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

Percentage Accurate: 60.5% → 87.6%

Time: 13.4s

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: 60.5% 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: 87.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t\_2} + \frac{t}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ t (+ x y)))
        (t_3 (/ (- (+ (* z (+ x y)) t_1) (* y b)) (+ y (+ x t)))))
   (if (<= t_3 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_3 5e+259)
       (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t)))
       (+ z (* a (+ (/ y t_2) (/ t t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = t + (x + y);
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_3 <= 5e+259) {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	} else {
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_3 <= 5e+259)
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$3, 5e+259], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $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)) < -inf.0

   1. Initial program 7.0%

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

   3. Taylor expanded in y around inf 85.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000033e259

   1. Initial program 99.0%

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

      1. fma-define 99.0%

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

      2. +-commutative 99.0%

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

      3. associate-+l+ 99.0%

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

      4. +-commutative 99.0%

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

   3. Simplified 99.0%

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

   if 5.00000000000000033e259 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.3%

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

   3. Taylor expanded in a around 0 29.7%

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

      1. associate--l+ 29.7%

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

      2. +-commutative 29.7%

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

      3. +-commutative 29.7%

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

      4. +-commutative 29.7%

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

      5. div-sub 29.7%

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

      6. +-commutative 29.7%

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

      7. *-commutative 29.7%

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

      8. +-commutative 29.7%

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

   5. Simplified 29.7%

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

   6. Taylor expanded in x around inf 68.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t\_1} + \frac{t}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (<= t_2 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_2 5e+259) t_2 (+ z (* a (+ (/ y t_1) (/ t t_1))))))))

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 * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_2 <= 5e+259) {
		tmp = t_2;
	} else {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	}
	return tmp;
}

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 * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + a) - b;
	} else if (t_2 <= 5e+259) {
		tmp = t_2;
	} else {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z + a) - b
	elif t_2 <= 5e+259:
		tmp = t_2
	else:
		tmp = z + (a * ((y / t_1) + (t / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_2 <= 5e+259)
		tmp = t_2;
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z + a) - b;
	elseif (t_2 <= 5e+259)
		tmp = t_2;
	else
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 5e+259], t$95$2, N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $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)) < -inf.0

   1. Initial program 7.0%

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

   3. Taylor expanded in y around inf 85.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000033e259

   1. Initial program 99.0%

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

   if 5.00000000000000033e259 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.3%

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

   3. Taylor expanded in a around 0 29.7%

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

      1. associate--l+ 29.7%

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

      2. +-commutative 29.7%

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

      3. +-commutative 29.7%

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

      4. +-commutative 29.7%

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

      5. div-sub 29.7%

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

      6. +-commutative 29.7%

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

      7. *-commutative 29.7%

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

      8. +-commutative 29.7%

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

   5. Simplified 29.7%

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

   6. Taylor expanded in x around inf 68.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+259}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+115} \lor \neg \left(b \leq 1.72 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot \frac{z \cdot \frac{x + y}{b} - y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t\_1} + \frac{t}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))))
   (if (or (<= b -2.9e+115) (not (<= b 1.72e+53)))
     (* b (/ (- (* z (/ (+ x y) b)) y) (+ y (+ x t))))
     (+ z (* a (+ (/ y t_1) (/ t t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double tmp;
	if ((b <= -2.9e+115) || !(b <= 1.72e+53)) {
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)));
	} else {
		tmp = z + (a * ((y / t_1) + (t / 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 = t + (x + y)
    if ((b <= (-2.9d+115)) .or. (.not. (b <= 1.72d+53))) then
        tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)))
    else
        tmp = z + (a * ((y / t_1) + (t / t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double tmp;
	if ((b <= -2.9e+115) || !(b <= 1.72e+53)) {
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)));
	} else {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	tmp = 0
	if (b <= -2.9e+115) or not (b <= 1.72e+53):
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)))
	else:
		tmp = z + (a * ((y / t_1) + (t / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	tmp = 0.0
	if ((b <= -2.9e+115) || !(b <= 1.72e+53))
		tmp = Float64(b * Float64(Float64(Float64(z * Float64(Float64(x + y) / b)) - y) / Float64(y + Float64(x + t))));
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	tmp = 0.0;
	if ((b <= -2.9e+115) || ~((b <= 1.72e+53)))
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)));
	else
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.9e+115], N[Not[LessEqual[b, 1.72e+53]], $MachinePrecision]], N[(b * N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.90000000000000005e115 or 1.72e53 < b

