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

Percentage Accurate: 99.9% → 99.9%

Time: 4.6s

Alternatives: 14

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[y], $MachinePrecision] * x + N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $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. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-log.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. +-commutative N/A

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

   8. associate--r+ N/A

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

   9. associate--l+ N/A

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift-log.f64 N/A

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

   15. lift-log.f64 N/A

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

   16. +-commutative N/A

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

   17. 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. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-log.f64 N/A

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

   4. lift-log.f64 N/A

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

   5. lift-fma.f64 N/A

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

   6. associate--l+ N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lift-log.f64 N/A

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

   10. associate--r+ N/A

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

   11. lower--.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lift-log.f64 99.9

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

6. Applied rewrites 99.9%

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

Alternative 2: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+112}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;\left(-z\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -5e+112)
     (- y)
     (if (<= t_1 5e+71) (+ (- z) (log t)) (* (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+112) {
		tmp = -y;
	} else if (t_1 <= 5e+71) {
		tmp = -z + log(t);
	} 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+112)) then
        tmp = -y
    else if (t_1 <= 5d+71) then
        tmp = -z + log(t)
    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+112) {
		tmp = -y;
	} else if (t_1 <= 5e+71) {
		tmp = -z + Math.log(t);
	} 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+112:
		tmp = -y
	elif t_1 <= 5e+71:
		tmp = -z + math.log(t)
	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+112)
		tmp = Float64(-y);
	elseif (t_1 <= 5e+71)
		tmp = Float64(Float64(-z) + log(t));
	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+112)
		tmp = -y;
	elseif (t_1 <= 5e+71)
		tmp = -z + log(t);
	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+112], (-y), If[LessEqual[t$95$1, 5e+71], N[((-z) + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5e112

   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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 53.2

         \[\leadsto -y \]

   5. Applied rewrites 53.2%

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

   if -5e112 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.99999999999999972e71

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if 4.99999999999999972e71 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 87.3

         \[\leadsto \log y \cdot x \]

   5. Applied rewrites 87.3%

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

Alternative 3: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+112}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -5e+112) (- y) (if (<= t_1 5e+71) (- 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+112) {
		tmp = -y;
	} else if (t_1 <= 5e+71) {
		tmp = -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+112)) then
        tmp = -y
    else if (t_1 <= 5d+71) then
        tmp = -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+112) {
		tmp = -y;
	} else if (t_1 <= 5e+71) {
		tmp = -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+112:
		tmp = -y
	elif t_1 <= 5e+71:
		tmp = -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+112)
		tmp = Float64(-y);
	elseif (t_1 <= 5e+71)
		tmp = Float64(-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+112)
		tmp = -y;
	elseif (t_1 <= 5e+71)
		tmp = -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+112], (-y), If[LessEqual[t$95$1, 5e+71], (-z), N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5e112

   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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 53.2

         \[\leadsto -y \]

   5. Applied rewrites 53.2%

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

   if -5e112 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.99999999999999972e71

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 55.4

         \[\leadsto -z \]

   5. Applied rewrites 55.4%

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

   if 4.99999999999999972e71 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 87.3

         \[\leadsto \log y \cdot x \]

   5. Applied rewrites 87.3%

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

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -510 \lor \neg \left(z \leq 2.2 \cdot 10^{-7}\right):\\ \;\;\;\;\log y \cdot x - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -510.0) (not (<= z 2.2e-7)))
   (- (* (log y) x) (+ z y))
   (- (fma (log y) x (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -510.0) || !(z <= 2.2e-7)) {
		tmp = (log(y) * x) - (z + y);
	} else {
		tmp = fma(log(y), x, log(t)) - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -510.0) || !(z <= 2.2e-7))
		tmp = Float64(Float64(log(y) * x) - Float64(z + y));
	else
		tmp = Float64(fma(log(y), x, log(t)) - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -510.0], N[Not[LessEqual[z, 2.2e-7]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -510 or 2.2000000000000001e-7 < z

   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. 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. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 99.5

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

   7. Applied rewrites 99.5%

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

   if -510 < z < 2.2000000000000001e-7

   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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -510 \lor \neg \left(z \leq 2.2 \cdot 10^{-7}\right):\\ \;\;\;\;\log y \cdot x - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00024:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t - z\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 0.00024) (fma (log y) x (- (log t) z)) (- (* (log y) x) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.00024) {
		tmp = fma(log(y), x, (log(t) - z));
	} else {
		tmp = (log(y) * x) - (z + y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 0.00024)
		tmp = fma(log(y), x, Float64(log(t) - z));
	else
		tmp = Float64(Float64(log(y) * x) - Float64(z + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 0.00024], N[(N[Log[y], $MachinePrecision] * x + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.40000000000000006e-4

   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

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--r+ N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift-log.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around 0

