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

Percentage Accurate: 99.9% → 99.9%

Time: 9.4s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

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

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

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: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 719999999999999990922812560065494956500148488933128463223546424600821760:\\ \;\;\;\;\left(t\_1 - z\right) + \log t\\ \mathbf{elif}\;y \leq 7999999999999999840027746779153609453350441543176068145509186494646179317019429803718315479439939518038208601448616296448:\\ \;\;\;\;\left(\log t + t\_1\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* x (log y))))
  (if (<=
       y
       719999999999999990922812560065494956500148488933128463223546424600821760)
    (+ (- t_1 z) (log t))
    (if (<=
         y
         7999999999999999840027746779153609453350441543176068145509186494646179317019429803718315479439939518038208601448616296448)
      (- (+ (log t) t_1) y)
      (- (log t) (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 7.2e+71) {
		tmp = (t_1 - z) + log(t);
	} else if (y <= 8e+120) {
		tmp = (log(t) + t_1) - y;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 7.2d+71) then
        tmp = (t_1 - z) + log(t)
    else if (y <= 8d+120) then
        tmp = (log(t) + t_1) - y
    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 t_1 = x * Math.log(y);
	double tmp;
	if (y <= 7.2e+71) {
		tmp = (t_1 - z) + Math.log(t);
	} else if (y <= 8e+120) {
		tmp = (Math.log(t) + t_1) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 7.2e+71:
		tmp = (t_1 - z) + math.log(t)
	elif y <= 8e+120:
		tmp = (math.log(t) + t_1) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 7.2e+71)
		tmp = Float64(Float64(t_1 - z) + log(t));
	elseif (y <= 8e+120)
		tmp = Float64(Float64(log(t) + t_1) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 7.2e+71)
		tmp = (t_1 - z) + log(t);
	elseif (y <= 8e+120)
		tmp = (log(t) + t_1) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 719999999999999990922812560065494956500148488933128463223546424600821760], N[(N[(t$95$1 - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7999999999999999840027746779153609453350441543176068145509186494646179317019429803718315479439939518038208601448616296448], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.1999999999999999e71

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   if 7.1999999999999999e71 < y < 7.9999999999999998e120

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 70.4%

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

   4. Applied rewrites 70.4%

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

   if 7.9999999999999998e120 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-+.f64 71.0%

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

   4. Applied rewrites 71.0%

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

Alternative 2: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\log t + x \cdot \log y\right) - y\\ \mathbf{if}\;x \leq -160000000000000003411267041512703499568201259402874391483893415936:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 205000000000000000712752045580635333763662595444401860644264900033085951117885440:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (- (+ (log t) (* x (log y))) y)))
  (if (<=
       x
       -160000000000000003411267041512703499568201259402874391483893415936)
    t_1
    (if (<=
         x
         205000000000000000712752045580635333763662595444401860644264900033085951117885440)
      (- (log t) (+ y z))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(t) + (x * log(y))) - y;
	double tmp;
	if (x <= -1.6e+65) {
		tmp = t_1;
	} else if (x <= 2.05e+80) {
		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(t) + (x * log(y))) - y
    if (x <= (-1.6d+65)) then
        tmp = t_1
    else if (x <= 2.05d+80) 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(t) + (x * Math.log(y))) - y;
	double tmp;
	if (x <= -1.6e+65) {
		tmp = t_1;
	} else if (x <= 2.05e+80) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.log(t) + (x * math.log(y))) - y
	tmp = 0
	if x <= -1.6e+65:
		tmp = t_1
	elif x <= 2.05e+80:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(t) + Float64(x * log(y))) - y)
	tmp = 0.0
	if (x <= -1.6e+65)
		tmp = t_1;
	elseif (x <= 2.05e+80)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (log(t) + (x * log(y))) - y;
	tmp = 0.0;
	if (x <= -1.6e+65)
		tmp = t_1;
	elseif (x <= 2.05e+80)
		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[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -160000000000000003411267041512703499568201259402874391483893415936], t$95$1, If[LessEqual[x, 205000000000000000712752045580635333763662595444401860644264900033085951117885440], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e65 or 2.05e80 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 70.4%

