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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 11

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate--l- N/A

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

   6. associate-+r- N/A

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

   7. lower--.f64 N/A

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

   8. +-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. +-commutative N/A

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

   13. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+174}:\\ \;\;\;\;\log t + \left(-y\right)\\ \mathbf{elif}\;t\_1 \leq -200000:\\ \;\;\;\;\left(\frac{-y}{z} - 1\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -5e+174)
     (+ (log t) (- y))
     (if (<= t_1 -200000.0)
       (* (- (/ (- y) z) 1.0) z)
       (if (<= t_1 5e+32) (- (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 <= -5e+174) {
		tmp = log(t) + -y;
	} else if (t_1 <= -200000.0) {
		tmp = ((-y / z) - 1.0) * z;
	} else if (t_1 <= 5e+32) {
		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 <= (-5d+174)) then
        tmp = log(t) + -y
    else if (t_1 <= (-200000.0d0)) then
        tmp = ((-y / z) - 1.0d0) * z
    else if (t_1 <= 5d+32) 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 <= -5e+174) {
		tmp = Math.log(t) + -y;
	} else if (t_1 <= -200000.0) {
		tmp = ((-y / z) - 1.0) * z;
	} else if (t_1 <= 5e+32) {
		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 <= -5e+174:
		tmp = math.log(t) + -y
	elif t_1 <= -200000.0:
		tmp = ((-y / z) - 1.0) * z
	elif t_1 <= 5e+32:
		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 <= -5e+174)
		tmp = Float64(log(t) + Float64(-y));
	elseif (t_1 <= -200000.0)
		tmp = Float64(Float64(Float64(Float64(-y) / z) - 1.0) * z);
	elseif (t_1 <= 5e+32)
		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 <= -5e+174)
		tmp = log(t) + -y;
	elseif (t_1 <= -200000.0)
		tmp = ((-y / z) - 1.0) * z;
	elseif (t_1 <= 5e+32)
		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, -5e+174], N[(N[Log[t], $MachinePrecision] + (-y)), $MachinePrecision], If[LessEqual[t$95$1, -200000.0], N[(N[(N[((-y) / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+32], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -4.9999999999999997e174

   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. lift-*.f64 N/A

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

      7. swap-sqr N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

   4. Applied rewrites 6.5%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot {y}^{2} + {x}^{2} \cdot {\log y}^{2}}{y + x \cdot \log y}} + \log t \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot {y}^{2} + {x}^{2} \cdot {\log y}^{2}}{y + x \cdot \log y}} + \log t \]

   7. Applied rewrites 6.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 6.8

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

   9. Applied rewrites 92.8%

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

   10. Taylor expanded in x around 0

       \[\leadsto \log t + -1 \cdot \color{blue}{y} \]
   11. Step-by-step derivation

   12. Applied rewrites 56.2%

       \[\leadsto \log t + \left(-y\right) \]

   if -4.9999999999999997e174 < (-.f64 (*.f64 x (log.f64 y)) y) < -2e5

   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

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 82.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 70.3%

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

   if -2e5 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999997e32

   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

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 98.5%

      \[\leadsto \log t - z \]

   if 4.9999999999999997e32 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. associate-+r- N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   6. 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 72.3

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

   7. Applied rewrites 72.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -5 \cdot 10^{+174}:\\ \;\;\;\;\log t + \left(-y\right)\\ \mathbf{elif}\;x \cdot \log y - y \leq -200000:\\ \;\;\;\;\left(\frac{-y}{z} - 1\right) \cdot z\\ \mathbf{elif}\;x \cdot \log y - y \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -200000:\\ \;\;\;\;\left(\frac{-y}{z} - 1\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -200000.0)
     (* (- (/ (- y) z) 1.0) z)
     (if (<= t_1 5e+32) (- (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 <= -200000.0) {
		tmp = ((-y / z) - 1.0) * z;
	} else if (t_1 <= 5e+32) {
		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 <= (-200000.0d0)) then
        tmp = ((-y / z) - 1.0d0) * z
    else if (t_1 <= 5d+32) 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 <= -200000.0) {
		tmp = ((-y / z) - 1.0) * z;
	} else if (t_1 <= 5e+32) {
		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 <= -200000.0:
		tmp = ((-y / z) - 1.0) * z
	elif t_1 <= 5e+32:
		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 <= -200000.0)
		tmp = Float64(Float64(Float64(Float64(-y) / z) - 1.0) * z);
	elseif (t_1 <= 5e+32)
		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 <= -200000.0)
		tmp = ((-y / z) - 1.0) * z;
	elseif (t_1 <= 5e+32)
		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, -200000.0], N[(N[(N[((-y) / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+32], 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) < -2e5