   1. Initial program 54.7%

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

   3. Taylor expanded in b around inf 55.0%

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

   4. Taylor expanded in a around 0 45.4%

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

      1. associate-/l* 57.7%

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

      2. associate-/l* 76.0%

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

      3. +-commutative 76.0%

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

      4. associate-+r+ 76.0%

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

      5. +-commutative 76.0%

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

   6. Simplified 76.0%

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

   if -2.90000000000000005e115 < b < 1.72e53

   1. Initial program 64.4%

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

   3. Taylor expanded in a around 0 79.8%

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

      1. associate--l+ 79.8%

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

      2. +-commutative 79.8%

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

      3. +-commutative 79.8%

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

      4. +-commutative 79.8%

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

      5. div-sub 79.8%

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

      6. +-commutative 79.8%

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

      7. *-commutative 79.8%

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

      8. +-commutative 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in x around inf 76.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+115} \lor \neg \left(b \leq 1.72 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot \frac{z \cdot \frac{x + y}{b} - y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+104} \lor \neg \left(b \leq 2700000000\right):\\ \;\;\;\;b \cdot \frac{z \cdot \frac{x + y}{b} - y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.9e+104) (not (<= b 2700000000.0)))
   (* b (/ (- (* z (/ (+ x y) b)) y) (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.9e+104) || !(b <= 2700000000.0)) {
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + 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 ((b <= (-4.9d+104)) .or. (.not. (b <= 2700000000.0d0))) then
        tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + 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 ((b <= -4.9e+104) || !(b <= 2700000000.0)) {
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.9e+104) or not (b <= 2700000000.0):
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.9e+104) || !(b <= 2700000000.0))
		tmp = Float64(b * Float64(Float64(Float64(z * Float64(Float64(x + y) / b)) - y) / Float64(y + Float64(x + 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 ((b <= -4.9e+104) || ~((b <= 2700000000.0)))
		tmp = b * (((z * ((x + y) / b)) - y) / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.9e+104], N[Not[LessEqual[b, 2700000000.0]], $MachinePrecision]], N[(b * N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.89999999999999985e104 or 2.7e9 < b

   1. Initial program 59.7%

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

   3. Taylor expanded in b around inf 60.0%

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

   4. Taylor expanded in a around 0 45.7%

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

      1. associate-/l* 56.1%

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

      2. associate-/l* 71.6%

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

      3. +-commutative 71.6%

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

      4. associate-+r+ 71.6%

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

      5. +-commutative 71.6%

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

   6. Simplified 71.6%

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

   if -4.89999999999999985e104 < b < 2.7e9

   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 y around inf 67.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+104} \lor \neg \left(b \leq 2700000000\right):\\ \;\;\;\;b \cdot \frac{z \cdot \frac{x + y}{b} - y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+51}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.8e+74)
   (* z (/ (+ x y) (+ y (+ x t))))
   (if (<= x 7.6e+51)
     (- (+ z a) b)
     (+ z (* a (+ (/ y (+ t (+ x y))) (/ t x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.8e+74) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (x <= 7.6e+51) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * ((y / (t + (x + y))) + (t / x)));
	}
	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 <= (-6.8d+74)) then
        tmp = z * ((x + y) / (y + (x + t)))
    else if (x <= 7.6d+51) then
        tmp = (z + a) - b
    else
        tmp = z + (a * ((y / (t + (x + y))) + (t / x)))
    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 <= -6.8e+74) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (x <= 7.6e+51) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * ((y / (t + (x + y))) + (t / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.8e+74:
		tmp = z * ((x + y) / (y + (x + t)))
	elif x <= 7.6e+51:
		tmp = (z + a) - b
	else:
		tmp = z + (a * ((y / (t + (x + y))) + (t / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.8e+74)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	elseif (x <= 7.6e+51)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y / Float64(t + Float64(x + y))) + Float64(t / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.8e+74)
		tmp = z * ((x + y) / (y + (x + t)));
	elseif (x <= 7.6e+51)
		tmp = (z + a) - b;
	else
		tmp = z + (a * ((y / (t + (x + y))) + (t / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.8e+74], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e+51], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a * N[(N[(y / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.7999999999999998e74

