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

Percentage Accurate: 60.9% → 88.1%

Time: 13.1s

Alternatives: 14

Speedup: 0.8×

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

real(8) function code(x, y, z, t, a, b)
    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

real(8) function code(x, y, z, t, a, b)
    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: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 -5e+251) t_2 (if (<= t_1 1e+308) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -5e+251) {
		tmp = t_2;
	} else if (t_1 <= 1e+308) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
    t_2 = (z + a) - b
    if (t_1 <= (-5d+251)) then
        tmp = t_2
    else if (t_1 <= 1d+308) then
        tmp = t_1
    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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -5e+251) {
		tmp = t_2;
	} else if (t_1 <= 1e+308) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -5e+251:
		tmp = t_2
	elif t_1 <= 1e+308:
		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(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= -5e+251)
		tmp = t_2;
	elseif (t_1 <= 1e+308)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -5e+251)
		tmp = t_2;
	elseif (t_1 <= 1e+308)
		tmp = t_1;
	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[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+251], t$95$2, If[LessEqual[t$95$1, 1e+308], 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)) < -5.0000000000000005e251 or 1e308 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.4%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 71.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 71.9%

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

   if -5.0000000000000005e251 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e308

   1. Initial program 99.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+251}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+308}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := z \cdot \left(\frac{a}{z} + \frac{1}{\frac{t\_1}{x + y}}\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 0.00055:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{1}{\frac{t\_1}{y + t}}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (* z (+ (/ a z) (/ 1.0 (/ t_1 (+ x y)))))))
   (if (<= z -2.45e-164)
     t_2
     (if (<= z 8.2e-98)
       (/ (- (* (+ y t) a) (* y b)) (+ y (+ x t)))
       (if (<= z 0.00055) (* a (+ (/ z a) (/ 1.0 (/ t_1 (+ y t))))) 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 = z * ((a / z) + (1.0 / (t_1 / (x + y))));
	double tmp;
	if (z <= -2.45e-164) {
		tmp = t_2;
	} else if (z <= 8.2e-98) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (z <= 0.00055) {
		tmp = a * ((z / a) + (1.0 / (t_1 / (y + t))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 = t + (x + y)
    t_2 = z * ((a / z) + (1.0d0 / (t_1 / (x + y))))
    if (z <= (-2.45d-164)) then
        tmp = t_2
    else if (z <= 8.2d-98) then
        tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
    else if (z <= 0.00055d0) then
        tmp = a * ((z / a) + (1.0d0 / (t_1 / (y + t))))
    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 = t + (x + y);
	double t_2 = z * ((a / z) + (1.0 / (t_1 / (x + y))));
	double tmp;
	if (z <= -2.45e-164) {
		tmp = t_2;
	} else if (z <= 8.2e-98) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (z <= 0.00055) {
		tmp = a * ((z / a) + (1.0 / (t_1 / (y + t))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = z * ((a / z) + (1.0 / (t_1 / (x + y))))
	tmp = 0
	if z <= -2.45e-164:
		tmp = t_2
	elif z <= 8.2e-98:
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
	elif z <= 0.00055:
		tmp = a * ((z / a) + (1.0 / (t_1 / (y + t))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(z * Float64(Float64(a / z) + Float64(1.0 / Float64(t_1 / Float64(x + y)))))
	tmp = 0.0
	if (z <= -2.45e-164)
		tmp = t_2;
	elseif (z <= 8.2e-98)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (z <= 0.00055)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(1.0 / Float64(t_1 / Float64(y + t)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = z * ((a / z) + (1.0 / (t_1 / (x + y))));
	tmp = 0.0;
	if (z <= -2.45e-164)
		tmp = t_2;
	elseif (z <= 8.2e-98)
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	elseif (z <= 0.00055)
		tmp = a * ((z / a) + (1.0 / (t_1 / (y + t))));
	else
		tmp = t_2;
	end
	tmp_2 = 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[(z * N[(N[(a / z), $MachinePrecision] + N[(1.0 / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e-164], t$95$2, If[LessEqual[z, 8.2e-98], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00055], N[(a * N[(N[(z / a), $MachinePrecision] + N[(1.0 / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4499999999999998e-164 or 5.50000000000000033e-4 < z

