Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 96.9% → 96.9%

Time: 3.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

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, a)
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), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

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, a)
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), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

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, a)
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), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

Alternative 2: 88.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y - z}{-z} \cdot a\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e+57)
   (- x (* (/ (- y z) (- z)) a))
   (if (<= z 2.1e+14)
     (- x (* a (/ y (+ 1.0 t))))
     (- x (/ (- y z) (/ (- z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+57) {
		tmp = x - (((y - z) / -z) * a);
	} else if (z <= 2.1e+14) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = x - ((y - z) / (-z / a));
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.8d+57)) then
        tmp = x - (((y - z) / -z) * a)
    else if (z <= 2.1d+14) then
        tmp = x - (a * (y / (1.0d0 + t)))
    else
        tmp = x - ((y - z) / (-z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+57) {
		tmp = x - (((y - z) / -z) * a);
	} else if (z <= 2.1e+14) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = x - ((y - z) / (-z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e+57:
		tmp = x - (((y - z) / -z) * a)
	elif z <= 2.1e+14:
		tmp = x - (a * (y / (1.0 + t)))
	else:
		tmp = x - ((y - z) / (-z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e+57)
		tmp = Float64(x - Float64(Float64(Float64(y - z) / Float64(-z)) * a));
	elseif (z <= 2.1e+14)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(-z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.8e+57)
		tmp = x - (((y - z) / -z) * a);
	elseif (z <= 2.1e+14)
		tmp = x - (a * (y / (1.0 + t)));
	else
		tmp = x - ((y - z) / (-z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e+57], N[(x - N[(N[(N[(y - z), $MachinePrecision] / (-z)), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+14], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000003e57

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{-1 \cdot z}}{a}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \frac{y - z}{\frac{\mathsf{neg}\left(z\right)}{a}} \]

      2. lower-neg.f64 84.8

         \[\leadsto x - \frac{y - z}{\frac{-z}{a}} \]

   4. Applied rewrites 84.8%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{-z}}{a}} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto x - \frac{\color{blue}{y - z}}{\frac{-z}{a}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y - z}{\frac{-z}{a}}} \]

      3. lift-/.f64 N/A

         \[\leadsto x - \frac{y - z}{\color{blue}{\frac{-z}{a}}} \]

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 89.3

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

   6. Applied rewrites 89.3%

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

   if -5.8000000000000003e57 < z < 2.1e14

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if 2.1e14 < z

   1. Initial program 94.6%

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

   2. Taylor expanded in z around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{-1 \cdot z}}{a}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \frac{y - z}{\frac{\mathsf{neg}\left(z\right)}{a}} \]

      2. lower-neg.f64 83.5

         \[\leadsto x - \frac{y - z}{\frac{-z}{a}} \]

   4. Applied rewrites 83.5%

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

Alternative 3: 87.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{-z} \cdot a\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y z) (- z)) a))))
   (if (<= z -5.8e+57)
     t_1
     (if (<= z 2.1e+14) (- x (* a (/ y (+ 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / -z) * a);
	double tmp;
	if (z <= -5.8e+57) {
		tmp = t_1;
	} else if (z <= 2.1e+14) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) / -z) * a)
    if (z <= (-5.8d+57)) then
        tmp = t_1
    else if (z <= 2.1d+14) then
        tmp = x - (a * (y / (1.0d0 + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / -z) * a);
	double tmp;
	if (z <= -5.8e+57) {
		tmp = t_1;
	} else if (z <= 2.1e+14) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) / -z) * a)
	tmp = 0
	if z <= -5.8e+57:
		tmp = t_1
	elif z <= 2.1e+14:
		tmp = x - (a * (y / (1.0 + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) / Float64(-z)) * a))
	tmp = 0.0
	if (z <= -5.8e+57)
		tmp = t_1;
	elseif (z <= 2.1e+14)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) / -z) * a);
	tmp = 0.0;
	if (z <= -5.8e+57)
		tmp = t_1;
	elseif (z <= 2.1e+14)
		tmp = x - (a * (y / (1.0 + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] / (-z)), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+57], t$95$1, If[LessEqual[z, 2.1e+14], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000003e57 or 2.1e14 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{-1 \cdot z}}{a}} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \frac{y - z}{\frac{\mathsf{neg}\left(z\right)}{a}} \]

      2. lower-neg.f64 84.1

         \[\leadsto x - \frac{y - z}{\frac{-z}{a}} \]

   4. Applied rewrites 84.1%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{-z}}{a}} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto x - \frac{\color{blue}{y - z}}{\frac{-z}{a}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y - z}{\frac{-z}{a}}} \]

      3. lift-/.f64 N/A

         \[\leadsto x - \frac{y - z}{\color{blue}{\frac{-z}{a}}} \]