   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

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.3%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 56.1%

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

   if -2e5 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.9999999999999997e32

   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

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 98.5%

      \[\leadsto \log t - z \]

   if 4.9999999999999997e32 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. associate-+r- N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   6. 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 72.3

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

   7. Applied rewrites 72.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -200000:\\ \;\;\;\;\left(\frac{-y}{z} - 1\right) \cdot z\\ \mathbf{elif}\;x \cdot \log y - y \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log y, x, \log t\right)\\ \mathbf{if}\;y \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+131}:\\ \;\;\;\;t\_1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (log y) x (log t))))
   (if (<= y 8.2e+67)
     (- t_1 z)
     (if (<= y 5.2e+131) (- t_1 y) (- (- (log t) y) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(log(y), x, log(t));
	double tmp;
	if (y <= 8.2e+67) {
		tmp = t_1 - z;
	} else if (y <= 5.2e+131) {
		tmp = t_1 - y;
	} else {
		tmp = (log(t) - y) - z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(log(y), x, log(t))
	tmp = 0.0
	if (y <= 8.2e+67)
		tmp = Float64(t_1 - z);
	elseif (y <= 5.2e+131)
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(Float64(log(t) - y) - 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[y, 8.2e+67], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[y, 5.2e+131], N[(t$95$1 - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.19999999999999959e67

   1. Initial program 99.8%

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

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

   5. Applied rewrites 94.0%

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

   if 8.19999999999999959e67 < y < 5.2e131

   1. Initial program 99.7%

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

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

   5. Applied rewrites 87.3%

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

   if 5.2e131 < 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 91.0

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

   5. Applied rewrites 91.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+112}:\\ \;\;\;\;\left(\frac{\log y \cdot x}{z} - 1\right) \cdot z\\ \mathbf{elif}\;z \leq 0.12:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\log y}{z} \cdot x - 1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.4e+112)
   (* (- (/ (* (log y) x) z) 1.0) z)
   (if (<= z 0.12)
     (- (fma (log y) x (log t)) y)
     (* (- (* (/ (log y) z) x) 1.0) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.4e+112) {
		tmp = (((log(y) * x) / z) - 1.0) * z;
	} else if (z <= 0.12) {
		tmp = fma(log(y), x, log(t)) - y;
	} else {
		tmp = (((log(y) / z) * x) - 1.0) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.4e+112)
		tmp = Float64(Float64(Float64(Float64(log(y) * x) / z) - 1.0) * z);
	elseif (z <= 0.12)
		tmp = Float64(fma(log(y), x, log(t)) - y);
	else
		tmp = Float64(Float64(Float64(Float64(log(y) / z) * x) - 1.0) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.4e+112], N[(N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 0.12], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[(N[(N[Log[y], $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.40000000000000008e112

   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

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 86.0%

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

   if -7.40000000000000008e112 < z < 0.12

   1. Initial program 99.8%

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

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

   5. Applied rewrites 96.0%

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

   if 0.12 < z

   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

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 96.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 84.6%

       \[\leadsto \left(\frac{\log y}{z} \cdot x - 1\right) \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+112}:\\ \;\;\;\;\left(\frac{\log y \cdot x}{z} - 1\right) \cdot z\\ \mathbf{elif}\;z \leq 0.12:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\log y}{z} \cdot x - 1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -200000:\\ \;\;\;\;\left(\frac{-y}{z} - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* x (log y)) y) -200000.0)
   (* (- (/ (- y) z) 1.0) z)
   (- (log t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * log(y)) - y) <= -200000.0) {
		tmp = ((-y / z) - 1.0) * z;
	} else {
		tmp = log(t) - 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 * log(y)) - y) <= (-200000.0d0)) then
        tmp = ((-y / z) - 1.0d0) * z
    else
        tmp = log(t) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * Math.log(y)) - y) <= -200000.0) {
		tmp = ((-y / z) - 1.0) * z;
	} else {
		tmp = Math.log(t) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * math.log(y)) - y) <= -200000.0:
		tmp = ((-y / z) - 1.0) * z
	else:
		tmp = math.log(t) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * log(y)) - y) <= -200000.0)
		tmp = Float64(Float64(Float64(Float64(-y) / z) - 1.0) * z);
	else
		tmp = Float64(log(t) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * log(y)) - y) <= -200000.0)
		tmp = ((-y / z) - 1.0) * z;
	else
		tmp = log(t) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], -200000.0], N[(N[(N[((-y) / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -2e5

   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

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.3%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 56.1%

