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

Percentage Accurate: 60.4% → 99.1%

Time: 25.2s

Alternatives: 14

Speedup: 1.2×

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: 60.4% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \mathsf{fma}\left(\frac{t + y}{t\_1}, a, \mathsf{fma}\left(\frac{z}{t\_1}, x, \frac{z - b}{t\_1} \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \mathsf{fma}\left(y, z - b, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (fma (/ (+ t y) t_1) a (fma (/ z t_1) x (* (/ (- z b) t_1) y)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 5e+224)
       (/ (fma (+ t y) a (fma y (- z b) (* z x))) 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 = fma(((t + y) / t_1), a, fma((z / t_1), x, (((z - b) / t_1) * y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 5e+224) {
		tmp = fma((t + y), a, fma(y, (z - b), (z * x))) / 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 = fma(Float64(Float64(t + y) / t_1), a, fma(Float64(z / t_1), x, Float64(Float64(Float64(z - b) / t_1) * y)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 5e+224)
		tmp = Float64(fma(Float64(t + y), a, fma(y, Float64(z - b), Float64(z * x))) / 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[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * a + N[(N[(z / t$95$1), $MachinePrecision] * x + N[(N[(N[(z - b), $MachinePrecision] / t$95$1), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 5e+224], N[(N[(N[(t + y), $MachinePrecision] * a + N[(y * N[(z - b), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 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 4.99999999999999964e224 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   5. Applied rewrites 93.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999964e224

   1. Initial program 60.4%

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

   3. Applied rewrites 60.6%

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

Alternative 2: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t\_1}, z - b, a\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \mathsf{fma}\left(y, z - b, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_1}, x + y, a - b\right)\\ \end{array} \end{array} \]

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 (<= t_2 (- INFINITY))
     (fma (/ y t_1) (- z b) a)
     (if (<= t_2 2e+268)
       (/ (fma (+ t y) a (fma y (- z b) (* z x))) t_1)
       (fma (/ z t_1) (+ x y) (- a b))))))

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)) {
		tmp = fma((y / t_1), (z - b), a);
	} else if (t_2 <= 2e+268) {
		tmp = fma((t + y), a, fma(y, (z - b), (z * x))) / t_1;
	} else {
		tmp = fma((z / t_1), (x + y), (a - b));
	}
	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))
		tmp = fma(Float64(y / t_1), Float64(z - b), a);
	elseif (t_2 <= 2e+268)
		tmp = Float64(fma(Float64(t + y), a, fma(y, Float64(z - b), Float64(z * x))) / t_1);
	else
		tmp = fma(Float64(z / t_1), Float64(x + y), Float64(a - b));
	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[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t$95$1), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$2, 2e+268], N[(N[(N[(t + y), $MachinePrecision] * a + N[(y * N[(z - b), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(z / t$95$1), $MachinePrecision] * N[(x + y), $MachinePrecision] + N[(a - b), $MachinePrecision]), $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 60.4%

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

   3. Applied rewrites 72.6%

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 67.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e268

   1. Initial program 60.4%

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

   3. Applied rewrites 60.6%

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

   if 1.9999999999999999e268 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.4%

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

   3. Applied rewrites 67.1%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 61.3%

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

Alternative 3: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \mathsf{fma}\left(\frac{t + y}{t\_1}, a, z - b\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-52}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t\_1}, z - b, a\right)\\ \mathbf{elif}\;x \leq 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)) (t_2 (fma (/ (+ t y) t_1) a (- z b))))
   (if (<= x -2e+138)
     t_2
     (if (<= x 3.4e-52)
       (fma (/ y t_1) (- z b) a)
       (if (<= x 1e+187) t_2 (+ z (/ (* y (- a b)) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = fma(((t + y) / t_1), a, (z - b));
	double tmp;
	if (x <= -2e+138) {
		tmp = t_2;
	} else if (x <= 3.4e-52) {
		tmp = fma((y / t_1), (z - b), a);
	} else if (x <= 1e+187) {
		tmp = t_2;
	} else {
		tmp = z + ((y * (a - b)) / (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = fma(Float64(Float64(t + y) / t_1), a, Float64(z - b))
	tmp = 0.0
	if (x <= -2e+138)
		tmp = t_2;
	elseif (x <= 3.4e-52)
		tmp = fma(Float64(y / t_1), Float64(z - b), a);
	elseif (x <= 1e+187)
		tmp = t_2;
	else
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	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[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+138], t$95$2, If[LessEqual[x, 3.4e-52], N[(N[(y / t$95$1), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[x, 1e+187], t$95$2, N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0000000000000001e138 or 3.40000000000000017e-52 < x < 9.99999999999999907e186

