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

Percentage Accurate: 60.9% → 98.7%

Time: 10.4s

Alternatives: 16

Speedup: 1.5×

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: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ \mathsf{fma}\left(\frac{x + y}{t\_1}, z, \frac{t + y}{t\_1} \cdot a - \frac{y}{t\_1} \cdot b\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))))
   (fma (/ (+ x y) t_1) z (- (* (/ (+ t y) t_1) a) (* (/ y t_1) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	return fma(((x + y) / t_1), z, ((((t + y) / t_1) * a) - ((y / t_1) * b)));
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	return fma(Float64(Float64(x + y) / t_1), z, Float64(Float64(Float64(Float64(t + y) / t_1) * a) - Float64(Float64(y / t_1) * b)))
end

Wolfram

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

Derivation

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. Taylor expanded in a around 0

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

4. Applied rewrites 71.9%

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

6. Applied rewrites 87.5%

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

8. Applied rewrites 98.7%

   \[\leadsto \mathsf{fma}\left(\frac{x + y}{t + \left(x + y\right)}, z, \frac{t + y}{t + \left(x + y\right)} \cdot a - \frac{y}{t + \left(x + y\right)} \cdot b\right) \]
9. Add Preprocessing

Alternative 2: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := t + \left(x + y\right)\\ t_3 := \mathsf{fma}\left(\frac{x + y}{t\_2}, z, a - \frac{y}{t\_2} \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ t (+ x y)))
        (t_3 (fma (/ (+ x y) t_2) z (- a (* (/ y t_2) b)))))
   (if (<= t_1 (- INFINITY)) t_3 (if (<= t_1 1e+257) t_1 t_3))))

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 t_2 = t + (x + y);
	double t_3 = fma(((x + y) / t_2), z, (a - ((y / t_2) * b)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_1 <= 1e+257) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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))
	t_2 = Float64(t + Float64(x + y))
	t_3 = fma(Float64(Float64(x + y) / t_2), z, Float64(a - Float64(Float64(y / t_2) * b)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_1 <= 1e+257)
		tmp = t_1;
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision] * z + N[(a - N[(N[(y / t$95$2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$3, If[LessEqual[t$95$1, 1e+257], t$95$1, t$95$3]]]]]

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 1.00000000000000003e257 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   6. Applied rewrites 87.5%

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

   8. Applied rewrites 98.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 84.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000003e257

   1. Initial program 60.9%

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

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \mathsf{fma}\left(\frac{x + y}{t + \left(x + y\right)}, z, a - b\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (fma (/ (+ x y) (+ t (+ x y))) z (- a b))))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 1e+257) t_1 t_2))))

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 t_2 = fma(((x + y) / (t + (x + y))), z, (a - b));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+257) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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))
	t_2 = fma(Float64(Float64(x + y) / Float64(t + Float64(x + y))), z, Float64(a - b))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+257)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+257], t$95$1, t$95$2]]]]

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 1.00000000000000003e257 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   6. Applied rewrites 87.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 63.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000003e257

   1. Initial program 60.9%

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

Alternative 4: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y}{t\_1}\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + y}{t\_1}, z, a - b\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+180}:\\ \;\;\;\;\left(a + z\right) - b \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (/ y t_1)))
   (if (<= z -1.46e+103)
     (fma (/ (+ x y) t_1) z (- a b))
     (if (<= z 4.3e+180) (- (+ a z) (* b t_2)) (* z (+ (/ x t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y / t_1;
	double tmp;
	if (z <= -1.46e+103) {
		tmp = fma(((x + y) / t_1), z, (a - b));
	} else if (z <= 4.3e+180) {
		tmp = (a + z) - (b * t_2);
	} else {
		tmp = z * ((x / t_1) + t_2);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if (z <= -1.46e+103)
		tmp = fma(Float64(Float64(x + y) / t_1), z, Float64(a - b));
	elseif (z <= 4.3e+180)
		tmp = Float64(Float64(a + z) - Float64(b * t_2));
	else
		tmp = Float64(z * Float64(Float64(x / t_1) + t_2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[z, -1.46e+103], N[(N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision] * z + N[(a - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+180], N[(N[(a + z), $MachinePrecision] - N[(b * t$95$2), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45999999999999998e103

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   6. Applied rewrites 87.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 63.4%