   1. Initial program 54.9%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\color{blue}{-1 \cdot \frac{x + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(0 - z\right), \left(\color{blue}{-1 \cdot \frac{x + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\color{blue}{-1 \cdot \frac{x + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)}\right), \color{blue}{\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

   5. Simplified 65.5%

      \[\leadsto \color{blue}{\left(0 - z\right) \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\left(\frac{1}{\frac{t + \left(y + x\right)}{\left(\mathsf{neg}\left(x\right)\right) - y}}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right)}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{t + \left(y + x\right)}{\left(\mathsf{neg}\left(x\right)\right) - y}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right)}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(t + \left(y + x\right)\right), \left(\left(\mathsf{neg}\left(x\right)\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \color{blue}{\mathsf{*.f64}\left(y, b\right)}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y + x\right)\right), \left(\left(\mathsf{neg}\left(x\right)\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(\left(\mathsf{neg}\left(x\right)\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(\left(0 - x\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      7. associate--l- N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(0 - \left(x + y\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(0 - \left(y + x\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \left(y + x\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      10. +-lowering-+.f64 65.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(y, x\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 65.5%

      \[\leadsto \left(0 - z\right) \cdot \left(\color{blue}{\frac{1}{\frac{t + \left(y + x\right)}{0 - \left(y + x\right)}}} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(y, x\right)\right)\right)\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 77.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(y, x\right)\right)\right)\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 77.4%

       \[\leadsto \left(0 - z\right) \cdot \left(\frac{1}{\frac{t + \left(y + x\right)}{0 - \left(y + x\right)}} - \color{blue}{\frac{a}{z}}\right) \]

   if -2.4499999999999998e-164 < z < 8.1999999999999996e-98

   1. Initial program 78.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(a \cdot \left(t + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot \left(t + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(t + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      5. *-lowering-*.f64 71.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 71.3%

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

   if 8.1999999999999996e-98 < z < 5.50000000000000033e-4

   1. Initial program 80.5%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(0 - a\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\left(-1 \cdot \frac{t + y}{t + \left(x + y\right)}\right), \color{blue}{\left(\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)}\right)\right) \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{\left(0 - a\right) \cdot \left(\frac{\left(-t\right) - y}{t + \left(y + x\right)} - \frac{z \cdot \left(y + x\right) - y \cdot b}{a \cdot \left(t + \left(y + x\right)\right)}\right)} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\left(\frac{1}{\frac{t + \left(y + x\right)}{\left(\mathsf{neg}\left(t\right)\right) - y}}\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right)}, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{t + \left(y + x\right)}{\left(\mathsf{neg}\left(t\right)\right) - y}\right)\right), \mathsf{/.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right)}, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(t + \left(y + x\right)\right), \left(\left(\mathsf{neg}\left(t\right)\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \color{blue}{\mathsf{*.f64}\left(y, b\right)}\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y + x\right)\right), \left(\left(\mathsf{neg}\left(t\right)\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, b\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(\left(\mathsf{neg}\left(t\right)\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(\left(0 - t\right) - y\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      7. associate--l- N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(0 - \left(t + y\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \left(t + y\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 80.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(t, y\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 80.4%

      \[\leadsto \left(0 - a\right) \cdot \left(\color{blue}{\frac{1}{\frac{t + \left(y + x\right)}{0 - \left(t + y\right)}}} - \frac{z \cdot \left(y + x\right) - y \cdot b}{a \cdot \left(t + \left(y + x\right)\right)}\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(t, y\right)\right)\right)\right), \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 81.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(t, y\right)\right)\right)\right), \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   10. Simplified 81.0%

