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

Percentage Accurate: 60.3% → 92.7%

Time: 11.4s

Alternatives: 12

Speedup: 1.1×

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: 60.3% 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: 92.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \frac{z - b}{\frac{t_1}{y}}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+89} \lor \neg \left(x \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;t_3 + \left(z + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(t_2 + \frac{x \cdot z}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ a (/ t_1 (+ y t))))
        (t_3 (/ (- z b) (/ t_1 y))))
   (if (or (<= x -4.5e+89) (not (<= x 2e+22)))
     (+ t_3 (+ z t_2))
     (+ t_3 (+ t_2 (/ (* x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z - b) / (t_1 / y);
	double tmp;
	if ((x <= -4.5e+89) || !(x <= 2e+22)) {
		tmp = t_3 + (z + t_2);
	} else {
		tmp = t_3 + (t_2 + ((x * z) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z - b) / (t_1 / y)
    if ((x <= (-4.5d+89)) .or. (.not. (x <= 2d+22))) then
        tmp = t_3 + (z + t_2)
    else
        tmp = t_3 + (t_2 + ((x * z) / 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 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z - b) / (t_1 / y);
	double tmp;
	if ((x <= -4.5e+89) || !(x <= 2e+22)) {
		tmp = t_3 + (z + t_2);
	} else {
		tmp = t_3 + (t_2 + ((x * z) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z - b) / (t_1 / y)
	tmp = 0
	if (x <= -4.5e+89) or not (x <= 2e+22):
		tmp = t_3 + (z + t_2)
	else:
		tmp = t_3 + (t_2 + ((x * z) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z - b) / Float64(t_1 / y))
	tmp = 0.0
	if ((x <= -4.5e+89) || !(x <= 2e+22))
		tmp = Float64(t_3 + Float64(z + t_2));
	else
		tmp = Float64(t_3 + Float64(t_2 + Float64(Float64(x * z) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z - b) / (t_1 / y);
	tmp = 0.0;
	if ((x <= -4.5e+89) || ~((x <= 2e+22)))
		tmp = t_3 + (z + t_2);
	else
		tmp = t_3 + (t_2 + ((x * z) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -4.5e+89], N[Not[LessEqual[x, 2e+22]], $MachinePrecision]], N[(t$95$3 + N[(z + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + N[(t$95$2 + N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e89 or 2e22 < x

   1. Initial program 46.1%

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

   3. Simplified 46.3%

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

   4. Taylor expanded in a around inf 45.9%

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

      1. associate-/l* 50.9%

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

      2. +-commutative 50.9%

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

      3. associate-/l* 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in x around inf 87.5%

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

   if -4.5e89 < x < 2e22

   1. Initial program 66.3%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in a around inf 66.3%

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

      1. associate-/l* 76.8%

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

      2. +-commutative 76.8%

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

      3. associate-/l* 97.5%

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

   6. Simplified 97.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+89} \lor \neg \left(x \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -1.5 \cdot 10^{+290} \lor \neg \left(t_1 \leq 2 \cdot 10^{+274}\right):\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* b y)) (+ y (+ x t)))))
   (if (or (<= t_1 -1.5e+290) (not (<= t_1 2e+274)))
     (+ a (/ (- z b) (/ (+ y t) y)))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1.5e+290) || !(t_1 <= 2e+274)) {
		tmp = a + ((z - b) / ((y + t) / 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 * (x + y)) + (a * (y + t))) - (b * y)) / (y + (x + t))
    if ((t_1 <= (-1.5d+290)) .or. (.not. (t_1 <= 2d+274))) then
        tmp = a + ((z - b) / ((y + t) / 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 * (x + y)) + (a * (y + t))) - (b * y)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -1.5e+290) || !(t_1 <= 2e+274)) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -1.5e+290) or not (t_1 <= 2e+274):
		tmp = a + ((z - b) / ((y + t) / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(b * y)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -1.5e+290) || !(t_1 <= 2e+274))
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -1.5e+290) || ~((t_1 <= 2e+274)))
		tmp = a + ((z - b) / ((y + t) / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1.5e+290], N[Not[LessEqual[t$95$1, 2e+274]], $MachinePrecision]], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.5e290 or 1.99999999999999984e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.5%