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 88.3

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

   6. Applied rewrites 88.3%

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

   if -5.8000000000000003e57 < z < 2.1e14

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 89.1

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

   4. Applied rewrites 89.1%

      \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x - a \cdot \frac{y}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+84)
   (- x a)
   (if (<= z 3.6e+15) (- x (* a (/ y (+ 1.0 t)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+84) {
		tmp = x - a;
	} else if (z <= 3.6e+15) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = x - a;
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+84)) then
        tmp = x - a
    else if (z <= 3.6d+15) then
        tmp = x - (a * (y / (1.0d0 + t)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+84) {
		tmp = x - a;
	} else if (z <= 3.6e+15) {
		tmp = x - (a * (y / (1.0 + t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+84:
		tmp = x - a
	elif z <= 3.6e+15:
		tmp = x - (a * (y / (1.0 + t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+84)
		tmp = Float64(x - a);
	elseif (z <= 3.6e+15)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 + t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+84)
		tmp = x - a;
	elseif (z <= 3.6e+15)
		tmp = x - (a * (y / (1.0 + t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+84], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.6e+15], N[(x - N[(a * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e84 or 3.6e15 < z

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 79.5%

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

   if -1.2e84 < z < 3.6e15

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 87.8

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

   4. Applied rewrites 87.8%

      \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{t} \cdot a\\ \mathbf{if}\;t \leq -2 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{y}{1 - z} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y z) t) a))))
   (if (<= t -2e+15) t_1 (if (<= t 7.5e+26) (- x (* (/ y (- 1.0 z)) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / t) * a);
	double tmp;
	if (t <= -2e+15) {
		tmp = t_1;
	} else if (t <= 7.5e+26) {
		tmp = x - ((y / (1.0 - z)) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) / t) * a)
    if (t <= (-2d+15)) then
        tmp = t_1
    else if (t <= 7.5d+26) then
        tmp = x - ((y / (1.0d0 - z)) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) / t) * a);
	double tmp;
	if (t <= -2e+15) {
		tmp = t_1;
	} else if (t <= 7.5e+26) {
		tmp = x - ((y / (1.0 - z)) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) / t) * a)
	tmp = 0
	if t <= -2e+15:
		tmp = t_1
	elif t <= 7.5e+26:
		tmp = x - ((y / (1.0 - z)) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) / t) * a))
	tmp = 0.0
	if (t <= -2e+15)
		tmp = t_1;
	elseif (t <= 7.5e+26)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 - z)) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) / t) * a);
	tmp = 0.0;
	if (t <= -2e+15)
		tmp = t_1;
	elseif (t <= 7.5e+26)
		tmp = x - ((y / (1.0 - z)) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+15], t$95$1, If[LessEqual[t, 7.5e+26], N[(x - N[(N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2e15 or 7.49999999999999941e26 < t

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 82.7%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto x - \frac{\color{blue}{y - z}}{\frac{t}{a}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y - z}{\frac{t}{a}}} \]

      3. lift-/.f64 N/A

         \[\leadsto x - \frac{y - z}{\color{blue}{\frac{t}{a}}} \]

      4. associate-/r/ N/A

         \[\leadsto x - \color{blue}{\frac{y - z}{t} \cdot a} \]

      5. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y - z}{t} \cdot a} \]

      6. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y - z}{t}} \cdot a \]

      7. lift--.f64 83.4

         \[\leadsto x - \frac{\color{blue}{y - z}}{t} \cdot a \]

   6. Applied rewrites 83.4%

      \[\leadsto x - \color{blue}{\frac{y - z}{t} \cdot a} \]

   if -2e15 < t < 7.49999999999999941e26

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 28.7%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 37.0%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]

   8. Taylor expanded in t around 0

      \[\leadsto x - \frac{y}{\frac{\color{blue}{1 - z}}{a}} \]
   9. Step-by-step derivation

      1. lower--.f64 75.1

         \[\leadsto x - \frac{y}{\frac{1 - \color{blue}{z}}{a}} \]

   10. Applied rewrites 75.1%

       \[\leadsto x - \frac{y}{\frac{\color{blue}{1 - z}}{a}} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto x - \color{blue}{\frac{y}{\frac{1 - z}{a}}} \]

       2. lift-/.f64 N/A

          \[\leadsto x - \frac{y}{\color{blue}{\frac{1 - z}{a}}} \]

       3. associate-/r/ N/A

          \[\leadsto x - \color{blue}{\frac{y}{1 - z} \cdot a} \]

       4. lower-*.f64 N/A

          \[\leadsto x - \color{blue}{\frac{y}{1 - z} \cdot a} \]

       5. lower-/.f64 75.6

          \[\leadsto x - \color{blue}{\frac{y}{1 - z}} \cdot a \]