       \[\leadsto \left(0 - a\right) \cdot \left(\frac{1}{\frac{t + \left(y + x\right)}{0 - \left(t + y\right)}} - \color{blue}{\frac{z}{a}}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \frac{1}{\frac{t + \left(x + y\right)}{x + y}}\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-98}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 0.00055:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + \frac{1}{\frac{t + \left(x + y\right)}{y + t}}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \frac{1}{\frac{t + \left(x + y\right)}{x + y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6400000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{-1}{\frac{t + \left(x + y\right)}{y \cdot b - z \cdot \left(x + y\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6400000000.0)
     t_1
     (if (<= y 3.6e-46)
       (* a (+ (/ t (+ x t)) (/ (* x z) (* a (+ x t)))))
       (if (<= y 3.5e+47)
         (/ -1.0 (/ (+ t (+ x y)) (- (* y b) (* z (+ x y)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6400000000.0) {
		tmp = t_1;
	} else if (y <= 3.6e-46) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else if (y <= 3.5e+47) {
		tmp = -1.0 / ((t + (x + y)) / ((y * b) - (z * (x + y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 + a) - b
    if (y <= (-6400000000.0d0)) then
        tmp = t_1
    else if (y <= 3.6d-46) then
        tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
    else if (y <= 3.5d+47) then
        tmp = (-1.0d0) / ((t + (x + y)) / ((y * b) - (z * (x + y))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6400000000.0) {
		tmp = t_1;
	} else if (y <= 3.6e-46) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else if (y <= 3.5e+47) {
		tmp = -1.0 / ((t + (x + y)) / ((y * b) - (z * (x + y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6400000000.0:
		tmp = t_1
	elif y <= 3.6e-46:
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
	elif y <= 3.5e+47:
		tmp = -1.0 / ((t + (x + y)) / ((y * b) - (z * (x + y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6400000000.0)
		tmp = t_1;
	elseif (y <= 3.6e-46)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(Float64(x * z) / Float64(a * Float64(x + t)))));
	elseif (y <= 3.5e+47)
		tmp = Float64(-1.0 / Float64(Float64(t + Float64(x + y)) / Float64(Float64(y * b) - Float64(z * Float64(x + y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6400000000.0)
		tmp = t_1;
	elseif (y <= 3.6e-46)
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	elseif (y <= 3.5e+47)
		tmp = -1.0 / ((t + (x + y)) / ((y * b) - (z * (x + y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6400000000.0], t$95$1, If[LessEqual[y, 3.6e-46], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(a * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+47], N[(-1.0 / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] - N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4e9 or 3.50000000000000015e47 < y

   1. Initial program 43.3%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 78.4%

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

   if -6.4e9 < y < 3.6e-46

   1. Initial program 73.7%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 61.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 61.3%

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

   6. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t}{t + x} + \frac{x \cdot z}{a \cdot \left(t + x\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(\frac{t}{t + x}\right), \color{blue}{\left(\frac{x \cdot z}{a \cdot \left(t + x\right)}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \left(t + x\right)\right), \left(\frac{\color{blue}{x \cdot z}}{a \cdot \left(t + x\right)}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \left(\frac{x \cdot \color{blue}{z}}{a \cdot \left(t + x\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{\left(a \cdot \left(t + x\right)\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\color{blue}{a} \cdot \left(t + x\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{*.f64}\left(a, \color{blue}{\left(t + x\right)}\right)\right)\right)\right) \]

      8. +-lowering-+.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right)\right)\right) \]

   8. Simplified 69.0%

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

   if 3.6e-46 < y < 3.50000000000000015e47

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      6. *-lowering-*.f64 77.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 77.3%