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 63.2%

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

   if -2.0000000000000001e138 < x < 3.40000000000000017e-52

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 67.4%

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

   if 9.99999999999999907e186 < x

   1. Initial program 60.4%

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

   3. Applied rewrites 67.1%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 49.2%

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

Alternative 4: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t\_1}, z - b, a\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+259}:\\ \;\;\;\;\mathsf{fma}\left(1, a, \frac{\mathsf{fma}\left(y, z - b, z \cdot x\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{t\_1}, a, z - b\right)\\ \end{array} \end{array} \]

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 (<= t_2 (- INFINITY))
     (fma (/ y t_1) (- z b) a)
     (if (<= t_2 1e+259)
       (fma 1.0 a (/ (fma y (- z b) (* z x)) t_1))
       (fma (/ (+ t y) t_1) a (- z b))))))

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)) {
		tmp = fma((y / t_1), (z - b), a);
	} else if (t_2 <= 1e+259) {
		tmp = fma(1.0, a, (fma(y, (z - b), (z * x)) / t_1));
	} else {
		tmp = fma(((t + y) / t_1), a, (z - b));
	}
	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))
		tmp = fma(Float64(y / t_1), Float64(z - b), a);
	elseif (t_2 <= 1e+259)
		tmp = fma(1.0, a, Float64(fma(y, Float64(z - b), Float64(z * x)) / t_1));
	else
		tmp = fma(Float64(Float64(t + y) / t_1), a, Float64(z - b));
	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[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t$95$1), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$2, 1e+259], N[(1.0 * a + N[(N[(y * N[(z - b), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $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 60.4%

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

   3. Applied rewrites 72.6%

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 67.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.999999999999999e258

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, a, \frac{\mathsf{fma}\left(y, z - b, z \cdot x\right)}{\left(x + t\right) + y}\right) \]

   6. Applied rewrites 60.2%

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, a, \frac{\mathsf{fma}\left(y, z - b, z \cdot x\right)}{\left(x + t\right) + y}\right) \]

   if 9.999999999999999e258 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 63.2%

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

Alternative 5: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t\_1}, z - b, a\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t + y, z \cdot \left(x + y\right)\right)}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_1}, x + y, a - b\right)\\ \end{array} \end{array} \]

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 (<= t_2 -1e+261)
     (fma (/ y t_1) (- z b) a)
     (if (<= t_2 2e+268)
       (/ (fma a (+ t y) (* z (+ x y))) (+ t (+ x y)))
       (fma (/ z t_1) (+ x y) (- a b))))))

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 <= -1e+261) {
		tmp = fma((y / t_1), (z - b), a);
	} else if (t_2 <= 2e+268) {
		tmp = fma(a, (t + y), (z * (x + y))) / (t + (x + y));
	} else {
		tmp = fma((z / t_1), (x + y), (a - b));
	}
	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 <= -1e+261)
		tmp = fma(Float64(y / t_1), Float64(z - b), a);
	elseif (t_2 <= 2e+268)
		tmp = Float64(fma(a, Float64(t + y), Float64(z * Float64(x + y))) / Float64(t + Float64(x + y)));
	else
		tmp = fma(Float64(z / t_1), Float64(x + y), Float64(a - b));
	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[LessEqual[t$95$2, -1e+261], N[(N[(y / t$95$1), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$2, 2e+268], N[(N[(a * N[(t + y), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / t$95$1), $MachinePrecision] * N[(x + y), $MachinePrecision] + N[(a - b), $MachinePrecision]), $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)) < -9.9999999999999993e260

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 67.4%

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

   if -9.9999999999999993e260 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e268

   1. Initial program 60.4%

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

   2. Taylor expanded in b around 0

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

   4. Applied rewrites 47.5%

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

   if 1.9999999999999999e268 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.4%

