AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 60.9% → 87.0%

Time: 8.7s

Alternatives: 13

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + 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, a, b)
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), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + 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, a, b)
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), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z - b}{a} \cdot \frac{y}{t + y} + \frac{t + y}{\left(t + x\right) + y}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 (- INFINITY))
     (- (+ a z) b)
     (if (<= t_1 2e+290)
       t_1
       (* (+ (* (/ (- z b) a) (/ y (+ t y))) (/ (+ t y) (+ (+ t x) y))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (a + z) - b;
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = ((((z - b) / a) * (y / (t + y))) + ((t + y) / ((t + x) + y))) * a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (a + z) - b;
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = ((((z - b) / a) * (y / (t + y))) + ((t + y) / ((t + x) + y))) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (a + z) - b
	elif t_1 <= 2e+290:
		tmp = t_1
	else:
		tmp = ((((z - b) / a) * (y / (t + y))) + ((t + y) / ((t + x) + y))) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(a + z) - b);
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(z - b) / a) * Float64(y / Float64(t + y))) + Float64(Float64(t + y) / Float64(Float64(t + x) + y))) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (a + z) - b;
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = ((((z - b) / a) * (y / (t + y))) + ((t + y) / ((t + x) + y))) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], t$95$1, N[(N[(N[(N[(N[(z - b), $MachinePrecision] / a), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0

   1. Initial program 6.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 69.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000012e290

   1. Initial program 99.1%

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

   if 2.00000000000000012e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.5%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 27.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.9%

      \[\leadsto \left(\frac{z - b}{a} \cdot \frac{y}{t + y} + \frac{t + y}{\left(t + x\right) + y}\right) \cdot a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+253}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+253))) (- (+ a z) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+253)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+253)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+253):
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+253))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+253)))
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+253]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999997e253 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 67.7%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999997e253

   1. Initial program 99.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+253}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+239} \lor \neg \left(t\_3 \leq 5 \cdot 10^{+253}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot x + t\_1\right) - y \cdot b}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2)))
   (if (or (<= t_3 -1e+239) (not (<= t_3 5e+253)))
     (- (+ a z) b)
     (/ (- (+ (* z x) t_1) (* y b)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -1e+239) || !(t_3 <= 5e+253)) {
		tmp = (a + z) - b;
	} else {
		tmp = (((z * x) + t_1) - (y * b)) / t_2;
	}
	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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t + y) * a
    t_2 = (x + t) + y
    t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2
    if ((t_3 <= (-1d+239)) .or. (.not. (t_3 <= 5d+253))) then
        tmp = (a + z) - b
    else
        tmp = (((z * x) + t_1) - (y * b)) / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -1e+239) || !(t_3 <= 5e+253)) {
		tmp = (a + z) - b;
	} else {
		tmp = (((z * x) + t_1) - (y * b)) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + y) * a
	t_2 = (x + t) + y
	t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -1e+239) or not (t_3 <= 5e+253):
		tmp = (a + z) - b
	else:
		tmp = (((z * x) + t_1) - (y * b)) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= -1e+239) || !(t_3 <= 5e+253))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(Float64(z * x) + t_1) - Float64(y * b)) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + y) * a;
	t_2 = (x + t) + y;
	t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -1e+239) || ~((t_3 <= 5e+253)))
		tmp = (a + z) - b;
	else
		tmp = (((z * x) + t_1) - (y * b)) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, -1e+239], N[Not[LessEqual[t$95$3, 5e+253]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(z * x), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999991e238 or 4.9999999999999997e253 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 68.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -9.99999999999999991e238 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999997e253

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 86.9%

      \[\leadsto \frac{\left(\color{blue}{z \cdot x} + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+239} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+253}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot x + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+198}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+198)))
     (- (+ a z) b)
     (/ (fma (+ t y) a (* (+ y x) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+198)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma((t + y), a, ((y + x) * z)) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+198))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+198]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000002e198 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 13.8%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 67.7%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000002e198

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 82.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}}{\left(x + t\right) + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+198}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+101} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+166}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, a \cdot t\right)}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+101) (not (<= t_1 4e+166)))
     (- (+ a z) b)
     (/ (fma z x (* a t)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+101) || !(t_1 <= 4e+166)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(z, x, (a * t)) / (x + t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+101) || !(t_1 <= 4e+166))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(z, x, Float64(a * t)) / Float64(x + t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+101], N[Not[LessEqual[t$95$1, 4e+166]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(z * x + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999989e101 or 3.99999999999999976e166 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 30.4%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 69.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -4.99999999999999989e101 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 3.99999999999999976e166

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, x, a \cdot t\right)}{x + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+101} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 4 \cdot 10^{+166}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, a \cdot t\right)}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+101} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+166}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+101) (not (<= t_1 4e+166)))
     (- (+ a z) b)
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+101) || !(t_1 <= 4e+166)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+101) || !(t_1 <= 4e+166))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+101], N[Not[LessEqual[t$95$1, 4e+166]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999989e101 or 3.99999999999999976e166 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 30.4%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 69.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -4.99999999999999989e101 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 3.99999999999999976e166