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

      1. clear-num N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(x + t\right) + y}{z \cdot \left(y + x\right) - y \cdot b}\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(t + x\right) + y}{\color{blue}{z} \cdot \left(y + x\right) - y \cdot b}\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{t + \left(x + y\right)}{\color{blue}{z \cdot \left(y + x\right)} - y \cdot b}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{t + \left(y + x\right)}{z \cdot \color{blue}{\left(y + x\right)} - y \cdot b}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(t + \left(y + x\right)\right), \color{blue}{\left(z \cdot \left(y + x\right) - y \cdot b\right)}\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left(y + x\right)\right), \left(\color{blue}{z \cdot \left(y + x\right)} - y \cdot b\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \left(z \cdot \color{blue}{\left(y + x\right)} - y \cdot b\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(y + x\right)\right), \color{blue}{\left(y \cdot b\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(\left(\left(y + x\right) \cdot z\right), \left(\color{blue}{y} \cdot b\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(y + x\right), z\right), \left(\color{blue}{y} \cdot b\right)\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, x\right), z\right), \left(y \cdot b\right)\right)\right)\right) \]

      13. *-lowering-*.f64 77.3%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, x\right), z\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right)\right)\right) \]

   7. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{t + \left(y + x\right)}{\left(y + x\right) \cdot z - y \cdot b}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6400000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{-1}{\frac{t + \left(x + y\right)}{y \cdot b - z \cdot \left(x + y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6000000000.0)
     t_1
     (if (<= y 7.5e-46)
       (* a (+ (/ t (+ x t)) (/ (* x z) (* a (+ x t)))))
       (if (<= y 5.2e+46) (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6000000000.0) {
		tmp = t_1;
	} else if (y <= 7.5e-46) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else if (y <= 5.2e+46) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 + a) - b
    if (y <= (-6000000000.0d0)) then
        tmp = t_1
    else if (y <= 7.5d-46) then
        tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
    else if (y <= 5.2d+46) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6000000000.0) {
		tmp = t_1;
	} else if (y <= 7.5e-46) {
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	} else if (y <= 5.2e+46) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6000000000.0:
		tmp = t_1
	elif y <= 7.5e-46:
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))))
	elif y <= 5.2e+46:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6000000000.0)
		tmp = t_1;
	elseif (y <= 7.5e-46)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(Float64(x * z) / Float64(a * Float64(x + t)))));
	elseif (y <= 5.2e+46)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6000000000.0)
		tmp = t_1;
	elseif (y <= 7.5e-46)
		tmp = a * ((t / (x + t)) + ((x * z) / (a * (x + t))));
	elseif (y <= 5.2e+46)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6000000000.0], t$95$1, If[LessEqual[y, 7.5e-46], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(a * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+46], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e9 or 5.20000000000000027e46 < y

   1. Initial program 43.3%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 78.4%

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

   if -6e9 < y < 7.50000000000000027e-46

   1. Initial program 73.7%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 61.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 61.3%

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

   6. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t}{t + x} + \frac{x \cdot z}{a \cdot \left(t + x\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(\frac{t}{t + x}\right), \color{blue}{\left(\frac{x \cdot z}{a \cdot \left(t + x\right)}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \left(t + x\right)\right), \left(\frac{\color{blue}{x \cdot z}}{a \cdot \left(t + x\right)}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \left(\frac{x \cdot \color{blue}{z}}{a \cdot \left(t + x\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{\left(a \cdot \left(t + x\right)\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\color{blue}{a} \cdot \left(t + x\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{*.f64}\left(a, \color{blue}{\left(t + x\right)}\right)\right)\right)\right) \]

      8. +-lowering-+.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right)\right)\right) \]