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

   4. Applied rewrites 70.4%

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

   if -1.6e65 < x < 2.05e80

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-+.f64 71.0%

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

   4. Applied rewrites 71.0%

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

Alternative 3: 75.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := z \cdot \frac{x \cdot \log y}{z}\\ \mathbf{if}\;x \leq -270000000000000018122005435148810426653307705375889715385990186589798761847755892638561432527845242977315312447781045472512060821564119056384:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10000000000000000159028911097599180468360808563945281389781327557747838772170381060813469985856815104:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* z (/ (* x (log y)) z))))
  (if (<=
       x
       -270000000000000018122005435148810426653307705375889715385990186589798761847755892638561432527845242977315312447781045472512060821564119056384)
    t_1
    (if (<=
         x
         10000000000000000159028911097599180468360808563945281389781327557747838772170381060813469985856815104)
      (- (log t) (+ y z))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((x * log(y)) / z);
	double tmp;
	if (x <= -2.7e+140) {
		tmp = t_1;
	} else if (x <= 1e+100) {
		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 = z * ((x * log(y)) / z)
    if (x <= (-2.7d+140)) then
        tmp = t_1
    else if (x <= 1d+100) 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 = z * ((x * Math.log(y)) / z);
	double tmp;
	if (x <= -2.7e+140) {
		tmp = t_1;
	} else if (x <= 1e+100) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((x * math.log(y)) / z)
	tmp = 0
	if x <= -2.7e+140:
		tmp = t_1
	elif x <= 1e+100:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(x * log(y)) / z))
	tmp = 0.0
	if (x <= -2.7e+140)
		tmp = t_1;
	elseif (x <= 1e+100)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((x * log(y)) / z);
	tmp = 0.0;
	if (x <= -2.7e+140)
		tmp = t_1;
	elseif (x <= 1e+100)
		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[(z * N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -270000000000000018122005435148810426653307705375889715385990186589798761847755892638561432527845242977315312447781045472512060821564119056384], t$95$1, If[LessEqual[x, 10000000000000000159028911097599180468360808563945281389781327557747838772170381060813469985856815104], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000002e140 or 1e100 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-/.f64 79.8%

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 30.4%

      \[\leadsto z \cdot -1 \]

   8. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{x \cdot \log y}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto z \cdot \frac{x \cdot \log y}{z} \]

      3. lower-log.f64 20.0%

         \[\leadsto z \cdot \frac{x \cdot \log y}{z} \]

   10. Applied rewrites 20.0%

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

   if -2.7000000000000002e140 < x < 1e100

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-+.f64 71.0%

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

   4. Applied rewrites 71.0%

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

Alternative 4: 71.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 = log(t) - (y + z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

   2. lower-log.f64 N/A

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

   3. lower-+.f64 71.0%

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

4. Applied rewrites 71.0%

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

Alternative 5: 61.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 280000000000000000321333304781609280627972100690964841222179916714808304467968:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     y
     280000000000000000321333304781609280627972100690964841222179916714808304467968)
  (- (log t) z)
  (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.8e+77) {
		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 <= 2.8d+77) 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 <= 2.8e+77) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.8e+77:
		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 <= 2.8e+77)
		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 <= 2.8e+77)
		tmp = log(t) - z;
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 280000000000000000321333304781609280627972100690964841222179916714808304467968], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.8e77

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-+.f64 71.0%

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

   4. Applied rewrites 71.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 43.0%

      \[\leadsto \log t - z \]

   if 2.8e77 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 70.4%

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

   4. Applied rewrites 70.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-log.f64 42.1%

         \[\leadsto \log t - y \]