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

   if -1.45999999999999998e103 < z < 4.2999999999999999e180

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

   if 4.2999999999999999e180 < z

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 40.3%

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

Alternative 5: 73.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \mathsf{fma}\left(\frac{x + y}{t\_1}, z, a - b\right)\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+52}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (fma (/ (+ x y) t_1) z (- a b))))
   (if (<= z -1.46e+103)
     t_2
     (if (<= z 4.1e+52) (- (+ a z) (* b (/ y t_1))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = fma(((x + y) / t_1), z, (a - b));
	double tmp;
	if (z <= -1.46e+103) {
		tmp = t_2;
	} else if (z <= 4.1e+52) {
		tmp = (a + z) - (b * (y / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = fma(Float64(Float64(x + y) / t_1), z, Float64(a - b))
	tmp = 0.0
	if (z <= -1.46e+103)
		tmp = t_2;
	elseif (z <= 4.1e+52)
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision] * z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.46e+103], t$95$2, If[LessEqual[z, 4.1e+52], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45999999999999998e103 or 4.1e52 < z

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   6. Applied rewrites 87.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 63.4%

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

   if -1.45999999999999998e103 < z < 4.1e52

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

Alternative 6: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - \frac{b \cdot y}{t + \left(x + y\right)}\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := \left(a + z\right) - b \cdot \frac{y}{t + y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) (/ (* b y) (+ t (+ x y)))))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_3 (- (+ a z) (* b (/ y (+ t y))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1e-84)
       t_1
       (if (<= t_2 2e-80)
         (/ (fma a t (* x z)) (+ t x))
         (if (<= t_2 5e+107) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - ((b * y) / (t + (x + y)));
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_3 = (a + z) - (b * (y / (t + y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e-84) {
		tmp = t_1;
	} else if (t_2 <= 2e-80) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (t_2 <= 5e+107) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - Float64(Float64(b * y) / Float64(t + Float64(x + y))))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(t + y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e-84)
		tmp = t_1;
	elseif (t_2 <= 2e-80)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (t_2 <= 5e+107)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e-84], t$95$1, If[LessEqual[t$95$2, 2e-80], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+107], t$95$1, t$95$3]]]]]]]

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 or 5.0000000000000002e107 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 64.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1e-84 or 1.99999999999999992e-80 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e107

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 59.7%

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

   if -1e-84 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999992e-80

   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. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

Alternative 7: 69.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))))
   (if (<= a -1.1e+63) (* a (/ (+ t y) t_1)) (- (+ a z) (* b (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double tmp;
	if (a <= -1.1e+63) {
		tmp = a * ((t + y) / t_1);
	} else {
		tmp = (a + z) - (b * (y / 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 + (x + y)
    if (a <= (-1.1d+63)) then
        tmp = a * ((t + y) / t_1)
    else
        tmp = (a + z) - (b * (y / 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 + (x + y);
	double tmp;
	if (a <= -1.1e+63) {
		tmp = a * ((t + y) / t_1);
	} else {
		tmp = (a + z) - (b * (y / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	tmp = 0
	if a <= -1.1e+63:
		tmp = a * ((t + y) / t_1)
	else:
		tmp = (a + z) - (b * (y / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (a <= -1.1e+63)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	else
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	tmp = 0.0;
	if (a <= -1.1e+63)
		tmp = a * ((t + y) / t_1);
	else
		tmp = (a + z) - (b * (y / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+63], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e63

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   6. Applied rewrites 87.5%

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

   7. Taylor expanded in a around inf

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

   9. Applied rewrites 39.8%

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

   11. Applied rewrites 39.8%

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

   if -1.0999999999999999e63 < a

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

Alternative 8: 69.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b \cdot \frac{y}{t + y}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-84}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+107}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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))
        (t_3 (- (+ a z) (* b (/ y (+ t y))))))
   (if (<= t_2 -1e-84)
     t_3
     (if (<= t_2 1e-77)
       (/ (fma a t (* x z)) (+ t x))
       (if (<= t_2 5e+107) (/ (* y (- z b)) t_1) t_3)))))

