Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+17}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -1e+18)
     (- (log t) y)
     (if (<= t_1 5e+17) (- (log t) z) (* (log y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = log(t) - y;
	} else if (t_1 <= 5e+17) {
		tmp = log(t) - z;
	} else {
		tmp = log(y) * 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if (t_1 <= (-1d+18)) then
        tmp = log(t) - y
    else if (t_1 <= 5d+17) then
        tmp = log(t) - z
    else
        tmp = log(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = Math.log(t) - y;
	} else if (t_1 <= 5e+17) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if t_1 <= -1e+18:
		tmp = math.log(t) - y
	elif t_1 <= 5e+17:
		tmp = math.log(t) - z
	else:
		tmp = math.log(y) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = Float64(log(t) - y);
	elseif (t_1 <= 5e+17)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = log(t) - y;
	elseif (t_1 <= 5e+17)
		tmp = log(t) - z;
	else
		tmp = log(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[t$95$1, 5e+17], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1e18

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   7. Step-by-step derivation

   8. Applied rewrites 54.1%

      \[\leadsto \log t - y \]

   if -1e18 < (-.f64 (*.f64 x (log.f64 y)) y) < 5e17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 98.9

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   7. Step-by-step derivation

   8. Applied rewrites 97.3%

      \[\leadsto \log t - z \]

   if 5e17 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

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

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 95.0%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left({\log y}^{2} \cdot x, \frac{x}{\mathsf{fma}\left(\log y, x, y\right)}, \frac{\left(-y\right) \cdot y}{\mathsf{fma}\left(\log y, x, y\right)}\right)} - z\right) + \log t \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift-fma.f64 N/A

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

      5. associate--l+ N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 97.4%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 81.5

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

   9. Applied rewrites 81.5%

      \[\leadsto \color{blue}{\log y \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+15} \lor \neg \left(z \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e+15) (not (<= z 5.5e-5)))
   (- (- (log t) y) z)
   (- (fma (log y) x (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+15) || !(z <= 5.5e-5)) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = fma(log(y), x, log(t)) - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e+15) || !(z <= 5.5e-5))
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = Float64(fma(log(y), x, log(t)) - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e+15], N[Not[LessEqual[z, 5.5e-5]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e15 or 5.5000000000000002e-5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. lower--.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -7.8e15 < z < 5.5000000000000002e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+15} \lor \neg \left(z \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log y, x, \log t\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+15}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1 - y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (log y) x (log t))))
   (if (<= z -7.8e+15)
     (- (- (log t) y) z)
     (if (<= z 4.6e+31) (- t_1 y) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(log(y), x, log(t));
	double tmp;
	if (z <= -7.8e+15) {
		tmp = (log(t) - y) - z;
	} else if (z <= 4.6e+31) {
		tmp = t_1 - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(log(y), x, log(t))
	tmp = 0.0
	if (z <= -7.8e+15)
		tmp = Float64(Float64(log(t) - y) - z);
	elseif (z <= 4.6e+31)
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+15], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[z, 4.6e+31], N[(t$95$1 - y), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. lower--.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 89.0

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

   5. Applied rewrites 89.0%

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

   if -7.8e15 < z < 4.5999999999999999e31

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if 4.5999999999999999e31 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 88.6

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

   5. Applied rewrites 88.6%

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

Alternative 5: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+76} \lor \neg \left(x \leq 9.5 \cdot 10^{+159}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.5e+76) (not (<= x 9.5e+159)))
   (* (log y) x)
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e+76) || !(x <= 9.5e+159)) {
		tmp = log(y) * x;
	} else {
		tmp = (log(t) - y) - z;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.5d+76)) .or. (.not. (x <= 9.5d+159))) then
        tmp = log(y) * x
    else
        tmp = (log(t) - y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e+76) || !(x <= 9.5e+159)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = (Math.log(t) - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.5e+76) or not (x <= 9.5e+159):
		tmp = math.log(y) * x
	else:
		tmp = (math.log(t) - y) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.5e+76) || !(x <= 9.5e+159))
		tmp = Float64(log(y) * x);
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.5e+76) || ~((x <= 9.5e+159)))
		tmp = log(y) * x;
	else
		tmp = (log(t) - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.5e+76], N[Not[LessEqual[x, 9.5e+159]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4999999999999995e76 or 9.5000000000000003e159 < x