   7. Applied rewrites 42.1%

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

Alternative 6: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -250000000000000011221428169518979196387328:\\ \;\;\;\;z \cdot -1\\ \mathbf{elif}\;z \leq 189999999999999989608532542244330147673668766518374709649109067702331020071656162984364219905818102044713301325679389780922989584734916918217015296:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;z \cdot -1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= z -250000000000000011221428169518979196387328)
  (* z -1)
  (if (<=
       z
       189999999999999989608532542244330147673668766518374709649109067702331020071656162984364219905818102044713301325679389780922989584734916918217015296)
    (- (log t) y)
    (* z -1))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+41) {
		tmp = z * -1.0;
	} else if (z <= 1.9e+146) {
		tmp = log(t) - y;
	} else {
		tmp = z * -1.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, 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 <= (-2.5d+41)) then
        tmp = z * (-1.0d0)
    else if (z <= 1.9d+146) then
        tmp = log(t) - y
    else
        tmp = z * (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+41) {
		tmp = z * -1.0;
	} else if (z <= 1.9e+146) {
		tmp = Math.log(t) - y;
	} else {
		tmp = z * -1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+41:
		tmp = z * -1.0
	elif z <= 1.9e+146:
		tmp = math.log(t) - y
	else:
		tmp = z * -1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+41)
		tmp = Float64(z * -1.0);
	elseif (z <= 1.9e+146)
		tmp = Float64(log(t) - y);
	else
		tmp = Float64(z * -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e+41)
		tmp = z * -1.0;
	elseif (z <= 1.9e+146)
		tmp = log(t) - y;
	else
		tmp = z * -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -250000000000000011221428169518979196387328], N[(z * -1), $MachinePrecision], If[LessEqual[z, 189999999999999989608532542244330147673668766518374709649109067702331020071656162984364219905818102044713301325679389780922989584734916918217015296], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], N[(z * -1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e41 or 1.8999999999999999e146 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-/.f64 79.8%

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 30.4%

      \[\leadsto z \cdot -1 \]

   if -2.5000000000000001e41 < z < 1.8999999999999999e146

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 70.4%

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

   4. Applied rewrites 70.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-log.f64 42.1%

         \[\leadsto \log t - y \]

   7. Applied rewrites 42.1%

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

Alternative 7: 39.7% accurate, 8.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq 280000000000000000321333304781609280627972100690964841222179916714808304467968:\\ \;\;\;\;z \cdot -1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{z} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     y
     280000000000000000321333304781609280627972100690964841222179916714808304467968)
  (* z -1)
  (* (/ (- y) z) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.8e+77) {
		tmp = z * -1.0;
	} 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 <= 2.8d+77) then
        tmp = z * (-1.0d0)
    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 <= 2.8e+77) {
		tmp = z * -1.0;
	} else {
		tmp = (-y / z) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.8e+77:
		tmp = z * -1.0
	else:
		tmp = (-y / z) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.8e+77)
		tmp = Float64(z * -1.0);
	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 <= 2.8e+77)
		tmp = z * -1.0;
	else
		tmp = (-y / z) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 280000000000000000321333304781609280627972100690964841222179916714808304467968], N[(z * -1), $MachinePrecision], N[(N[((-y) / z), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.8e77

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-/.f64 79.8%

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot -1 \]
   6. Step-by-step derivation

   7. Applied rewrites 30.4%

      \[\leadsto z \cdot -1 \]

   if 2.8e77 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-/.f64 79.8%

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 20.2%

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

   7. Applied rewrites 20.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 20.2%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. lift-neg.f64 N/A

         \[\leadsto \frac{-y}{z} \cdot z \]

      9. lower-/.f64 20.2%

         \[\leadsto \frac{-y}{z} \cdot z \]

   9. Applied rewrites 20.2%

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

Alternative 8: 30.4% accurate, 35.8× speedup

Math

\[z \cdot -1 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (* z -1))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, 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 * (-1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(z * -1), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower-log.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-log.f64 N/A

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

   9. lower-+.f64 N/A

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

   10. lower-/.f64 79.8%

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

4. Applied rewrites 79.8%

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

5. Taylor expanded in z around inf

   \[\leadsto z \cdot -1 \]
6. Step-by-step derivation

7. Applied rewrites 30.4%

   \[\leadsto z \cdot -1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(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)))