A

         \[\leadsto \left(1 + \log \left({\left(\frac{1}{y}\right)}^{1}\right)\right) \cdot y - z \]

      5. inv-pow N/A

         \[\leadsto \left(1 + \log \left({\left({y}^{-1}\right)}^{1}\right)\right) \cdot y - z \]

      6. pow-unpow N/A

         \[\leadsto \left(1 + \log \left({y}^{\left(-1 \cdot 1\right)}\right)\right) \cdot y - z \]

      7. metadata-eval N/A

         \[\leadsto \left(1 + \log \left({y}^{-1}\right)\right) \cdot y - z \]

      8. log-pow-rev N/A

         \[\leadsto \left(1 + -1 \cdot \log y\right) \cdot y - z \]

      9. metadata-eval N/A

         \[\leadsto \left(1 + \left(\mathsf{neg}\left(1\right)\right) \cdot \log y\right) \cdot y - z \]

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

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y - z \]

      11. lower-*.f64 N/A

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

      12. lift-log.f64 N/A

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y - z \]

      13. lift-*.f64 N/A

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y - z \]

      14. lift--.f64 86.8

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y - z \]

      15. lift-*.f64 N/A

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y - z \]

      16. lift-log.f64 N/A

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y - z \]

      17. *-lft-identity N/A

          \[\leadsto \left(1 - \log y\right) \cdot y - z \]

      18. lift-log.f64 86.8

          \[\leadsto \left(1 - \log y\right) \cdot y - z \]

   8. Applied rewrites 86.8%

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

Alternative 6: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;x - \mathsf{fma}\left(\log y, 0.5, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \log y \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.6e+79) (- x (fma (log y) 0.5 z)) (- (+ y x) (* (log y) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+79) {
		tmp = x - fma(log(y), 0.5, z);
	} else {
		tmp = (y + x) - (log(y) * y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.6e+79)
		tmp = Float64(x - fma(log(y), 0.5, z));
	else
		tmp = Float64(Float64(y + x) - Float64(log(y) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.6e+79], N[(x - N[(N[Log[y], $MachinePrecision] * 0.5 + z), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] - N[(N[Log[y], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6000000000000001e79

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 92.5

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

   5. Applied rewrites 92.5%

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

   if 4.6000000000000001e79 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. lower--.f64 79.8

          \[\leadsto \left(y + x\right) - \log y \cdot \left(y - \color{blue}{-0.5}\right) \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\left(y + x\right) - \log y \cdot \left(y - -0.5\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(y + x\right) - \log y \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 79.8%

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

Alternative 7: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{+81}:\\ \;\;\;\;x - \mathsf{fma}\left(\log y, 0.5, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.8e+81) (- x (fma (log y) 0.5 z)) (* (- 1.0 (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.8e+81) {
		tmp = x - fma(log(y), 0.5, z);
	} else {
		tmp = (1.0 - log(y)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.8e+81)
		tmp = Float64(x - fma(log(y), 0.5, z));
	else
		tmp = Float64(Float64(1.0 - log(y)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.8e+81], N[(x - N[(N[Log[y], $MachinePrecision] * 0.5 + z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.79999999999999995e81

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 92.5

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

   5. Applied rewrites 92.5%

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

   if 2.79999999999999995e81 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(1 - -1 \cdot \log \left(\frac{1}{y}\right)\right) \cdot y \]

      4. log-pow-rev N/A

         \[\leadsto \left(1 - \log \left({\left(\frac{1}{y}\right)}^{-1}\right)\right) \cdot y \]

      5. inv-pow N/A

         \[\leadsto \left(1 - \log \left({\left({y}^{-1}\right)}^{-1}\right)\right) \cdot y \]

      6. pow-pow N/A

         \[\leadsto \left(1 - \log \left({y}^{\left(-1 \cdot -1\right)}\right)\right) \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \left(1 - \log \left({y}^{1}\right)\right) \cdot y \]

      8. log-pow-rev N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      9. lower-*.f64 N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      10. lift-log.f64 66.6

          \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

   5. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      2. lift-log.f64 N/A

         \[\leadsto \left(1 - 1 \cdot \log y\right) \cdot y \]

      3. *-lft-identity N/A

         \[\leadsto \left(1 - \log y\right) \cdot y \]

      4. lift-log.f64 66.6

         \[\leadsto \left(1 - \log y\right) \cdot y \]

   7. Applied rewrites 66.6%

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

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0

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

   1. associate--l+ N/A

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

   2. lower-+.f64 N/A

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

   3. lower--.f64 N/A

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

   4. +-commutative N/A

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

   5. +-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lift-log.f64 N/A

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

   8. metadata-eval N/A

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

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

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

   10. metadata-eval N/A

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

   11. metadata-eval N/A

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

   12. lower--.f64 99.8

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

5. Applied rewrites 99.8%

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

Alternative 9: 48.2% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+14} \lor \neg \left(z \leq 5.6 \cdot 10^{+85}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.6e+14) (not (<= z 5.6e+85))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e+14) || !(z <= 5.6e+85)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.6d+14)) .or. (.not. (z <= 5.6d+85))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e+14) || !(z <= 5.6e+85)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.6e+14) or not (z <= 5.6e+85):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.6e+14) || !(z <= 5.6e+85))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.6e+14) || ~((z <= 5.6e+85)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.6e+14], N[Not[LessEqual[z, 5.6e+85]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if z < -8.6e14 or 5.5999999999999998e85 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. lower-neg.f64 65.2

         \[\leadsto -z \]

   5. Applied rewrites 65.2%

      \[\leadsto \color{blue}{-z} \]

   if -8.6e14 < z < 5.5999999999999998e85

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 36.1%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+14} \lor \neg \left(z \leq 5.6 \cdot 10^{+85}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.4% accurate, 29.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - 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 - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 55.7%

   \[\leadsto \color{blue}{x} - z \]
6. Add Preprocessing

Alternative 11: 30.1% accurate, 118.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 28.3%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025052 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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