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 t_3 = (a + z) - (b * (y / (t + y)));
	double tmp;
	if (t_2 <= -1e-84) {
		tmp = t_3;
	} else if (t_2 <= 1e-77) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (t_2 <= 5e+107) {
		tmp = (y * (z - b)) / t_1;
	} else {
		tmp = t_3;
	}
	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)
	t_3 = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(t + y))))
	tmp = 0.0
	if (t_2 <= -1e-84)
		tmp = t_3;
	elseif (t_2 <= 1e-77)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (t_2 <= 5e+107)
		tmp = Float64(Float64(y * Float64(z - b)) / t_1);
	else
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-84], t$95$3, If[LessEqual[t$95$2, 1e-77], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+107], N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]

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)) < -1e-84 or 5.0000000000000002e107 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 64.6%

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

   if -1e-84 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999993e-78

   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. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

   if 9.9999999999999993e-78 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e107

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 30.4%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 22.5%

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

Alternative 9: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b \cdot \frac{y}{t + y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) (* b (/ y (+ t y))))))
   (if (<= t_1 -1e-84)
     t_2
     (if (<= t_1 1e-63) (/ (fma a t (* x z)) (+ t x)) t_2))))

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 t_2 = (a + z) - (b * (y / (t + y)));
	double tmp;
	if (t_1 <= -1e-84) {
		tmp = t_2;
	} else if (t_1 <= 1e-63) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else {
		tmp = t_2;
	}
	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))
	t_2 = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(t + y))))
	tmp = 0.0
	if (t_1 <= -1e-84)
		tmp = t_2;
	elseif (t_1 <= 1e-63)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-84], t$95$2, If[LessEqual[t$95$1, 1e-63], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

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)) < -1e-84 or 1.00000000000000007e-63 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 64.6%

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

   if -1e-84 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000007e-63

   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. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

Alternative 10: 64.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \frac{t + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.1e+63)
   (* a (/ (+ t y) (+ t (+ x y))))
   (- (+ a z) (* b (/ y (+ t y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.1e+63) {
		tmp = a * ((t + y) / (t + (x + y)));
	} else {
		tmp = (a + z) - (b * (y / (t + y)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-1.1d+63)) then
        tmp = a * ((t + y) / (t + (x + y)))
    else
        tmp = (a + z) - (b * (y / (t + y)))
    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 <= -1.1e+63) {
		tmp = a * ((t + y) / (t + (x + y)));
	} else {
		tmp = (a + z) - (b * (y / (t + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.1e+63:
		tmp = a * ((t + y) / (t + (x + y)))
	else:
		tmp = (a + z) - (b * (y / (t + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.1e+63)
		tmp = Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y))));
	else
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(t + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.1e+63)
		tmp = a * ((t + y) / (t + (x + y)));
	else
		tmp = (a + z) - (b * (y / (t + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.1e+63], N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e63

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 71.9%

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

   6. Applied rewrites 87.5%

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

   7. Taylor expanded in a around inf

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

   9. Applied rewrites 39.8%

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

   11. Applied rewrites 39.8%

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

   if -1.0999999999999999e63 < a

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 64.6%

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

Alternative 11: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-63}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 -4e+96)
     t_2
     (if (<= t_1 1e-63) (/ (fma a t (* x z)) (+ t x)) t_2))))

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 t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -4e+96) {
		tmp = t_2;
	} else if (t_1 <= 1e-63) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else {
		tmp = t_2;
	}
	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))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= -4e+96)
		tmp = t_2;
	elseif (t_1 <= 1e-63)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+96], t$95$2, If[LessEqual[t$95$1, 1e-63], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

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)) < -4.0000000000000002e96 or 1.00000000000000007e-63 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 55.8%

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

   if -4.0000000000000002e96 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000007e-63

   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. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

Alternative 12: 59.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+198}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.5e+84)
   (- (+ a z) (* b (/ y t)))
   (if (<= t 7.2e+198) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+84) {
		tmp = (a + z) - (b * (y / t));
	} else if (t <= 7.2e+198) {
		tmp = (a + z) - b;
	} else {
		tmp = 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, 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 (t <= (-1.5d+84)) then
        tmp = (a + z) - (b * (y / t))
    else if (t <= 7.2d+198) then
        tmp = (a + z) - b
    else
        tmp = a
    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 (t <= -1.5e+84) {
		tmp = (a + z) - (b * (y / t));
	} else if (t <= 7.2e+198) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.5e+84:
		tmp = (a + z) - (b * (y / t))
	elif t <= 7.2e+198:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.5e+84)
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / t)));
	elseif (t <= 7.2e+198)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.5e+84)
		tmp = (a + z) - (b * (y / t));
	elseif (t <= 7.2e+198)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.5e+84], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+198], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if t < -1.49999999999999998e84