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

   3. Simplified 8.1%

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

   4. Taylor expanded in x around 0 11.9%

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

   5. Taylor expanded in a around 0 37.7%

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

      1. +-commutative 37.7%

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

      2. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

   if -1.5e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999984e274

   1. Initial program 99.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -1.5 \cdot 10^{+290} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 2 \cdot 10^{+274}\right):\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -1.5 \cdot 10^{+290}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(z + \frac{a}{\frac{t_1}{y + t}}\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+274}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* b y)) t_1)))
   (if (<= t_2 -1.5e+290)
     (+ (/ (- z b) (/ t_1 y)) (+ z (/ a (/ t_1 (+ y t)))))
     (if (<= t_2 2e+274) t_2 (+ a (/ (- z b) (/ (+ y t) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / t_1;
	double tmp;
	if (t_2 <= -1.5e+290) {
		tmp = ((z - b) / (t_1 / y)) + (z + (a / (t_1 / (y + t))));
	} else if (t_2 <= 2e+274) {
		tmp = t_2;
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	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 + (x + t)
    t_2 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / t_1
    if (t_2 <= (-1.5d+290)) then
        tmp = ((z - b) / (t_1 / y)) + (z + (a / (t_1 / (y + t))))
    else if (t_2 <= 2d+274) then
        tmp = t_2
    else
        tmp = a + ((z - b) / ((y + t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / t_1;
	double tmp;
	if (t_2 <= -1.5e+290) {
		tmp = ((z - b) / (t_1 / y)) + (z + (a / (t_1 / (y + t))));
	} else if (t_2 <= 2e+274) {
		tmp = t_2;
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / t_1
	tmp = 0
	if t_2 <= -1.5e+290:
		tmp = ((z - b) / (t_1 / y)) + (z + (a / (t_1 / (y + t))))
	elif t_2 <= 2e+274:
		tmp = t_2
	else:
		tmp = a + ((z - b) / ((y + t) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(b * y)) / t_1)
	tmp = 0.0
	if (t_2 <= -1.5e+290)
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(z + Float64(a / Float64(t_1 / Float64(y + t)))));
	elseif (t_2 <= 2e+274)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (b * y)) / t_1;
	tmp = 0.0;
	if (t_2 <= -1.5e+290)
		tmp = ((z - b) / (t_1 / y)) + (z + (a / (t_1 / (y + t))));
	elseif (t_2 <= 2e+274)
		tmp = t_2;
	else
		tmp = a + ((z - b) / ((y + t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1.5e+290], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+274], t$95$2, N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.5e290

   1. Initial program 8.7%

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

   3. Simplified 8.4%

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

   4. Taylor expanded in a around inf 8.2%

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

      1. associate-/l* 22.9%

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

      2. +-commutative 22.9%

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

      3. associate-/l* 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in x around inf 87.9%

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

   if -1.5e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999984e274

   1. Initial program 99.6%

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

   if 1.99999999999999984e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.4%

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

   3. Simplified 7.8%

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

   4. Taylor expanded in x around 0 10.8%

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

   5. Taylor expanded in a around 0 31.6%

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

      1. +-commutative 31.6%

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

      2. associate-/l* 82.5%

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

   7. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{z - b}{\frac{y + t}{y}} + a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -1.5 \cdot 10^{+290}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \]