   1. Initial program 35.1%

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

   3. Taylor expanded in z around inf 20.3%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. associate-+r+ 68.6%

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

   5. Simplified 68.6%

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

   if -6.7999999999999998e74 < x < 7.5999999999999994e51

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 65.7%

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

   if 7.5999999999999994e51 < x

   1. Initial program 56.8%

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

   3. Taylor expanded in a around 0 62.4%

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

      1. associate--l+ 62.4%

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

      2. +-commutative 62.4%

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

      3. +-commutative 62.4%

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

      4. +-commutative 62.4%

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

      5. div-sub 62.4%

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

      6. +-commutative 62.4%

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

      7. *-commutative 62.4%

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

      8. +-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in x around inf 78.0%

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

   7. Taylor expanded in x around inf 74.5%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+51}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+233}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-94}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-247}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+149}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2e+233)
   z
   (if (<= x -5.2e-94)
     (+ z a)
     (if (<= x 4.8e-247) (- a b) (if (<= x 1.05e+149) (+ z a) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2e+233) {
		tmp = z;
	} else if (x <= -5.2e-94) {
		tmp = z + a;
	} else if (x <= 4.8e-247) {
		tmp = a - b;
	} else if (x <= 1.05e+149) {
		tmp = z + 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 <= (-2d+233)) then
        tmp = z
    else if (x <= (-5.2d-94)) then
        tmp = z + a
    else if (x <= 4.8d-247) then
        tmp = a - b
    else if (x <= 1.05d+149) then
        tmp = z + 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 <= -2e+233) {
		tmp = z;
	} else if (x <= -5.2e-94) {
		tmp = z + a;
	} else if (x <= 4.8e-247) {
		tmp = a - b;
	} else if (x <= 1.05e+149) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2e+233:
		tmp = z
	elif x <= -5.2e-94:
		tmp = z + a
	elif x <= 4.8e-247:
		tmp = a - b
	elif x <= 1.05e+149:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2e+233)
		tmp = z;
	elseif (x <= -5.2e-94)
		tmp = Float64(z + a);
	elseif (x <= 4.8e-247)
		tmp = Float64(a - b);
	elseif (x <= 1.05e+149)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2e+233)
		tmp = z;
	elseif (x <= -5.2e-94)
		tmp = z + a;
	elseif (x <= 4.8e-247)
		tmp = a - b;
	elseif (x <= 1.05e+149)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2e+233], z, If[LessEqual[x, -5.2e-94], N[(z + a), $MachinePrecision], If[LessEqual[x, 4.8e-247], N[(a - b), $MachinePrecision], If[LessEqual[x, 1.05e+149], N[(z + a), $MachinePrecision], z]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.99999999999999995e233 or 1.0500000000000001e149 < x

   1. Initial program 45.1%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -1.99999999999999995e233 < x < -5.19999999999999988e-94 or 4.80000000000000022e-247 < x < 1.0500000000000001e149

