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

Percentage Accurate: 61.0% → 87.0%

Time: 12.3s

Alternatives: 12

Speedup: 1.0×

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: 61.0% 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: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+196}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+196))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+196)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+196)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+196):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+196))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+196)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+196]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $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)) < -inf.0 or 9.9999999999999995e195 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.5%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999995e195

   1. Initial program 99.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+196}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 57.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-227}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-282}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{-29}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)) (t_3 (* z (/ (+ x y) t_1))))
   (if (<= y -6e-12)
     t_2
     (if (<= y -8.3e-227)
       (* a (/ (+ y t) t_1))
       (if (<= y -6.9e-282)
         t_3
         (if (<= y 1.25e-253)
           (* a (/ t (+ x t)))
           (if (<= y 7.9e-29) t_3 t_2)))))))

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 + a) - b;
	double t_3 = z * ((x + y) / t_1);
	double tmp;
	if (y <= -6e-12) {
		tmp = t_2;
	} else if (y <= -8.3e-227) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= -6.9e-282) {
		tmp = t_3;
	} else if (y <= 1.25e-253) {
		tmp = a * (t / (x + t));
	} else if (y <= 7.9e-29) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    t_3 = z * ((x + y) / t_1)
    if (y <= (-6d-12)) then
        tmp = t_2
    else if (y <= (-8.3d-227)) then
        tmp = a * ((y + t) / t_1)
    else if (y <= (-6.9d-282)) then
        tmp = t_3
    else if (y <= 1.25d-253) then
        tmp = a * (t / (x + t))
    else if (y <= 7.9d-29) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = z * ((x + y) / t_1);
	double tmp;
	if (y <= -6e-12) {
		tmp = t_2;
	} else if (y <= -8.3e-227) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= -6.9e-282) {
		tmp = t_3;
	} else if (y <= 1.25e-253) {
		tmp = a * (t / (x + t));
	} else if (y <= 7.9e-29) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	t_3 = z * ((x + y) / t_1)
	tmp = 0
	if y <= -6e-12:
		tmp = t_2
	elif y <= -8.3e-227:
		tmp = a * ((y + t) / t_1)
	elif y <= -6.9e-282:
		tmp = t_3
	elif y <= 1.25e-253:
		tmp = a * (t / (x + t))
	elif y <= 7.9e-29:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (y <= -6e-12)
		tmp = t_2;
	elseif (y <= -8.3e-227)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (y <= -6.9e-282)
		tmp = t_3;
	elseif (y <= 1.25e-253)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	elseif (y <= 7.9e-29)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	t_3 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (y <= -6e-12)
		tmp = t_2;
	elseif (y <= -8.3e-227)
		tmp = a * ((y + t) / t_1);
	elseif (y <= -6.9e-282)
		tmp = t_3;
	elseif (y <= 1.25e-253)
		tmp = a * (t / (x + t));
	elseif (y <= 7.9e-29)
		tmp = t_3;
	else
		tmp = t_2;
	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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e-12], t$95$2, If[LessEqual[y, -8.3e-227], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.9e-282], t$95$3, If[LessEqual[y, 1.25e-253], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.9e-29], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.0000000000000003e-12 or 7.9000000000000001e-29 < y

   1. Initial program 37.0%

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

   3. Taylor expanded in y around inf 78.4%

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

   if -6.0000000000000003e-12 < y < -8.2999999999999996e-227

   1. Initial program 85.1%

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

   3. Taylor expanded in a around inf 51.9%

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

      1. associate-/l* 59.2%

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

      2. +-commutative 59.2%

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

      3. associate-+r+ 59.2%

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

      4. +-commutative 59.2%

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

      5. associate-+l+ 59.2%

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

   5. Simplified 59.2%

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

   if -8.2999999999999996e-227 < y < -6.89999999999999967e-282 or 1.24999999999999993e-253 < y < 7.9000000000000001e-29

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf 54.3%

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

      1. associate-/l* 62.3%

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

      2. +-commutative 62.3%

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

      3. +-commutative 62.3%

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

      4. associate-+r+ 62.3%

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

      5. +-commutative 62.3%

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

      6. associate-+l+ 62.3%

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

   5. Simplified 62.3%

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

   if -6.89999999999999967e-282 < y < 1.24999999999999993e-253

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 63.3%

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

      1. *-commutative 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. associate-/l* 61.7%