Alternative 4: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + y \cdot \frac{z - b}{t_1}\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+71}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+221} \lor \neg \left(x \leq 2.5 \cdot 10^{+273}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ z (* y (/ (- z b) t_1)))))
   (if (<= x -1.5e+106)
     t_2
     (if (<= x 2.9e+71)
       (+ a (/ (- z b) (/ (+ y t) y)))
       (if (or (<= x 3.4e+221) (not (<= x 2.5e+273)))
         t_2
         (* (+ y t) (/ a t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z + (y * ((z - b) / t_1));
	double tmp;
	if (x <= -1.5e+106) {
		tmp = t_2;
	} else if (x <= 2.9e+71) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if ((x <= 3.4e+221) || !(x <= 2.5e+273)) {
		tmp = t_2;
	} else {
		tmp = (y + t) * (a / 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) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z + (y * ((z - b) / t_1))
    if (x <= (-1.5d+106)) then
        tmp = t_2
    else if (x <= 2.9d+71) then
        tmp = a + ((z - b) / ((y + t) / y))
    else if ((x <= 3.4d+221) .or. (.not. (x <= 2.5d+273))) then
        tmp = t_2
    else
        tmp = (y + t) * (a / 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 = y + (x + t);
	double t_2 = z + (y * ((z - b) / t_1));
	double tmp;
	if (x <= -1.5e+106) {
		tmp = t_2;
	} else if (x <= 2.9e+71) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if ((x <= 3.4e+221) || !(x <= 2.5e+273)) {
		tmp = t_2;
	} else {
		tmp = (y + t) * (a / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z + (y * ((z - b) / t_1))
	tmp = 0
	if x <= -1.5e+106:
		tmp = t_2
	elif x <= 2.9e+71:
		tmp = a + ((z - b) / ((y + t) / y))
	elif (x <= 3.4e+221) or not (x <= 2.5e+273):
		tmp = t_2
	else:
		tmp = (y + t) * (a / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z + Float64(y * Float64(Float64(z - b) / t_1)))
	tmp = 0.0
	if (x <= -1.5e+106)
		tmp = t_2;
	elseif (x <= 2.9e+71)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	elseif ((x <= 3.4e+221) || !(x <= 2.5e+273))
		tmp = t_2;
	else
		tmp = Float64(Float64(y + t) * Float64(a / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z + (y * ((z - b) / t_1));
	tmp = 0.0;
	if (x <= -1.5e+106)
		tmp = t_2;
	elseif (x <= 2.9e+71)
		tmp = a + ((z - b) / ((y + t) / y));
	elseif ((x <= 3.4e+221) || ~((x <= 2.5e+273)))
		tmp = t_2;
	else
		tmp = (y + t) * (a / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(y * N[(N[(z - b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+106], t$95$2, If[LessEqual[x, 2.9e+71], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.4e+221], N[Not[LessEqual[x, 2.5e+273]], $MachinePrecision]], t$95$2, N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e106 or 2.90000000000000007e71 < x < 3.3999999999999998e221 or 2.4999999999999998e273 < x