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

      1. lift-log.f64 99.5

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

   9. Applied rewrites 99.5%

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

   if 2.40000000000000006e-4 < y

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 97.9

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

   7. Applied rewrites 97.9%

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

Alternative 6: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00024:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 0.00024) (- (fma (log y) x (log t)) z) (- (* (log y) x) (+ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 0.00024) {
		tmp = fma(log(y), x, log(t)) - z;
	} else {
		tmp = (log(y) * x) - (z + y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 0.00024)
		tmp = Float64(fma(log(y), x, log(t)) - z);
	else
		tmp = Float64(Float64(log(y) * x) - Float64(z + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 0.00024], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.40000000000000006e-4

   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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 99.5

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

   5. Applied rewrites 99.5%

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

   if 2.40000000000000006e-4 < y

   1. Initial program 100.0%

      \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 97.9

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

   7. Applied rewrites 97.9%

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

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

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. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-log.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. +-commutative N/A

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

   8. associate--r+ N/A

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

   9. associate--l+ N/A

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift-log.f64 N/A

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

   15. lift-log.f64 N/A

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

   16. +-commutative N/A

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

   17. 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 8: 56.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \left(-y\right) + \log t\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)) (t_2 (+ (- y) (log t))))
   (if (<= z -1.15e+54)
     (- z)
     (if (<= z -1.55e-290)
       t_2
       (if (<= z 7e-137)
         t_1
         (if (<= z 3.7e-26) t_2 (if (<= z 2.45e+20) t_1 (- z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double t_2 = -y + log(t);
	double tmp;
	if (z <= -1.15e+54) {
		tmp = -z;
	} else if (z <= -1.55e-290) {
		tmp = t_2;
	} else if (z <= 7e-137) {
		tmp = t_1;
	} else if (z <= 3.7e-26) {
		tmp = t_2;
	} else if (z <= 2.45e+20) {
		tmp = t_1;
	} else {
		tmp = -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) :: t_2
    real(8) :: tmp
    t_1 = log(y) * x
    t_2 = -y + log(t)
    if (z <= (-1.15d+54)) then
        tmp = -z
    else if (z <= (-1.55d-290)) then
        tmp = t_2
    else if (z <= 7d-137) then
        tmp = t_1
    else if (z <= 3.7d-26) then
        tmp = t_2
    else if (z <= 2.45d+20) then
        tmp = t_1
    else
        tmp = -z
    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 t_2 = -y + Math.log(t);
	double tmp;
	if (z <= -1.15e+54) {
		tmp = -z;
	} else if (z <= -1.55e-290) {
		tmp = t_2;
	} else if (z <= 7e-137) {
		tmp = t_1;
	} else if (z <= 3.7e-26) {
		tmp = t_2;
	} else if (z <= 2.45e+20) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	t_2 = -y + math.log(t)
	tmp = 0
	if z <= -1.15e+54:
		tmp = -z
	elif z <= -1.55e-290:
		tmp = t_2
	elif z <= 7e-137:
		tmp = t_1
	elif z <= 3.7e-26:
		tmp = t_2
	elif z <= 2.45e+20:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	t_2 = Float64(Float64(-y) + log(t))
	tmp = 0.0
	if (z <= -1.15e+54)
		tmp = Float64(-z);
	elseif (z <= -1.55e-290)
		tmp = t_2;
	elseif (z <= 7e-137)
		tmp = t_1;
	elseif (z <= 3.7e-26)
		tmp = t_2;
	elseif (z <= 2.45e+20)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	t_2 = -y + log(t);
	tmp = 0.0;
	if (z <= -1.15e+54)
		tmp = -z;
	elseif (z <= -1.55e-290)
		tmp = t_2;
	elseif (z <= 7e-137)
		tmp = t_1;
	elseif (z <= 3.7e-26)
		tmp = t_2;
	elseif (z <= 2.45e+20)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[((-y) + N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+54], (-z), If[LessEqual[z, -1.55e-290], t$95$2, If[LessEqual[z, 7e-137], t$95$1, If[LessEqual[z, 3.7e-26], t$95$2, If[LessEqual[z, 2.45e+20], t$95$1, (-z)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999997e54 or 2.45e20 < 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 70.2

         \[\leadsto -z \]

   5. Applied rewrites 70.2%

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

   if -1.14999999999999997e54 < z < -1.54999999999999995e-290 or 7.0000000000000002e-137 < z < 3.6999999999999999e-26

   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 inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) + \log t \]

      2. lower-neg.f64 63.0

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

   5. Applied rewrites 63.0%

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

   if -1.54999999999999995e-290 < z < 7.0000000000000002e-137 or 3.6999999999999999e-26 < z < 2.45e20

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 71.1

         \[\leadsto \log y \cdot x \]