   1. Initial program 64.1%

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

   3. Taylor expanded in a around 0 77.9%

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

      1. associate--l+ 77.9%

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

      2. +-commutative 77.9%

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

      3. +-commutative 77.9%

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

      4. +-commutative 77.9%

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

      5. div-sub 77.9%

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

      6. +-commutative 77.9%

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

      7. *-commutative 77.9%

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

      8. +-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in x around inf 63.5%

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

   7. Taylor expanded in y around inf 55.2%

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

   if -5.19999999999999988e-94 < x < 4.80000000000000022e-247

   1. Initial program 68.3%

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

   3. Taylor expanded in y around inf 73.0%

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

   4. Taylor expanded in z around 0 69.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+233}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-94}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-247}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+149}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+188} \lor \neg \left(x \leq 8.5 \cdot 10^{+124}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.75e+188) (not (<= x 8.5e+124)))
   (+ z (* a (/ (+ y t) x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.75e+188) || !(x <= 8.5e+124)) {
		tmp = z + (a * ((y + t) / x));
	} 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 ((x <= (-1.75d+188)) .or. (.not. (x <= 8.5d+124))) then
        tmp = z + (a * ((y + t) / x))
    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 ((x <= -1.75e+188) || !(x <= 8.5e+124)) {
		tmp = z + (a * ((y + t) / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.75e+188) or not (x <= 8.5e+124):
		tmp = z + (a * ((y + t) / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.75e+188) || !(x <= 8.5e+124))
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / x)));
	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 ((x <= -1.75e+188) || ~((x <= 8.5e+124)))
		tmp = z + (a * ((y + t) / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.75e+188], N[Not[LessEqual[x, 8.5e+124]], $MachinePrecision]], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000004e188 or 8.4999999999999997e124 < x

   1. Initial program 45.8%

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

   3. Taylor expanded in a around 0 48.2%

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

      1. associate--l+ 48.2%

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

      2. +-commutative 48.2%

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

      3. +-commutative 48.2%

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

      4. +-commutative 48.2%

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

      5. div-sub 48.2%

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

      6. +-commutative 48.2%

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

      7. *-commutative 48.2%

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

      8. +-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in x around inf 79.5%

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

   7. Taylor expanded in x around inf 69.8%

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

      1. associate-/l* 74.7%

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

      2. +-commutative 74.7%

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

   9. Simplified 74.7%

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

   if -1.75000000000000004e188 < x < 8.4999999999999997e124

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf 64.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+188} \lor \neg \left(x \leq 8.5 \cdot 10^{+124}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+124}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e+74)
   (* z (/ (+ x y) (+ y (+ x t))))
   (if (<= x 2.25e+124) (- (+ z a) b) (+ z (* a (/ (+ y t) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+74) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (x <= 2.25e+124) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * ((y + t) / x));
	}
	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 <= (-6.2d+74)) then
        tmp = z * ((x + y) / (y + (x + t)))
    else if (x <= 2.25d+124) then
        tmp = (z + a) - b
    else
        tmp = z + (a * ((y + t) / x))
    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 <= -6.2e+74) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else if (x <= 2.25e+124) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * ((y + t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e+74:
		tmp = z * ((x + y) / (y + (x + t)))
	elif x <= 2.25e+124:
		tmp = (z + a) - b
	else:
		tmp = z + (a * ((y + t) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e+74)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	elseif (x <= 2.25e+124)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.2e+74)
		tmp = z * ((x + y) / (y + (x + t)));
	elseif (x <= 2.25e+124)
		tmp = (z + a) - b;
	else
		tmp = z + (a * ((y + t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e+74], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+124], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000043e74

   1. Initial program 35.1%

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

   3. Taylor expanded in z around inf 20.3%

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

      1. associate-/l* 68.6%

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

      2. +-commutative 68.6%

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

      3. associate-+r+ 68.6%

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

   5. Simplified 68.6%

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

   if -6.20000000000000043e74 < x < 2.2500000000000002e124

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 65.0%

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

   if 2.2500000000000002e124 < x

   1. Initial program 54.0%

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

   3. Taylor expanded in a around 0 57.2%

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

      1. associate--l+ 57.2%

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

      2. +-commutative 57.2%

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

      3. +-commutative 57.2%

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

      4. +-commutative 57.2%

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

      5. div-sub 57.2%

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

      6. +-commutative 57.2%

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

      7. *-commutative 57.2%

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

      8. +-commutative 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in x around inf 81.8%