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

   3. Applied rewrites 67.1%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 61.3%

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

Alternative 6: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+186}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(x + t\right) + y}, z - b, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y)))))
   (if (<= x -7.4e+172)
     t_1
     (if (<= x 5.2e+186) (fma (/ y (+ (+ x t) y)) (- z b) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double tmp;
	if (x <= -7.4e+172) {
		tmp = t_1;
	} else if (x <= 5.2e+186) {
		tmp = fma((y / ((x + t) + y)), (z - b), a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	tmp = 0.0
	if (x <= -7.4e+172)
		tmp = t_1;
	elseif (x <= 5.2e+186)
		tmp = fma(Float64(y / Float64(Float64(x + t) + y)), Float64(z - b), a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.4e+172], t$95$1, If[LessEqual[x, 5.2e+186], N[(N[(y / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.39999999999999944e172 or 5.2000000000000001e186 < x

   1. Initial program 60.4%

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

   3. Applied rewrites 67.1%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 49.2%

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

   if -7.39999999999999944e172 < x < 5.2000000000000001e186

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 67.4%

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

Alternative 7: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-124}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-78}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (- b a))))
   (if (<= y -1.45e+65)
     t_1
     (if (<= y -2.6e-124)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= y 1.75e-78)
         (/ (fma a t (* x z)) (+ t x))
         (if (<= y 1.3e+103) (+ a (/ (* y (- z b)) (+ t y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b - a);
	double tmp;
	if (y <= -1.45e+65) {
		tmp = t_1;
	} else if (y <= -2.6e-124) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 1.75e-78) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (y <= 1.3e+103) {
		tmp = a + ((y * (z - b)) / (t + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (y <= -1.45e+65)
		tmp = t_1;
	elseif (y <= -2.6e-124)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 1.75e-78)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (y <= 1.3e+103)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / Float64(t + y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+65], t$95$1, If[LessEqual[y, -2.6e-124], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-78], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+103], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.45e65 or 1.3000000000000001e103 < y

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 55.1%

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

   6. Applied rewrites 55.1%

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

   if -1.45e65 < y < -2.6e-124

   1. Initial program 60.4%

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

   3. Applied rewrites 67.1%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 49.2%

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

   if -2.6e-124 < y < 1.75e-78

   1. Initial program 60.4%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.1%

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

   if 1.75e-78 < y < 1.3000000000000001e103

   1. Initial program 60.4%

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

   3. Applied rewrites 72.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 50.9%

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

Alternative 8: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y)))) (t_2 (- z (- b a))))
   (if (<= y -1.45e+65)
     t_2
     (if (<= y -2.6e-124)
       t_1
       (if (<= y 5.4e-111)
         (/ (fma a t (* x z)) (+ t x))
         (if (<= y 8e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = z - (b - a);
	double tmp;
	if (y <= -1.45e+65) {
		tmp = t_2;
	} else if (y <= -2.6e-124) {
		tmp = t_1;
	} else if (y <= 5.4e-111) {
		tmp = fma(a, t, (x * z)) / (t + x);
	} else if (y <= 8e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (y <= -1.45e+65)
		tmp = t_2;
	elseif (y <= -2.6e-124)
		tmp = t_1;
	elseif (y <= 5.4e-111)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(t + x));
	elseif (y <= 8e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+65], t$95$2, If[LessEqual[y, -2.6e-124], t$95$1, If[LessEqual[y, 5.4e-111], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e65 or 8.00000000000000046e84 < y

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 55.1%

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

   6. Applied rewrites 55.1%

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

   if -1.45e65 < y < -2.6e-124 or 5.39999999999999977e-111 < y < 8.00000000000000046e84

   1. Initial program 60.4%

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

   3. Applied rewrites 67.1%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 49.2%

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

   if -2.6e-124 < y < 5.39999999999999977e-111

   1. Initial program 60.4%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.1%

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

Alternative 9: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (- z (- b a))))
   (if (<= t_1 -5e+218)
     t_2
     (if (<= t_1 5e+157) (/ (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 = z - (b - a);
	double tmp;
	if (t_1 <= -5e+218) {
		tmp = t_2;
	} else if (t_1 <= 5e+157) {
		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(z - Float64(b - a))
	tmp = 0.0
	if (t_1 <= -5e+218)
		tmp = t_2;
	elseif (t_1 <= 5e+157)
		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[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+218], t$95$2, If[LessEqual[t$95$1, 5e+157], 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)) < -4.99999999999999983e218 or 4.99999999999999976e157 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 55.1%

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

   6. Applied rewrites 55.1%

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

   if -4.99999999999999983e218 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999976e157