   8. Simplified 69.0%

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

   if 7.50000000000000027e-46 < y < 5.20000000000000027e46

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      6. *-lowering-*.f64 77.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 77.3%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{x \cdot z}{a \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+46}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.6e-35)
     t_1
     (if (<= y 5.5e-46)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 4e+46) (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.6e-35) {
		tmp = t_1;
	} else if (y <= 5.5e-46) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4e+46) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 + a) - b
    if (y <= (-3.6d-35)) then
        tmp = t_1
    else if (y <= 5.5d-46) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4d+46) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.6e-35) {
		tmp = t_1;
	} else if (y <= 5.5e-46) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4e+46) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.6e-35:
		tmp = t_1
	elif y <= 5.5e-46:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4e+46:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.6e-35)
		tmp = t_1;
	elseif (y <= 5.5e-46)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4e+46)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.6e-35)
		tmp = t_1;
	elseif (y <= 5.5e-46)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4e+46)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.6e-35], t$95$1, If[LessEqual[y, 5.5e-46], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+46], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000019e-35 or 4e46 < y

   1. Initial program 45.5%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 75.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 75.1%

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

   if -3.60000000000000019e-35 < y < 5.49999999999999983e-46

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 63.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 63.4%

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

   if 5.49999999999999983e-46 < y < 4e46

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      6. *-lowering-*.f64 77.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 77.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+46}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-45}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.2e-35)
     t_1
     (if (<= y 1.15e-45)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 3.45e+47) (/ (* y t_1) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.2e-35) {
		tmp = t_1;
	} else if (y <= 1.15e-45) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3.45e+47) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 + a) - b
    if (y <= (-3.2d-35)) then
        tmp = t_1
    else if (y <= 1.15d-45) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 3.45d+47) then
        tmp = (y * t_1) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.2e-35) {
		tmp = t_1;
	} else if (y <= 1.15e-45) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3.45e+47) {
		tmp = (y * t_1) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.2e-35:
		tmp = t_1
	elif y <= 1.15e-45:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 3.45e+47:
		tmp = (y * t_1) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.2e-35)
		tmp = t_1;
	elseif (y <= 1.15e-45)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 3.45e+47)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.2e-35)
		tmp = t_1;
	elseif (y <= 1.15e-45)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 3.45e+47)
		tmp = (y * t_1) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.2e-35], t$95$1, If[LessEqual[y, 1.15e-45], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.45e+47], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1999999999999998e-35 or 3.4500000000000002e47 < y

   1. Initial program 45.5%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 75.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 75.1%

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

   if -3.1999999999999998e-35 < y < 1.14999999999999996e-45

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 63.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 63.4%

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

   if 1.14999999999999996e-45 < y < 3.4500000000000002e47

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y \cdot \left(\left(a + z\right) - b\right)\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(a + z\right) - b\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(a + z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      3. +-lowering-+.f64 70.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

   5. Simplified 70.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-45}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 720000000000:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{1}{t + \left(x + y\right)} \cdot \left(y \cdot \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6e-35)
     t_1
     (if (<= y 720000000000.0)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 8.9e+46) (* (/ 1.0 (+ t (+ x y))) (* y (- z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6e-35) {
		tmp = t_1;
	} else if (y <= 720000000000.0) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 8.9e+46) {
		tmp = (1.0 / (t + (x + y))) * (y * (z - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 + a) - b
    if (y <= (-6d-35)) then
        tmp = t_1
    else if (y <= 720000000000.0d0) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 8.9d+46) then
        tmp = (1.0d0 / (t + (x + y))) * (y * (z - b))
    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 + a) - b;
	double tmp;
	if (y <= -6e-35) {
		tmp = t_1;
	} else if (y <= 720000000000.0) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 8.9e+46) {
		tmp = (1.0 / (t + (x + y))) * (y * (z - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6e-35:
		tmp = t_1
	elif y <= 720000000000.0:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 8.9e+46:
		tmp = (1.0 / (t + (x + y))) * (y * (z - b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6e-35)
		tmp = t_1;
	elseif (y <= 720000000000.0)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 8.9e+46)
		tmp = Float64(Float64(1.0 / Float64(t + Float64(x + y))) * Float64(y * Float64(z - b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6e-35)
		tmp = t_1;
	elseif (y <= 720000000000.0)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 8.9e+46)
		tmp = (1.0 / (t + (x + y))) * (y * (z - b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6e-35], t$95$1, If[LessEqual[y, 720000000000.0], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.9e+46], N[(N[(1.0 / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999978e-35 or 8.8999999999999997e46 < y