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

   7. Taylor expanded in x around inf 73.6%

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

      1. associate-/l* 74.3%

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

      2. +-commutative 74.3%

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

   9. Simplified 74.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+124}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+190}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.1e+190) z (if (<= x 1.85e+131) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+190) {
		tmp = z;
	} else if (x <= 1.85e+131) {
		tmp = (z + a) - b;
	} 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 <= (-2.1d+190)) then
        tmp = z
    else if (x <= 1.85d+131) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+190) {
		tmp = z;
	} else if (x <= 1.85e+131) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.1e+190:
		tmp = z
	elif x <= 1.85e+131:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.1e+190)
		tmp = z;
	elseif (x <= 1.85e+131)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.1e+190)
		tmp = z;
	elseif (x <= 1.85e+131)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.1e+190], z, If[LessEqual[x, 1.85e+131], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e190 or 1.84999999999999998e131 < x

   1. Initial program 45.8%

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

   3. Taylor expanded in x around inf 64.1%

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

   if -2.1000000000000001e190 < x < 1.84999999999999998e131

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf 64.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+190}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+233}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+144}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.4e+233) z (if (<= x 1.32e+144) (+ z a) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.4e+233) {
		tmp = z;
	} else if (x <= 1.32e+144) {
		tmp = z + 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 <= (-2.4d+233)) then
        tmp = z
    else if (x <= 1.32d+144) then
        tmp = z + 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 <= -2.4e+233) {
		tmp = z;
	} else if (x <= 1.32e+144) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.4e+233:
		tmp = z
	elif x <= 1.32e+144:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.4e+233)
		tmp = z;
	elseif (x <= 1.32e+144)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.4e+233)
		tmp = z;
	elseif (x <= 1.32e+144)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.4e+233], z, If[LessEqual[x, 1.32e+144], N[(z + a), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000003e233 or 1.32e144 < x

   1. Initial program 45.1%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -2.40000000000000003e233 < x < 1.32e144

   1. Initial program 65.5%

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

   3. Taylor expanded in a around 0 79.8%

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

      1. associate--l+ 79.8%

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

      2. +-commutative 79.8%

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

      3. +-commutative 79.8%

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

      4. +-commutative 79.8%

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

      5. div-sub 79.8%

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

      6. +-commutative 79.8%

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

      7. *-commutative 79.8%

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

      8. +-commutative 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in x around inf 60.4%

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

   7. Taylor expanded in y around inf 54.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+233}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+144}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+65}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+51}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.1e+65) z (if (<= x 9.2e+51) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.1e+65) {
		tmp = z;
	} else if (x <= 9.2e+51) {
		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 <= (-6.1d+65)) then
        tmp = z
    else if (x <= 9.2d+51) 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 <= -6.1e+65) {
		tmp = z;
	} else if (x <= 9.2e+51) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.1e+65:
		tmp = z
	elif x <= 9.2e+51:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.1e+65)
		tmp = z;
	elseif (x <= 9.2e+51)
		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 <= -6.1e+65)
		tmp = z;
	elseif (x <= 9.2e+51)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.1e+65], z, If[LessEqual[x, 9.2e+51], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -6.09999999999999965e65 or 9.2000000000000002e51 < x

   1. Initial program 48.8%

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

   3. Taylor expanded in x around inf 57.9%

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

   if -6.09999999999999965e65 < x < 9.2000000000000002e51

   1. Initial program 68.2%

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

   3. Taylor expanded in t around inf 49.5%

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

Alternative 12: 32.7% 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 61.0%

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

3. Taylor expanded in t around inf 35.4%

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

Developer Target 1: 81.9% 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 2024135 
(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)))