   1. Initial program 51.4%

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

   3. Simplified 51.4%

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

   4. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 52.7%

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

      2. +-commutative 52.7%

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

      3. associate-/l* 62.7%

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

   6. Simplified 62.7%

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

   7. Taylor expanded in x around inf 89.2%

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

   8. Taylor expanded in a around 0 57.0%

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

      1. associate-*l/ 67.5%

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

      2. +-commutative 67.5%

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

      3. *-commutative 67.5%

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

   10. Simplified 67.5%

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

   if -1.5e106 < x < 2.90000000000000007e71

   1. Initial program 63.0%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in x around 0 52.3%

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

   5. Taylor expanded in a around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. associate-/l* 85.6%

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

   7. Simplified 85.6%

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

   if 3.3999999999999998e221 < x < 2.4999999999999998e273

   1. Initial program 38.6%

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

   2. Taylor expanded in a around inf 31.4%

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

      1. associate-/l* 51.6%

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

   4. Simplified 51.6%

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

      1. associate-/r/ 65.2%

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

      2. +-commutative 65.2%

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

   6. Applied egg-rr 65.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+106}:\\ \;\;\;\;z + y \cdot \frac{z - b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+71}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+221} \lor \neg \left(x \leq 2.5 \cdot 10^{+273}\right):\\ \;\;\;\;z + y \cdot \frac{z - b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+59} \lor \neg \left(x \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{a}{\frac{x}{y + t}} + \left(z + \frac{z - b}{\frac{x}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5e+59) (not (<= x 5e+61)))
   (+ (/ a (/ x (+ y t))) (+ z (/ (- z b) (/ x y))))
   (+ a (/ (- z b) (/ (+ y t) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5e+59) || !(x <= 5e+61)) {
		tmp = (a / (x / (y + t))) + (z + ((z - b) / (x / y)));
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	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 ((x <= (-5d+59)) .or. (.not. (x <= 5d+61))) then
        tmp = (a / (x / (y + t))) + (z + ((z - b) / (x / y)))
    else
        tmp = a + ((z - b) / ((y + t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5e+59) || !(x <= 5e+61)) {
		tmp = (a / (x / (y + t))) + (z + ((z - b) / (x / y)));
	} else {
		tmp = a + ((z - b) / ((y + t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5e+59) or not (x <= 5e+61):
		tmp = (a / (x / (y + t))) + (z + ((z - b) / (x / y)))
	else:
		tmp = a + ((z - b) / ((y + t) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5e+59) || !(x <= 5e+61))
		tmp = Float64(Float64(a / Float64(x / Float64(y + t))) + Float64(z + Float64(Float64(z - b) / Float64(x / y))));
	else
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5e+59) || ~((x <= 5e+61)))
		tmp = (a / (x / (y + t))) + (z + ((z - b) / (x / y)));
	else
		tmp = a + ((z - b) / ((y + t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5e+59], N[Not[LessEqual[x, 5e+61]], $MachinePrecision]], N[(N[(a / N[(x / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(N[(z - b), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999997e59 or 5.00000000000000018e61 < x

   1. Initial program 49.5%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in a around inf 49.2%

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

      1. associate-/l* 50.6%

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

      2. +-commutative 50.6%

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

      3. associate-/l* 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in x around inf 87.6%

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

   8. Taylor expanded in x around inf 60.7%

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

      1. associate-/l* 62.8%

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

      2. associate-/l* 70.4%

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

   10. Simplified 70.4%

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

   if -4.9999999999999997e59 < x < 5.00000000000000018e61

   1. Initial program 63.4%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in x around 0 53.5%

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

   5. Taylor expanded in a around 0 68.1%

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

      1. +-commutative 68.1%

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

      2. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+59} \lor \neg \left(x \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{a}{\frac{x}{y + t}} + \left(z + \frac{z - b}{\frac{x}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \end{array} \]

Alternative 6: 69.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{x + t}{x}}\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+270}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (/ (+ x t) x))))
   (if (<= x -1.25e+106)
     t_1
     (if (<= x 2.3e+84)
       (+ a (/ (- z b) (/ (+ y t) y)))
       (if (<= x 2.6e+141)
         t_1
         (if (<= x 3.3e+270) (* (+ y t) (/ a (+ y (+ x t)))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / ((x + t) / x);
	double tmp;
	if (x <= -1.25e+106) {
		tmp = t_1;
	} else if (x <= 2.3e+84) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if (x <= 2.6e+141) {
		tmp = t_1;
	} else if (x <= 3.3e+270) {
		tmp = (y + t) * (a / (y + (x + t)));
	} else {
		tmp = z;
	}
	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 / ((x + t) / x)
    if (x <= (-1.25d+106)) then
        tmp = t_1
    else if (x <= 2.3d+84) then
        tmp = a + ((z - b) / ((y + t) / y))
    else if (x <= 2.6d+141) then
        tmp = t_1
    else if (x <= 3.3d+270) then
        tmp = (y + t) * (a / (y + (x + t)))
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / ((x + t) / x);
	double tmp;
	if (x <= -1.25e+106) {
		tmp = t_1;
	} else if (x <= 2.3e+84) {
		tmp = a + ((z - b) / ((y + t) / y));
	} else if (x <= 2.6e+141) {
		tmp = t_1;
	} else if (x <= 3.3e+270) {
		tmp = (y + t) * (a / (y + (x + t)));
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / ((x + t) / x)
	tmp = 0
	if x <= -1.25e+106:
		tmp = t_1
	elif x <= 2.3e+84:
		tmp = a + ((z - b) / ((y + t) / y))
	elif x <= 2.6e+141:
		tmp = t_1
	elif x <= 3.3e+270:
		tmp = (y + t) * (a / (y + (x + t)))
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(Float64(x + t) / x))
	tmp = 0.0
	if (x <= -1.25e+106)
		tmp = t_1;
	elseif (x <= 2.3e+84)
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + t) / y)));
	elseif (x <= 2.6e+141)
		tmp = t_1;
	elseif (x <= 3.3e+270)
		tmp = Float64(Float64(y + t) * Float64(a / Float64(y + Float64(x + t))));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z / ((x + t) / x);
	tmp = 0.0;
	if (x <= -1.25e+106)
		tmp = t_1;
	elseif (x <= 2.3e+84)
		tmp = a + ((z - b) / ((y + t) / y));
	elseif (x <= 2.6e+141)
		tmp = t_1;
	elseif (x <= 3.3e+270)
		tmp = (y + t) * (a / (y + (x + t)));
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+106], t$95$1, If[LessEqual[x, 2.3e+84], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+141], t$95$1, If[LessEqual[x, 3.3e+270], N[(N[(y + t), $MachinePrecision] * N[(a / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], z]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.25e106 or 2.2999999999999999e84 < x < 2.5999999999999999e141