   1. Initial program 45.5%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 75.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 75.1%

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

   if -5.99999999999999978e-35 < y < 7.2e11

   1. Initial program 79.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 60.8%

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

   if 7.2e11 < y < 8.8999999999999997e46

   1. Initial program 87.9%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      6. *-lowering-*.f64 88.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 88.3%

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

      1. clear-num N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. associate-/r/ N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{t + \left(y + x\right)}\right), \color{blue}{\left(z \cdot \left(y + x\right) - y \cdot b\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(t + \left(y + x\right)\right)\right), \left(\color{blue}{z \cdot \left(y + x\right)} - y \cdot b\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \left(y + x\right)\right)\right), \left(z \cdot \color{blue}{\left(y + x\right)} - y \cdot b\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \left(z \cdot \left(y + \color{blue}{x}\right) - y \cdot b\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(y + x\right)\right), \color{blue}{\left(y \cdot b\right)}\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{\_.f64}\left(\left(\left(y + x\right) \cdot z\right), \left(\color{blue}{y} \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(y + x\right), z\right), \left(\color{blue}{y} \cdot b\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, x\right), z\right), \left(y \cdot b\right)\right)\right) \]

      14. *-lowering-*.f64 88.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, x\right), z\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right)\right) \]

   7. Applied egg-rr 88.3%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \color{blue}{\left(y \cdot \left(z - b\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(z - b\right)}\right)\right) \]

      2. --lowering--.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{b}\right)\right)\right) \]

   10. Simplified 88.2%

       \[\leadsto \frac{1}{t + \left(y + x\right)} \cdot \color{blue}{\left(y \cdot \left(z - b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 720000000000:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 8.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{1}{t + \left(x + y\right)} \cdot \left(y \cdot \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1350000000000:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot b}{\left(0 - y\right) - \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5.5e-35)
     t_1
     (if (<= y 1350000000000.0)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 4.1e+46) (/ (* y b) (- (- 0.0 y) (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.5e-35) {
		tmp = t_1;
	} else if (y <= 1350000000000.0) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.1e+46) {
		tmp = (y * b) / ((0.0 - y) - (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 + a) - b
    if (y <= (-5.5d-35)) then
        tmp = t_1
    else if (y <= 1350000000000.0d0) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4.1d+46) then
        tmp = (y * b) / ((0.0d0 - y) - (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.5e-35) {
		tmp = t_1;
	} else if (y <= 1350000000000.0) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.1e+46) {
		tmp = (y * b) / ((0.0 - y) - (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5.5e-35:
		tmp = t_1
	elif y <= 1350000000000.0:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4.1e+46:
		tmp = (y * b) / ((0.0 - y) - (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.5e-35)
		tmp = t_1;
	elseif (y <= 1350000000000.0)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4.1e+46)
		tmp = Float64(Float64(y * b) / Float64(Float64(0.0 - y) - Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.5e-35)
		tmp = t_1;
	elseif (y <= 1350000000000.0)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4.1e+46)
		tmp = (y * b) / ((0.0 - y) - (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.5e-35], t$95$1, If[LessEqual[y, 1350000000000.0], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+46], N[(N[(y * b), $MachinePrecision] / N[(N[(0.0 - y), $MachinePrecision] - N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999997e-35 or 4.1e46 < y

   1. Initial program 45.5%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 75.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 75.1%

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

   if -5.4999999999999997e-35 < y < 1.35e12

   1. Initial program 79.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 60.8%

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

   if 1.35e12 < y < 4.1e46

   1. Initial program 87.9%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      6. *-lowering-*.f64 88.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 88.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{neg.f64}\left(\left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      3. *-lowering-*.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(b, y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