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

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

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

      4. div-add N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 81.7%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left({\log y}^{2} \cdot x, \frac{x}{\mathsf{fma}\left(\log y, x, y\right)}, \frac{\left(-y\right) \cdot y}{\mathsf{fma}\left(\log y, x, y\right)}\right)} - z\right) + \log t \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift-fma.f64 N/A

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

      5. associate--l+ N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 98.2%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 75.5

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

   9. Applied rewrites 75.5%

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

   if -7.4999999999999995e76 < x < 9.5000000000000003e159

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. lower--.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 91.6

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

   5. Applied rewrites 91.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+76} \lor \neg \left(x \leq 9.5 \cdot 10^{+159}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+60} \lor \neg \left(z \leq 4.6 \cdot 10^{+31}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e+60) (not (<= z 4.6e+31))) (- z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e+60) || !(z <= 4.6e+31)) {
		tmp = -z;
	} else {
		tmp = log(t) - 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d+60)) .or. (.not. (z <= 4.6d+31))) then
        tmp = -z
    else
        tmp = log(t) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e+60) || !(z <= 4.6e+31)) {
		tmp = -z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e+60) or not (z <= 4.6e+31):
		tmp = -z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e+60) || !(z <= 4.6e+31))
		tmp = Float64(-z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e+60) || ~((z <= 4.6e+31)))
		tmp = -z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e+60], N[Not[LessEqual[z, 4.6e+31]], $MachinePrecision]], (-z), N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e60 or 4.5999999999999999e31 < z

   1. Initial program 100.0%

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

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

      2. lower-neg.f64 71.8

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

   5. Applied rewrites 71.8%

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

   if -1.0500000000000001e60 < z < 4.5999999999999999e31

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 97.7

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   7. Step-by-step derivation

   8. Applied rewrites 61.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+60} \lor \neg \left(z \leq 4.6 \cdot 10^{+31}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 11500000000:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 11500000000.0) (- (log t) z) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 11500000000.0) {
		tmp = log(t) - z;
	} else {
		tmp = log(t) - 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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 11500000000.0d0) then
        tmp = log(t) - z
    else
        tmp = log(t) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 11500000000.0) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 11500000000.0:
		tmp = math.log(t) - z
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 11500000000.0)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 11500000000.0)
		tmp = log(t) - z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 11500000000.0], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.15e10

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   7. Step-by-step derivation

   8. Applied rewrites 63.5%

      \[\leadsto \log t - z \]

   if 1.15e10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. /-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. /-rgt-identity N/A

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

      6. /-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 83.1

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   7. Step-by-step derivation

   8. Applied rewrites 64.7%

      \[\leadsto \log t - y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 38.0% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 13200000000:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{z} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 13200000000.0) (- z) (* (/ (- y) z) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 13200000000.0) {
		tmp = -z;
	} else {
		tmp = (-y / z) * z;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 13200000000.0d0) then
        tmp = -z
    else
        tmp = (-y / z) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 13200000000.0) {
		tmp = -z;
	} else {
		tmp = (-y / z) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 13200000000.0:
		tmp = -z
	else:
		tmp = (-y / z) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 13200000000.0)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(Float64(-y) / z) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 13200000000.0)
		tmp = -z;
	else
		tmp = (-y / z) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 13200000000.0], (-z), N[(N[((-y) / z), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.32e10

   1. Initial program 99.9%

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

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

      2. lower-neg.f64 36.8

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

   5. Applied rewrites 36.8%

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

   if 1.32e10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. lower--.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-lft-identity N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 81.5

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 60.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 43.5%

       \[\leadsto \frac{-y}{z} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 29.8% accurate, 71.7× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-z)

Derivation

1. Initial program 99.9%

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

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

   2. lower-neg.f64 29.6

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

5. Applied rewrites 29.6%

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

Reproduce

herbie shell --seed 2024359 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))