   1. Initial program 49.5%

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

   3. Simplified 49.5%

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

   4. Taylor expanded in a around 0 40.4%

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

   5. Taylor expanded in y around 0 27.1%

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

      1. associate-/l* 61.9%

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

   7. Simplified 61.9%

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

   if -1.25e106 < x < 2.2999999999999999e84

   1. Initial program 63.5%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in x around 0 52.3%

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

   5. Taylor expanded in a around 0 66.2%

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

      1. +-commutative 66.2%

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

      2. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

   if 2.5999999999999999e141 < x < 3.29999999999999992e270

   1. Initial program 33.4%

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

   2. Taylor expanded in a around inf 24.5%

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

      1. associate-/l* 49.3%

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

   4. Simplified 49.3%

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

      1. associate-/r/ 53.5%

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

      2. +-commutative 53.5%

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

   6. Applied egg-rr 53.5%

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

   if 3.29999999999999992e270 < x

   1. Initial program 78.2%

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

   2. Taylor expanded in x around inf 57.3%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+106}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;a + \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+141}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+270}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 58.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+110} \lor \neg \left(t \leq 10^{+28}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.35e+110) (not (<= t 1e+28)))
   (/ a (/ (+ x t) t))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.35e+110) || !(t <= 1e+28)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = (z + a) - b;
	}
	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 <= (-1.35d+110)) .or. (.not. (t <= 1d+28))) then
        tmp = a / ((x + t) / t)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.35e+110) || !(t <= 1e+28)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.35e+110) or not (t <= 1e+28):
		tmp = a / ((x + t) / t)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.35e+110) || !(t <= 1e+28))
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.35e+110) || ~((t <= 1e+28)))
		tmp = a / ((x + t) / t);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.35e+110], N[Not[LessEqual[t, 1e+28]], $MachinePrecision]], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000005e110 or 9.99999999999999958e27 < t

   1. Initial program 45.3%

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

   2. Taylor expanded in a around inf 29.6%

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

      1. associate-/l* 62.7%

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

   4. Simplified 62.7%

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

   5. Taylor expanded in y around 0 31.4%

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

      1. associate-/l* 62.2%

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

      2. +-commutative 62.2%

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

   7. Simplified 62.2%

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

   if -1.35000000000000005e110 < t < 9.99999999999999958e27

   1. Initial program 66.4%

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

   2. Taylor expanded in y around inf 58.0%

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

      1. +-commutative 58.0%

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

   4. Simplified 58.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+110} \lor \neg \left(t \leq 10^{+28}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 57.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+183}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e+183) a (if (<= t 3.1e-81) (- (+ z a) b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+183) {
		tmp = a;
	} else if (t <= 3.1e-81) {
		tmp = (z + a) - b;
	} else {
		tmp = z + 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 <= (-1d+183)) then
        tmp = a
    else if (t <= 3.1d-81) then
        tmp = (z + a) - b
    else
        tmp = z + 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 <= -1e+183) {
		tmp = a;
	} else if (t <= 3.1e-81) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e+183:
		tmp = a
	elif t <= 3.1e-81:
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e+183)
		tmp = a;
	elseif (t <= 3.1e-81)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e+183)
		tmp = a;
	elseif (t <= 3.1e-81)
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e+183], a, If[LessEqual[t, 3.1e-81], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999947e182