   8. Simplified 68.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1350000000000:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot b}{\left(0 - y\right) - \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ t (+ x y))))))
   (if (<= t -8.6e+79) t_1 (if (<= t 1.18e+119) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (t <= -8.6e+79) {
		tmp = t_1;
	} else if (t <= 1.18e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 = a * ((y + t) / (t + (x + y)))
    if (t <= (-8.6d+79)) then
        tmp = t_1
    else if (t <= 1.18d+119) then
        tmp = (z + a) - b
    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 = a * ((y + t) / (t + (x + y)));
	double tmp;
	if (t <= -8.6e+79) {
		tmp = t_1;
	} else if (t <= 1.18e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (t + (x + y)))
	tmp = 0
	if t <= -8.6e+79:
		tmp = t_1
	elif t <= 1.18e+119:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (t <= -8.6e+79)
		tmp = t_1;
	elseif (t <= 1.18e+119)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (t + (x + y)));
	tmp = 0.0;
	if (t <= -8.6e+79)
		tmp = t_1;
	elseif (t <= 1.18e+119)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+79], t$95$1, If[LessEqual[t, 1.18e+119], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6000000000000006e79 or 1.1799999999999999e119 < t

   1. Initial program 54.1%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(0 - a\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(\color{blue}{-1 \cdot \frac{t + y}{t + \left(x + y\right)}} + -1 \cdot \frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \left(-1 \cdot \frac{t + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, a\right), \mathsf{\_.f64}\left(\left(-1 \cdot \frac{t + y}{t + \left(x + y\right)}\right), \color{blue}{\left(\frac{\frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{a}\right)}\right)\right) \]

   5. Simplified 80.7%

      \[\leadsto \color{blue}{\left(0 - a\right) \cdot \left(\frac{\left(-t\right) - y}{t + \left(y + x\right)} - \frac{z \cdot \left(y + x\right) - y \cdot b}{a \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t + y\right)\right), \color{blue}{\left(t + \left(x + y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t + y\right)\right), \left(\color{blue}{t} + \left(x + y\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y + t\right)\right), \left(t + \left(x + y\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(y, t\right)\right), \left(t + \left(x + y\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(y, t\right)\right), \mathsf{+.f64}\left(t, \color{blue}{\left(x + y\right)}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(y, t\right)\right), \mathsf{+.f64}\left(t, \left(y + \color{blue}{x}\right)\right)\right) \]

      7. +-lowering-+.f64 32.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(y, t\right)\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 32.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y + t}{t + \left(y + x\right)}\right), \color{blue}{a}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t + y}{t + \left(y + x\right)}\right), a\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t + y\right), \left(t + \left(y + x\right)\right)\right), a\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), \left(t + \left(y + x\right)\right)\right), a\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), \mathsf{+.f64}\left(t, \left(y + x\right)\right)\right), a\right) \]

      8. +-lowering-+.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), a\right) \]

   10. Applied egg-rr 65.1%

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

   if -8.6000000000000006e79 < t < 1.1799999999999999e119

   1. Initial program 69.4%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 61.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 61.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t}{x + t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ t (+ x t)))))
   (if (<= t -6.8e+71) t_1 (if (<= t 5.4e+123) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t / (x + t));
	double tmp;
	if (t <= -6.8e+71) {
		tmp = t_1;
	} else if (t <= 5.4e+123) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 = a * (t / (x + t))
    if (t <= (-6.8d+71)) then
        tmp = t_1
    else if (t <= 5.4d+123) then
        tmp = (z + a) - b
    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 = a * (t / (x + t));
	double tmp;
	if (t <= -6.8e+71) {
		tmp = t_1;
	} else if (t <= 5.4e+123) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t / (x + t))
	tmp = 0
	if t <= -6.8e+71:
		tmp = t_1
	elif t <= 5.4e+123:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t / Float64(x + t)))
	tmp = 0.0
	if (t <= -6.8e+71)
		tmp = t_1;
	elseif (t <= 5.4e+123)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t / (x + t));
	tmp = 0.0;
	if (t <= -6.8e+71)
		tmp = t_1;
	elseif (t <= 5.4e+123)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+71], t$95$1, If[LessEqual[t, 5.4e+123], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.7999999999999997e71 or 5.40000000000000026e123 < t