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 63.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+101} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 4 \cdot 10^{+166}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{\left(t + x\right) + y} \cdot a\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-132}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + y}{\left(x + t\right) + y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (+ t y) (+ (+ t x) y)) a)))
   (if (<= a -2.15e+86)
     t_1
     (if (<= a -2.45e-132)
       (- (+ a z) b)
       (if (<= a 1.25e+16) (* (/ (+ x y) (+ (+ x t) y)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) / ((t + x) + y)) * a;
	double tmp;
	if (a <= -2.15e+86) {
		tmp = t_1;
	} else if (a <= -2.45e-132) {
		tmp = (a + z) - b;
	} else if (a <= 1.25e+16) {
		tmp = ((x + y) / ((x + t) + y)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) / ((t + x) + y)) * a
    if (a <= (-2.15d+86)) then
        tmp = t_1
    else if (a <= (-2.45d-132)) then
        tmp = (a + z) - b
    else if (a <= 1.25d+16) then
        tmp = ((x + y) / ((x + t) + y)) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) / ((t + x) + y)) * a;
	double tmp;
	if (a <= -2.15e+86) {
		tmp = t_1;
	} else if (a <= -2.45e-132) {
		tmp = (a + z) - b;
	} else if (a <= 1.25e+16) {
		tmp = ((x + y) / ((x + t) + y)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) / ((t + x) + y)) * a
	tmp = 0
	if a <= -2.15e+86:
		tmp = t_1
	elif a <= -2.45e-132:
		tmp = (a + z) - b
	elif a <= 1.25e+16:
		tmp = ((x + y) / ((x + t) + y)) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) / Float64(Float64(t + x) + y)) * a)
	tmp = 0.0
	if (a <= -2.15e+86)
		tmp = t_1;
	elseif (a <= -2.45e-132)
		tmp = Float64(Float64(a + z) - b);
	elseif (a <= 1.25e+16)
		tmp = Float64(Float64(Float64(x + y) / Float64(Float64(x + t) + y)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) / ((t + x) + y)) * a;
	tmp = 0.0;
	if (a <= -2.15e+86)
		tmp = t_1;
	elseif (a <= -2.45e-132)
		tmp = (a + z) - b;
	elseif (a <= 1.25e+16)
		tmp = ((x + y) / ((x + t) + y)) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -2.15e+86], t$95$1, If[LessEqual[a, -2.45e-132], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 1.25e+16], N[(N[(N[(x + y), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1500000000000001e86 or 1.25e16 < a

   1. Initial program 48.6%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 70.5%

      \[\leadsto \frac{t + y}{\left(t + x\right) + y} \cdot a \]

   if -2.1500000000000001e86 < a < -2.4499999999999999e-132

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -2.4499999999999999e-132 < a < 1.25e16

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.9%

      \[\leadsto \frac{x + y}{\left(x + t\right) + y} \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 58.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+86} \lor \neg \left(a \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t + y}{\left(t + x\right) + y} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.15e+86) (not (<= a 1.9e+16)))
   (* (/ (+ t y) (+ (+ t x) y)) a)
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e+86) || !(a <= 1.9e+16)) {
		tmp = ((t + y) / ((t + x) + y)) * a;
	} else {
		tmp = (a + z) - b;
	}
	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, b)
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), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.15d+86)) .or. (.not. (a <= 1.9d+16))) then
        tmp = ((t + y) / ((t + x) + y)) * a
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e+86) || !(a <= 1.9e+16)) {
		tmp = ((t + y) / ((t + x) + y)) * a;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.15e+86) or not (a <= 1.9e+16):
		tmp = ((t + y) / ((t + x) + y)) * a
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.15e+86) || !(a <= 1.9e+16))
		tmp = Float64(Float64(Float64(t + y) / Float64(Float64(t + x) + y)) * a);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.15e+86) || ~((a <= 1.9e+16)))
		tmp = ((t + y) / ((t + x) + y)) * a;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.15e+86], N[Not[LessEqual[a, 1.9e+16]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1500000000000001e86 or 1.9e16 < a