   1. Initial program 33.0%

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

   2. Taylor expanded in t around inf 71.2%

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

   if -9.99999999999999947e182 < t < 3.09999999999999988e-81

   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. Taylor expanded in y around inf 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   if 3.09999999999999988e-81 < t

   1. Initial program 60.0%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in a around inf 59.9%

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

      1. associate-/l* 63.4%

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

      2. +-commutative 63.4%

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

      3. associate-/l* 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around inf 71.0%

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

   8. Taylor expanded in t around inf 53.9%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+183}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-81}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 9: 57.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+181}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+181)
   (* a (- 1.0 (/ x t)))
   (if (<= t 1.8e-80) (- (+ z a) b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+181) {
		tmp = a * (1.0 - (x / t));
	} else if (t <= 1.8e-80) {
		tmp = (z + a) - b;
	} else {
		tmp = z + 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 <= (-9.5d+181)) then
        tmp = a * (1.0d0 - (x / t))
    else if (t <= 1.8d-80) then
        tmp = (z + a) - b
    else
        tmp = z + 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 <= -9.5e+181) {
		tmp = a * (1.0 - (x / t));
	} else if (t <= 1.8e-80) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+181:
		tmp = a * (1.0 - (x / t))
	elif t <= 1.8e-80:
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+181)
		tmp = Float64(a * Float64(1.0 - Float64(x / t)));
	elseif (t <= 1.8e-80)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+181)
		tmp = a * (1.0 - (x / t));
	elseif (t <= 1.8e-80)
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+181], N[(a * N[(1.0 - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-80], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000032e181

   1. Initial program 33.0%

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

   3. Simplified 33.4%

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

   4. Taylor expanded in t around inf 53.4%

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

   5. Taylor expanded in a around inf 71.2%

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

   if -9.50000000000000032e181 < t < 1.8e-80

   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. Taylor expanded in y around inf 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   if 1.8e-80 < t

   1. Initial program 60.0%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in a around inf 59.9%

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

      1. associate-/l* 63.4%

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

      2. +-commutative 63.4%

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

      3. associate-/l* 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around inf 71.0%

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

   8. Taylor expanded in t around inf 53.9%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+181}:\\ \;\;\;\;a \cdot \left(1 - \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 10: 43.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+103}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+67}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.2e+103) z (if (<= x 1.32e+67) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+103) {
		tmp = z;
	} else if (x <= 1.32e+67) {
		tmp = a;
	} else {
		tmp = z;
	}
	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 (x <= (-9.2d+103)) then
        tmp = z
    else if (x <= 1.32d+67) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+103) {
		tmp = z;
	} else if (x <= 1.32e+67) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.2e+103:
		tmp = z
	elif x <= 1.32e+67:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.2e+103)
		tmp = z;
	elseif (x <= 1.32e+67)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.2e+103)
		tmp = z;
	elseif (x <= 1.32e+67)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.2e+103], z, If[LessEqual[x, 1.32e+67], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -9.20000000000000034e103 or 1.3200000000000001e67 < x

   1. Initial program 49.4%

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

   2. Taylor expanded in x around inf 51.6%

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

   if -9.20000000000000034e103 < x < 1.3200000000000001e67

   1. Initial program 63.0%

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

   2. Taylor expanded in t around inf 48.5%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+103}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+67}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 11: 52.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+220}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t -4e+220) a (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+220) {
		tmp = a;
	} else {
		tmp = z + 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 <= (-4d+220)) then
        tmp = a
    else
        tmp = z + 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 <= -4e+220) {
		tmp = a;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+220:
		tmp = a
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+220)
		tmp = a;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4e+220)
		tmp = a;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+220], a, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4e220

   1. Initial program 34.8%

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

   2. Taylor expanded in t around inf 79.6%

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

   if -4e220 < t

   1. Initial program 60.1%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in a around inf 60.0%

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

      1. associate-/l* 67.4%

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

      2. +-commutative 67.4%

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

      3. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in x around inf 78.2%

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

   8. Taylor expanded in t around inf 52.0%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+220}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 12: 32.5% 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 58.2%

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

2. Taylor expanded in t around inf 36.3%

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

3. Final simplification 36.3%

   \[\leadsto a \]

Developer target: 82.1% 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 2023196 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ 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)))