   1. Initial program 54.1%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 42.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 42.8%

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

   6. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t}{t + x}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(t, \color{blue}{\left(t + x\right)}\right)\right) \]

      4. +-lowering-+.f64 63.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 63.1%

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

   if -6.7999999999999997e71 < t < 5.40000000000000026e123

   1. Initial program 69.4%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 61.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 61.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+123}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+81}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+181}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9e+81) a (if (<= t 2.95e+181) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+81) {
		tmp = a;
	} else if (t <= 2.95e+181) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 <= (-9d+81)) then
        tmp = a
    else if (t <= 2.95d+181) then
        tmp = (z + a) - 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 <= -9e+81) {
		tmp = a;
	} else if (t <= 2.95e+181) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9e+81:
		tmp = a
	elif t <= 2.95e+181:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9e+81)
		tmp = a;
	elseif (t <= 2.95e+181)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9e+81)
		tmp = a;
	elseif (t <= 2.95e+181)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9e+81], a, If[LessEqual[t, 2.95e+181], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000034e81 or 2.9499999999999999e181 < t

   1. Initial program 51.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 64.2%

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

   if -9.00000000000000034e81 < t < 2.9499999999999999e181

   1. Initial program 69.5%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 61.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 61.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+81}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+181}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-119}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+116}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e-119) a (if (<= t 2.5e+116) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e-119) {
		tmp = a;
	} else if (t <= 2.5e+116) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 <= (-1.05d-119)) then
        tmp = a
    else if (t <= 2.5d+116) then
        tmp = 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 <= -1.05e-119) {
		tmp = a;
	} else if (t <= 2.5e+116) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e-119:
		tmp = a
	elif t <= 2.5e+116:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e-119)
		tmp = a;
	elseif (t <= 2.5e+116)
		tmp = Float64(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 <= -1.05e-119)
		tmp = a;
	elseif (t <= 2.5e+116)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e-119], a, If[LessEqual[t, 2.5e+116], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e-119 or 2.50000000000000013e116 < t

   1. Initial program 59.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 56.0%

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

   if -1.05e-119 < t < 2.50000000000000013e116

   1. Initial program 68.9%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(b \cdot y\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \left(y \cdot b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      6. *-lowering-*.f64 51.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

   5. Simplified 51.3%

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

   6. Taylor expanded in y around inf

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

      1. --lowering--.f64 48.0%

         \[\leadsto \mathsf{\_.f64}\left(z, \color{blue}{b}\right) \]

   8. Simplified 48.0%

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

Alternative 13: 42.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-114}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 950:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.6e-114) a (if (<= t 950.0) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.6e-114) {
		tmp = a;
	} else if (t <= 950.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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 <= (-1.6d-114)) then
        tmp = a
    else if (t <= 950.0d0) 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 (t <= -1.6e-114) {
		tmp = a;
	} else if (t <= 950.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.6e-114:
		tmp = a
	elif t <= 950.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.6e-114)
		tmp = a;
	elseif (t <= 950.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.6e-114)
		tmp = a;
	elseif (t <= 950.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.6e-114], a, If[LessEqual[t, 950.0], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6000000000000001e-114 or 950 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 52.4%

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

   if -1.6000000000000001e-114 < t < 950

   1. Initial program 67.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 48.9%

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

Alternative 14: 32.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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 64.0%

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

3. Taylor expanded in t around inf

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

5. Simplified 38.9%

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

Developer Target 1: 82.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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