   12. Applied rewrites 75.6%

       \[\leadsto x - \color{blue}{\frac{y}{1 - z} \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0032:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{y}{1 - z} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -0.0032)
   (- x (/ y (/ t a)))
   (if (<= t 7.5e+26) (- x (* (/ y (- 1.0 z)) a)) (- x (* (/ y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.0032) {
		tmp = x - (y / (t / a));
	} else if (t <= 7.5e+26) {
		tmp = x - ((y / (1.0 - z)) * a);
	} else {
		tmp = x - ((y / t) * a);
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (t <= (-0.0032d0)) then
        tmp = x - (y / (t / a))
    else if (t <= 7.5d+26) then
        tmp = x - ((y / (1.0d0 - z)) * a)
    else
        tmp = x - ((y / t) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.0032) {
		tmp = x - (y / (t / a));
	} else if (t <= 7.5e+26) {
		tmp = x - ((y / (1.0 - z)) * a);
	} else {
		tmp = x - ((y / t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -0.0032:
		tmp = x - (y / (t / a))
	elif t <= 7.5e+26:
		tmp = x - ((y / (1.0 - z)) * a)
	else:
		tmp = x - ((y / t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.0032)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (t <= 7.5e+26)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 - z)) * a));
	else
		tmp = Float64(x - Float64(Float64(y / t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -0.0032)
		tmp = x - (y / (t / a));
	elseif (t <= 7.5e+26)
		tmp = x - ((y / (1.0 - z)) * a);
	else
		tmp = x - ((y / t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.0032], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+26], N[(x - N[(N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.00320000000000000015

   1. Initial program 96.0%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 81.0%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.9%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]

   if -0.00320000000000000015 < t < 7.49999999999999941e26

   1. Initial program 97.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 27.9%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 36.3%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]

   8. Taylor expanded in t around 0

      \[\leadsto x - \frac{y}{\frac{\color{blue}{1 - z}}{a}} \]
   9. Step-by-step derivation

      1. lower--.f64 75.7

         \[\leadsto x - \frac{y}{\frac{1 - \color{blue}{z}}{a}} \]

   10. Applied rewrites 75.7%

       \[\leadsto x - \frac{y}{\frac{\color{blue}{1 - z}}{a}} \]
   11. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto x - \color{blue}{\frac{y}{\frac{1 - z}{a}}} \]

       2. lift-/.f64 N/A

          \[\leadsto x - \frac{y}{\color{blue}{\frac{1 - z}{a}}} \]

       3. associate-/r/ N/A

          \[\leadsto x - \color{blue}{\frac{y}{1 - z} \cdot a} \]

       4. lower-*.f64 N/A

          \[\leadsto x - \color{blue}{\frac{y}{1 - z} \cdot a} \]

       5. lower-/.f64 76.3

          \[\leadsto x - \color{blue}{\frac{y}{1 - z}} \cdot a \]

   12. Applied rewrites 76.3%

       \[\leadsto x - \color{blue}{\frac{y}{1 - z} \cdot a} \]

   if 7.49999999999999941e26 < t

   1. Initial program 96.8%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 82.8%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 77.9%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{a}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{\color{blue}{\frac{t}{a}}} \]

      3. associate-/r/ N/A

         \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

      4. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

      5. lower-/.f64 78.5

         \[\leadsto x - \color{blue}{\frac{y}{t}} \cdot a \]

   9. Applied rewrites 78.5%

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

Alternative 7: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0032:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -0.0032)
   (- x (/ y (/ t a)))
   (if (<= t 1.0) (- x (* a y)) (- x (* (/ y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.0032) {
		tmp = x - (y / (t / a));
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - ((y / t) * a);
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (t <= (-0.0032d0)) then
        tmp = x - (y / (t / a))
    else if (t <= 1.0d0) then
        tmp = x - (a * y)
    else
        tmp = x - ((y / t) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.0032) {
		tmp = x - (y / (t / a));
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - ((y / t) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -0.0032:
		tmp = x - (y / (t / a))
	elif t <= 1.0:
		tmp = x - (a * y)
	else:
		tmp = x - ((y / t) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.0032)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (t <= 1.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - Float64(Float64(y / t) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -0.0032)
		tmp = x - (y / (t / a));
	elseif (t <= 1.0)
		tmp = x - (a * y);
	else
		tmp = x - ((y / t) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.0032], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.00320000000000000015

   1. Initial program 96.0%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 81.0%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.9%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]

   if -0.00320000000000000015 < t < 1

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 67.3

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

   4. Applied rewrites 67.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 67.2%

      \[\leadsto x - a \cdot y \]

   if 1 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 80.9%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 76.3%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{a}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{\color{blue}{\frac{t}{a}}} \]