   1. Initial program 60.4%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.1%

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

Alternative 10: 58.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (- b a))))
   (if (<= y -1.5e-71) t_1 (if (<= y 9.6e-119) (* (/ t (+ t x)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b - a);
	double tmp;
	if (y <= -1.5e-71) {
		tmp = t_1;
	} else if (y <= 9.6e-119) {
		tmp = (t / (t + x)) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, 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 = z - (b - a)
    if (y <= (-1.5d-71)) then
        tmp = t_1
    else if (y <= 9.6d-119) then
        tmp = (t / (t + x)) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b - a);
	double tmp;
	if (y <= -1.5e-71) {
		tmp = t_1;
	} else if (y <= 9.6e-119) {
		tmp = (t / (t + x)) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (b - a)
	tmp = 0
	if y <= -1.5e-71:
		tmp = t_1
	elif y <= 9.6e-119:
		tmp = (t / (t + x)) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (y <= -1.5e-71)
		tmp = t_1;
	elseif (y <= 9.6e-119)
		tmp = Float64(Float64(t / Float64(t + x)) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (b - a);
	tmp = 0.0;
	if (y <= -1.5e-71)
		tmp = t_1;
	elseif (y <= 9.6e-119)
		tmp = (t / (t + x)) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-71], t$95$1, If[LessEqual[y, 9.6e-119], N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e-71 or 9.60000000000000034e-119 < y

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 55.1%

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

   6. Applied rewrites 55.1%

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

   if -1.5000000000000001e-71 < y < 9.60000000000000034e-119

   1. Initial program 60.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 25.2%

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

   6. Applied rewrites 40.8%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 31.9%

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

Alternative 11: 55.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z - \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e+29) a (- z (- b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+29) {
		tmp = a;
	} else {
		tmp = z - (b - 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 <= (-1.35d+29)) then
        tmp = a
    else
        tmp = z - (b - 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 <= -1.35e+29) {
		tmp = a;
	} else {
		tmp = z - (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e+29:
		tmp = a
	else:
		tmp = z - (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e+29)
		tmp = a;
	else
		tmp = Float64(z - Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.35e+29)
		tmp = a;
	else
		tmp = z - (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e+29], a, N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e29

   1. Initial program 60.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 33.2%

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

   if -1.35e29 < t

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 55.1%

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

   6. Applied rewrites 55.1%

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

Alternative 12: 44.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-6}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+103}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e-6) a (if (<= a 1.05e+103) z (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e-6) {
		tmp = a;
	} else if (a <= 1.05e+103) {
		tmp = z;
	} else {
		tmp = a - 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 <= (-3.1d-6)) then
        tmp = a
    else if (a <= 1.05d+103) then
        tmp = z
    else
        tmp = a - 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 <= -3.1e-6) {
		tmp = a;
	} else if (a <= 1.05e+103) {
		tmp = z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e-6:
		tmp = a
	elif a <= 1.05e+103:
		tmp = z
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e-6)
		tmp = a;
	elseif (a <= 1.05e+103)
		tmp = z;
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.1e-6)
		tmp = a;
	elseif (a <= 1.05e+103)
		tmp = z;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e-6], a, If[LessEqual[a, 1.05e+103], z, N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1e-6

   1. Initial program 60.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 33.2%

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

   if -3.1e-6 < a < 1.0500000000000001e103

   1. Initial program 60.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 31.6%

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

   if 1.0500000000000001e103 < a

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 55.1%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 37.2%

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

Alternative 13: 44.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-6}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+103}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e-6) a (if (<= a 1.06e+103) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e-6) {
		tmp = a;
	} else if (a <= 1.06e+103) {
		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 <= (-3.1d-6)) then
        tmp = a
    else if (a <= 1.06d+103) 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 <= -3.1e-6) {
		tmp = a;
	} else if (a <= 1.06e+103) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e-6:
		tmp = a
	elif a <= 1.06e+103:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e-6)
		tmp = a;
	elseif (a <= 1.06e+103)
		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 <= -3.1e-6)
		tmp = a;
	elseif (a <= 1.06e+103)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e-6], a, If[LessEqual[a, 1.06e+103], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1e-6 or 1.0599999999999999e103 < a

   1. Initial program 60.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 33.2%

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

   if -3.1e-6 < a < 1.0599999999999999e103

   1. Initial program 60.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 31.6%

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

Alternative 14: 33.2% 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 60.4%

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

2. Taylor expanded in t around inf

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

4. Applied rewrites 33.2%

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

Reproduce

herbie shell --seed 2025153 
(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)))