   5. Applied rewrites 71.1%

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

Alternative 9: 99.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \lor \neg \left(x \leq 1.5\right):\\ \;\;\;\;\log y \cdot x - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.2) (not (<= x 1.5)))
   (- (* (log y) x) (+ z y))
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.2) || !(x <= 1.5)) {
		tmp = (log(y) * x) - (z + 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) :: tmp
    if ((x <= (-2.2d0)) .or. (.not. (x <= 1.5d0))) then
        tmp = (log(y) * x) - (z + 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 tmp;
	if ((x <= -2.2) || !(x <= 1.5)) {
		tmp = (Math.log(y) * x) - (z + y);
	} else {
		tmp = (Math.log(t) - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.2) or not (x <= 1.5):
		tmp = (math.log(y) * x) - (z + y)
	else:
		tmp = (math.log(t) - y) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.2) || !(x <= 1.5))
		tmp = Float64(Float64(log(y) * x) - Float64(z + y));
	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 <= -2.2) || ~((x <= 1.5)))
		tmp = (log(y) * x) - (z + y);
	else
		tmp = (log(t) - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.2], N[Not[LessEqual[x, 1.5]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000002 or 1.5 < 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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 98.6

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

   7. Applied rewrites 98.6%

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

   if -2.2000000000000002 < x < 1.5

   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

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 99.2

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

   5. Applied rewrites 99.2%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \lor \neg \left(x \leq 1.5\right):\\ \;\;\;\;\log y \cdot x - \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+78} \lor \neg \left(x \leq 9.5 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e+78) (not (<= x 9.5e+96)))
   (fma (log y) x (- y))
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e+78) || !(x <= 9.5e+96)) {
		tmp = fma(log(y), x, -y);
	} else {
		tmp = (log(t) - y) - z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.35e+78) || !(x <= 9.5e+96))
		tmp = fma(log(y), x, Float64(-y));
	else
		tmp = Float64(Float64(log(t) - y) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.35e+78], N[Not[LessEqual[x, 9.5e+96]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000002e78 or 9.50000000000000089e96 < 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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--r+ N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift-log.f64 99.7

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

   6. Applied rewrites 99.7%

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

   7. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.6

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

   9. Applied rewrites 86.6%

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

   if -1.35000000000000002e78 < x < 9.50000000000000089e96

   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

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 93.4

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

   5. Applied rewrites 93.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+78} \lor \neg \left(x \leq 9.5 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+90}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e+78)
   (fma (log y) x (- y))
   (if (<= x 1.85e+90) (- (- (log t) y) z) (fma (log y) x (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e+78) {
		tmp = fma(log(y), x, -y);
	} else if (x <= 1.85e+90) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = fma(log(y), x, -z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e+78)
		tmp = fma(log(y), x, Float64(-y));
	elseif (x <= 1.85e+90)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = fma(log(y), x, Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e+78], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision], If[LessEqual[x, 1.85e+90], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35000000000000002e78

   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--r+ N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift-log.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 88.4

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

   9. Applied rewrites 88.4%

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

   if -1.35000000000000002e78 < x < 1.85e90

   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

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 93.3

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

   5. Applied rewrites 93.3%

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

   if 1.85e90 < x

   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. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

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

      9. associate--l+ N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. lift-log.f64 N/A

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

      16. +-commutative N/A

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

      17. 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--r+ N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift-log.f64 99.7

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

   6. Applied rewrites 99.7%

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

   7. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 92.1

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

   9. Applied rewrites 92.1%

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

Alternative 12: 83.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+138} \lor \neg \left(x \leq 9.5 \cdot 10^{+115}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.9e+138) (not (<= x 9.5e+115)))
   (* (log y) x)
   (- (- (log t) y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+138) || !(x <= 9.5e+115)) {
		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 <= (-1.9d+138)) .or. (.not. (x <= 9.5d+115))) 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 <= -1.9e+138) || !(x <= 9.5e+115)) {
		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 <= -1.9e+138) or not (x <= 9.5e+115):
		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 <= -1.9e+138) || !(x <= 9.5e+115))
		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 <= -1.9e+138) || ~((x <= 9.5e+115)))
		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, -1.9e+138], N[Not[LessEqual[x, 9.5e+115]], $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 < -1.90000000000000006e138 or 9.4999999999999997e115 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 77.3

         \[\leadsto \log y \cdot x \]

   5. Applied rewrites 77.3%

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

   if -1.90000000000000006e138 < x < 9.4999999999999997e115

   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

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 90.2

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

   5. Applied rewrites 90.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+138} \lor \neg \left(x \leq 9.5 \cdot 10^{+115}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.1% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+54} \lor \neg \left(z \leq 800000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+54) (not (<= z 800000000000.0))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+54) || !(z <= 800000000000.0)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.15d+54)) .or. (.not. (z <= 800000000000.0d0))) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+54) || !(z <= 800000000000.0)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+54) or not (z <= 800000000000.0):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+54) || !(z <= 800000000000.0))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+54) || ~((z <= 800000000000.0)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+54], N[Not[LessEqual[z, 800000000000.0]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999997e54 or 8e11 < 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 69.6

         \[\leadsto -z \]

   5. Applied rewrites 69.6%

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

   if -1.14999999999999997e54 < z < 8e11

   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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 31.3

         \[\leadsto -y \]

   5. Applied rewrites 31.3%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+54} \lor \neg \left(z \leq 800000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.6% accurate, 71.7× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 y around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 23.8

      \[\leadsto -y \]

5. Applied rewrites 23.8%

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

Reproduce

herbie shell --seed 2025064 
(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)))