   1. Initial program 48.6%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 70.5%

      \[\leadsto \frac{t + y}{\left(t + x\right) + y} \cdot a \]

   if -2.1500000000000001e86 < a < 1.9e16

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 54.4%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+86} \lor \neg \left(a \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t + y}{\left(t + x\right) + y} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+201} \lor \neg \left(b \leq 3.4 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{y}{\left(t + x\right) + y} \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.08e+201) (not (<= b 3.4e+170)))
   (* (/ y (+ (+ t x) y)) (- b))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.08e+201) || !(b <= 3.4e+170)) {
		tmp = (y / ((t + x) + y)) * -b;
	} else {
		tmp = (a + z) - b;
	}
	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, b)
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), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.08d+201)) .or. (.not. (b <= 3.4d+170))) then
        tmp = (y / ((t + x) + y)) * -b
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.08e+201) || !(b <= 3.4e+170)) {
		tmp = (y / ((t + x) + y)) * -b;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.08e+201) or not (b <= 3.4e+170):
		tmp = (y / ((t + x) + y)) * -b
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.08e+201) || !(b <= 3.4e+170))
		tmp = Float64(Float64(y / Float64(Float64(t + x) + y)) * Float64(-b));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.08e+201) || ~((b <= 3.4e+170)))
		tmp = (y / ((t + x) + y)) * -b;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.08e+201], N[Not[LessEqual[b, 3.4e+170]], $MachinePrecision]], N[(N[(y / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * (-b)), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.08000000000000006e201 or 3.4000000000000001e170 < b

   1. Initial program 49.8%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 63.2%

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

   if -1.08000000000000006e201 < b < 3.4000000000000001e170

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 56.9%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+201} \lor \neg \left(b \leq 3.4 \cdot 10^{+170}\right):\\ \;\;\;\;\frac{y}{\left(t + x\right) + y} \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+200} \lor \neg \left(b \leq 1.8 \cdot 10^{+234}\right):\\ \;\;\;\;\left(-y\right) \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.8e+200) (not (<= b 1.8e+234)))
   (* (- y) (/ b (+ (+ t x) y)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.8e+200) || !(b <= 1.8e+234)) {
		tmp = -y * (b / ((t + x) + y));
	} else {
		tmp = (a + z) - b;
	}
	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, b)
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), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.8d+200)) .or. (.not. (b <= 1.8d+234))) then
        tmp = -y * (b / ((t + x) + y))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.8e+200) || !(b <= 1.8e+234)) {
		tmp = -y * (b / ((t + x) + y));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.8e+200) or not (b <= 1.8e+234):
		tmp = -y * (b / ((t + x) + y))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.8e+200) || !(b <= 1.8e+234))
		tmp = Float64(Float64(-y) * Float64(b / Float64(Float64(t + x) + y)));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.8e+200) || ~((b <= 1.8e+234)))
		tmp = -y * (b / ((t + x) + y));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.8e+200], N[Not[LessEqual[b, 1.8e+234]], $MachinePrecision]], N[((-y) * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.8000000000000001e200 or 1.8e234 < b

   1. Initial program 47.2%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 67.1%

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

   7. Applied rewrites 64.8%

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

   if -4.8000000000000001e200 < b < 1.8e234

   1. Initial program 61.1%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 56.3%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+200} \lor \neg \left(b \leq 1.8 \cdot 10^{+234}\right):\\ \;\;\;\;\left(-y\right) \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+178}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+117}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3e+178) z (if (<= x 2.15e+117) (- (+ a z) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+178) {
		tmp = z;
	} else if (x <= 2.15e+117) {
		tmp = (a + z) - b;
	} 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, a, b)
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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3d+178)) then
        tmp = z
    else if (x <= 2.15d+117) then
        tmp = (a + z) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+178) {
		tmp = z;
	} else if (x <= 2.15e+117) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3e+178:
		tmp = z
	elif x <= 2.15e+117:
		tmp = (a + z) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3e+178)
		tmp = z;
	elseif (x <= 2.15e+117)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3e+178)
		tmp = z;
	elseif (x <= 2.15e+117)
		tmp = (a + z) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3e+178], z, If[LessEqual[x, 2.15e+117], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000016e178 or 2.14999999999999999e117 < x

   1. Initial program 44.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 53.0%

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

   if -3.00000000000000016e178 < x < 2.14999999999999999e117

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 59.5%

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

Alternative 12: 44.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+35}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+128}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.6e+35) z (if (<= z 1.65e+128) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+35) {
		tmp = z;
	} else if (z <= 1.65e+128) {
		tmp = a;
	} 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, a, b)
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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.6d+35)) then
        tmp = z
    else if (z <= 1.65d+128) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+35) {
		tmp = z;
	} else if (z <= 1.65e+128) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.6e+35:
		tmp = z
	elif z <= 1.65e+128:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.6e+35)
		tmp = z;
	elseif (z <= 1.65e+128)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.6e+35)
		tmp = z;
	elseif (z <= 1.65e+128)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.6e+35], z, If[LessEqual[z, 1.65e+128], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999997e35 or 1.65e128 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 55.3%

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

   if -5.59999999999999997e35 < z < 1.65e128

   1. Initial program 66.9%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 40.9%

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

Alternative 13: 32.7% accurate, 45.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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, b)
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), intent (in) :: b
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 58.8%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 32.2%

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

Developer Target 1: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2025019 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))