   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. Taylor expanded in z around 0

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

   4. Applied rewrites 72.7%

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

   6. Applied rewrites 79.7%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 70.4%

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

   10. Taylor expanded in t around inf

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

   12. Applied rewrites 39.2%

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

   if -1.49999999999999998e84 < t < 7.2000000000000004e198

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 55.8%

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

   if 7.2000000000000004e198 < t

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.5%

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

Alternative 13: 58.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-63}:\\ \;\;\;\;\frac{a \cdot t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 -5e-92) t_2 (if (<= t_1 1e-63) (/ (* a t) (+ t x)) t_2))))

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 t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -5e-92) {
		tmp = t_2;
	} else if (t_1 <= 1e-63) {
		tmp = (a * t) / (t + x);
	} else {
		tmp = 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) :: tmp
    t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
    t_2 = (a + z) - b
    if (t_1 <= (-5d-92)) then
        tmp = t_2
    else if (t_1 <= 1d-63) then
        tmp = (a * t) / (t + x)
    else
        tmp = 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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -5e-92) {
		tmp = t_2;
	} else if (t_1 <= 1e-63) {
		tmp = (a * t) / (t + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = (a + z) - b
	tmp = 0
	if t_1 <= -5e-92:
		tmp = t_2
	elif t_1 <= 1e-63:
		tmp = (a * t) / (t + x)
	else:
		tmp = t_2
	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))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= -5e-92)
		tmp = t_2;
	elseif (t_1 <= 1e-63)
		tmp = Float64(Float64(a * t) / Float64(t + x));
	else
		tmp = t_2;
	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);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (t_1 <= -5e-92)
		tmp = t_2;
	elseif (t_1 <= 1e-63)
		tmp = (a * t) / (t + x);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-92], t$95$2, If[LessEqual[t$95$1, 1e-63], N[(N[(a * t), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

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)) < -5.00000000000000011e-92 or 1.00000000000000007e-63 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 55.8%

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

   if -5.00000000000000011e-92 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000007e-63

   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. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 21.7%

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

Alternative 14: 57.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+221}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+198}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3e+221) a (if (<= t 7.2e+198) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3e+221) {
		tmp = a;
	} else if (t <= 7.2e+198) {
		tmp = (a + z) - b;
	} else {
		tmp = 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, 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 (t <= (-3d+221)) then
        tmp = a
    else if (t <= 7.2d+198) then
        tmp = (a + z) - b
    else
        tmp = a
    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 (t <= -3e+221) {
		tmp = a;
	} else if (t <= 7.2e+198) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3e+221:
		tmp = a
	elif t <= 7.2e+198:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3e+221)
		tmp = a;
	elseif (t <= 7.2e+198)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3e+221)
		tmp = a;
	elseif (t <= 7.2e+198)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3e+221], a, If[LessEqual[t, 7.2e+198], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0000000000000001e221 or 7.2000000000000004e198 < t

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.5%

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

   if -3.0000000000000001e221 < t < 7.2000000000000004e198

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 55.8%

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

Alternative 15: 44.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.16 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+105}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.16e-16) a (if (<= a 3.6e+105) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.16e-16) {
		tmp = a;
	} else if (a <= 3.6e+105) {
		tmp = z;
	} else {
		tmp = 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, 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 <= (-2.16d-16)) then
        tmp = a
    else if (a <= 3.6d+105) then
        tmp = z
    else
        tmp = a
    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 <= -2.16e-16) {
		tmp = a;
	} else if (a <= 3.6e+105) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.16e-16:
		tmp = a
	elif a <= 3.6e+105:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.16e-16)
		tmp = a;
	elseif (a <= 3.6e+105)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.16e-16)
		tmp = a;
	elseif (a <= 3.6e+105)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.16e-16], a, If[LessEqual[a, 3.6e+105], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1600000000000001e-16 or 3.5999999999999999e105 < a

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.5%

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

   if -2.1600000000000001e-16 < a < 3.5999999999999999e105

   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. Taylor expanded in x around inf

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

   4. Applied rewrites 32.9%

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

Alternative 16: 32.5% accurate, 29.5× 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 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. Taylor expanded in t around inf

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

4. Applied rewrites 32.5%

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

Reproduce

herbie shell --seed 2025161 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64
  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))