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

   if -2e5 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.8%

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

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

   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 73.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -200000:\\ \;\;\;\;\left(\frac{-y}{z} - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;\left(\frac{t\_1}{z} - 1\right) \cdot z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+146}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -5.2e+193)
     t_1
     (if (<= x -1.1e+38)
       (* (- (/ t_1 z) 1.0) z)
       (if (<= x 3.5e+146) (- (- (log t) y) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -5.2e+193) {
		tmp = t_1;
	} else if (x <= -1.1e+38) {
		tmp = ((t_1 / z) - 1.0) * z;
	} else if (x <= 3.5e+146) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	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 = log(y) * x
    if (x <= (-5.2d+193)) then
        tmp = t_1
    else if (x <= (-1.1d+38)) then
        tmp = ((t_1 / z) - 1.0d0) * z
    else if (x <= 3.5d+146) then
        tmp = (log(t) - y) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -5.2e+193) {
		tmp = t_1;
	} else if (x <= -1.1e+38) {
		tmp = ((t_1 / z) - 1.0) * z;
	} else if (x <= 3.5e+146) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -5.2e+193:
		tmp = t_1
	elif x <= -1.1e+38:
		tmp = ((t_1 / z) - 1.0) * z
	elif x <= 3.5e+146:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -5.2e+193)
		tmp = t_1;
	elseif (x <= -1.1e+38)
		tmp = Float64(Float64(Float64(t_1 / z) - 1.0) * z);
	elseif (x <= 3.5e+146)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -5.2e+193)
		tmp = t_1;
	elseif (x <= -1.1e+38)
		tmp = ((t_1 / z) - 1.0) * z;
	elseif (x <= 3.5e+146)
		tmp = (log(t) - y) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -5.2e+193], t$95$1, If[LessEqual[x, -1.1e+38], N[(N[(N[(t$95$1 / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 3.5e+146], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.20000000000000026e193 or 3.5000000000000001e146 < x

   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

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. associate-+r- N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   6. 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 75.8

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

   7. Applied rewrites 75.8%

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

   if -5.20000000000000026e193 < x < -1.10000000000000003e38

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 79.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 73.1%

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

   if -1.10000000000000003e38 < x < 3.5000000000000001e146

   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 95.6

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

   5. Applied rewrites 95.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+193}:\\ \;\;\;\;\log y \cdot x\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;\left(\frac{\log y \cdot x}{z} - 1\right) \cdot z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+146}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+38} \lor \neg \left(x \leq 3.5 \cdot 10^{+146}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e+38) (not (<= x 3.5e+146)))
   (* (log y) x)
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+38) || !(x <= 3.5e+146)) {
		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 <= (-1.6d+38)) .or. (.not. (x <= 3.5d+146))) 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 <= -1.6e+38) || !(x <= 3.5e+146)) {
		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 <= -1.6e+38) or not (x <= 3.5e+146):
		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 <= -1.6e+38) || !(x <= 3.5e+146))
		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 <= -1.6e+38) || ~((x <= 3.5e+146)))
		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, -1.6e+38], N[Not[LessEqual[x, 3.5e+146]], $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 < -1.59999999999999993e38 or 3.5000000000000001e146 < x

   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

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. associate-+r- N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   6. 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 67.2

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

   7. Applied rewrites 67.2%

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

   if -1.59999999999999993e38 < x < 3.5000000000000001e146

   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 95.6

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

   5. Applied rewrites 95.6%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+38} \lor \neg \left(x \leq 3.5 \cdot 10^{+146}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.7% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{z} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.9e+68) (- z) (* (/ (- y) z) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9e+68) {
		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 <= 1.9d+68) 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 <= 1.9e+68) {
		tmp = -z;
	} else {
		tmp = (-y / z) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.9e+68:
		tmp = -z
	else:
		tmp = (-y / z) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.9e+68)
		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 <= 1.9e+68)
		tmp = -z;
	else
		tmp = (-y / z) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.9e+68], (-z), N[(N[((-y) / z), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.9e68

   1. Initial program 99.8%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   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 37.9

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

   5. Applied rewrites 37.9%

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

   if 1.9e68 < y

   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

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 48.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+68}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{z} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.0% accurate, 9.8× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* (- (/ (- y) z) 1.0) z))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[((-y) / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision]

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

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

5. Applied rewrites 84.9%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 72.2%

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

9. Taylor expanded in y around inf

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

11. Applied rewrites 48.9%

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

12. Final simplification 48.9%

    \[\leadsto \left(\frac{-y}{z} - 1\right) \cdot z \]
13. Add Preprocessing

Alternative 11: 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 30.7

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

5. Applied rewrites 30.7%

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

6. Final simplification 30.7%

   \[\leadsto -z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025015 
(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)))