      3. associate-/r/ N/A

         \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

      4. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

      5. lower-/.f64 76.8

         \[\leadsto x - \color{blue}{\frac{y}{t}} \cdot a \]

   9. Applied rewrites 76.8%

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

Alternative 8: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{t} \cdot a\\ \mathbf{if}\;t \leq -0.0032:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y t) a))))
   (if (<= t -0.0032) t_1 (if (<= t 1.0) (- x (* a y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / t) * a);
	double tmp;
	if (t <= -0.0032) {
		tmp = t_1;
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / t) * a)
    if (t <= (-0.0032d0)) then
        tmp = t_1
    else if (t <= 1.0d0) then
        tmp = x - (a * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / t) * a);
	double tmp;
	if (t <= -0.0032) {
		tmp = t_1;
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / t) * a)
	tmp = 0
	if t <= -0.0032:
		tmp = t_1
	elif t <= 1.0:
		tmp = x - (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / t) * a))
	tmp = 0.0
	if (t <= -0.0032)
		tmp = t_1;
	elseif (t <= 1.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / t) * a);
	tmp = 0.0;
	if (t <= -0.0032)
		tmp = t_1;
	elseif (t <= 1.0)
		tmp = x - (a * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0032], t$95$1, If[LessEqual[t, 1.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.00320000000000000015 or 1 < t

   1. Initial program 96.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]
   3. Step-by-step derivation

   4. Applied rewrites 81.0%

      \[\leadsto x - \frac{y - z}{\frac{\color{blue}{t}}{a}} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 75.6%

      \[\leadsto x - \frac{\color{blue}{y}}{\frac{t}{a}} \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{a}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x - \frac{y}{\color{blue}{\frac{t}{a}}} \]

      3. associate-/r/ N/A

         \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

      4. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

      5. lower-/.f64 76.5

         \[\leadsto x - \color{blue}{\frac{y}{t}} \cdot a \]

   9. Applied rewrites 76.5%

      \[\leadsto x - \color{blue}{\frac{y}{t} \cdot a} \]

   if -0.00320000000000000015 < t < 1

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 67.3

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

   4. Applied rewrites 67.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 67.2%

      \[\leadsto x - a \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 71.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-100}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+83)
   (- x a)
   (if (<= z 1.02e-100) (- x (* a y)) (if (<= z 4.2e+49) x (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+83) {
		tmp = x - a;
	} else if (z <= 1.02e-100) {
		tmp = x - (a * y);
	} else if (z <= 4.2e+49) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.3d+83)) then
        tmp = x - a
    else if (z <= 1.02d-100) then
        tmp = x - (a * y)
    else if (z <= 4.2d+49) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+83) {
		tmp = x - a;
	} else if (z <= 1.02e-100) {
		tmp = x - (a * y);
	} else if (z <= 4.2e+49) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+83:
		tmp = x - a
	elif z <= 1.02e-100:
		tmp = x - (a * y)
	elif z <= 4.2e+49:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+83)
		tmp = Float64(x - a);
	elseif (z <= 1.02e-100)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 4.2e+49)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+83)
		tmp = x - a;
	elseif (z <= 1.02e-100)
		tmp = x - (a * y);
	elseif (z <= 4.2e+49)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+83], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.02e-100], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+49], x, N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e83 or 4.20000000000000022e49 < z

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 80.8%

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

   if -4.3e83 < z < 1.02e-100

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 88.8

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

   4. Applied rewrites 88.8%

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

   5. Taylor expanded in t around 0

      \[\leadsto x - a \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 69.2%

      \[\leadsto x - a \cdot y \]

   if 1.02e-100 < z < 4.20000000000000022e49

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 54.7%

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

Alternative 10: 66.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -450000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -450000000.0) (- x a) (if (<= z 4.2e+49) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -450000000.0) {
		tmp = x - a;
	} else if (z <= 4.2e+49) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= (-450000000.0d0)) then
        tmp = x - a
    else if (z <= 4.2d+49) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -450000000.0) {
		tmp = x - a;
	} else if (z <= 4.2e+49) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -450000000.0:
		tmp = x - a
	elif z <= 4.2e+49:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -450000000.0)
		tmp = Float64(x - a);
	elseif (z <= 4.2e+49)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -450000000.0)
		tmp = x - a;
	elseif (z <= 4.2e+49)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -450000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.2e+49], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e8 or 4.20000000000000022e49 < z

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 78.0%

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

   if -4.5e8 < z < 4.20000000000000022e49

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 57.3%

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

Alternative 11: 54.1% accurate, 18.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 54.1%

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

Reproduce

herbie shell --seed 2025112 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64
  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))