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

      2. +-commutative 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-12}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-227}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-282}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(\frac{y}{x + y} + \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= t -2.7e+91)
     t_2
     (if (<= t 1.05e-303)
       t_1
       (if (<= t 1.4e-21)
         (* a (+ (/ y (+ x y)) (/ z a)))
         (if (<= t 4.2e+42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (t <= -2.7e+91) {
		tmp = t_2;
	} else if (t <= 1.05e-303) {
		tmp = t_1;
	} else if (t <= 1.4e-21) {
		tmp = a * ((y / (x + y)) + (z / a));
	} else if (t <= 4.2e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((y + t) / (y + (x + t)))
    if (t <= (-2.7d+91)) then
        tmp = t_2
    else if (t <= 1.05d-303) then
        tmp = t_1
    else if (t <= 1.4d-21) then
        tmp = a * ((y / (x + y)) + (z / a))
    else if (t <= 4.2d+42) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (t <= -2.7e+91) {
		tmp = t_2;
	} else if (t <= 1.05e-303) {
		tmp = t_1;
	} else if (t <= 1.4e-21) {
		tmp = a * ((y / (x + y)) + (z / a));
	} else if (t <= 4.2e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((y + t) / (y + (x + t)))
	tmp = 0
	if t <= -2.7e+91:
		tmp = t_2
	elif t <= 1.05e-303:
		tmp = t_1
	elif t <= 1.4e-21:
		tmp = a * ((y / (x + y)) + (z / a))
	elif t <= 4.2e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (t <= -2.7e+91)
		tmp = t_2;
	elseif (t <= 1.05e-303)
		tmp = t_1;
	elseif (t <= 1.4e-21)
		tmp = Float64(a * Float64(Float64(y / Float64(x + y)) + Float64(z / a)));
	elseif (t <= 4.2e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((y + t) / (y + (x + t)));
	tmp = 0.0;
	if (t <= -2.7e+91)
		tmp = t_2;
	elseif (t <= 1.05e-303)
		tmp = t_1;
	elseif (t <= 1.4e-21)
		tmp = a * ((y / (x + y)) + (z / a));
	elseif (t <= 4.2e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+91], t$95$2, If[LessEqual[t, 1.05e-303], t$95$1, If[LessEqual[t, 1.4e-21], N[(a * N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e91 or 4.19999999999999991e42 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in a around inf 32.0%

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

      1. associate-/l* 62.2%

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

      2. +-commutative 62.2%

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

      3. associate-+r+ 62.2%

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

      4. +-commutative 62.2%

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

      5. associate-+l+ 62.2%

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

   5. Simplified 62.2%

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

   if -2.7e91 < t < 1.05e-303 or 1.40000000000000002e-21 < t < 4.19999999999999991e42

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf 70.5%

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

   if 1.05e-303 < t < 1.40000000000000002e-21

   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 a around inf 59.5%

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

      1. associate--l+ 59.5%

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

      2. +-commutative 59.5%

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

      3. +-commutative 59.5%

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

      4. associate-/l* 68.9%

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

      5. +-commutative 68.9%

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

      6. +-commutative 68.9%

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

      7. *-commutative 68.9%

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

      8. +-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in b around 0 54.5%

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

      1. associate-/l* 64.0%

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

      2. associate-/r* 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in t around 0 66.0%

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

       1. +-commutative 66.0%

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

   11. Simplified 66.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-303}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(\frac{y}{x + y} + \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{t}{x + t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ t (+ x t)))))
   (if (<= t -2.7e+91)
     t_2
     (if (<= t -1.9e-306)
       t_1
       (if (<= t 4.6e-123) z (if (<= t 4.4e+42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * (t / (x + t));
	double tmp;
	if (t <= -2.7e+91) {
		tmp = t_2;
	} else if (t <= -1.9e-306) {
		tmp = t_1;
	} else if (t <= 4.6e-123) {
		tmp = z;
	} else if (t <= 4.4e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * (t / (x + t))
    if (t <= (-2.7d+91)) then
        tmp = t_2
    else if (t <= (-1.9d-306)) then
        tmp = t_1
    else if (t <= 4.6d-123) then
        tmp = z
    else if (t <= 4.4d+42) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * (t / (x + t));
	double tmp;
	if (t <= -2.7e+91) {
		tmp = t_2;
	} else if (t <= -1.9e-306) {
		tmp = t_1;
	} else if (t <= 4.6e-123) {
		tmp = z;
	} else if (t <= 4.4e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * (t / (x + t))
	tmp = 0
	if t <= -2.7e+91:
		tmp = t_2
	elif t <= -1.9e-306:
		tmp = t_1
	elif t <= 4.6e-123:
		tmp = z
	elif t <= 4.4e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(t / Float64(x + t)))
	tmp = 0.0
	if (t <= -2.7e+91)
		tmp = t_2;
	elseif (t <= -1.9e-306)
		tmp = t_1;
	elseif (t <= 4.6e-123)
		tmp = z;
	elseif (t <= 4.4e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * (t / (x + t));
	tmp = 0.0;
	if (t <= -2.7e+91)
		tmp = t_2;
	elseif (t <= -1.9e-306)
		tmp = t_1;
	elseif (t <= 4.6e-123)
		tmp = z;
	elseif (t <= 4.4e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+91], t$95$2, If[LessEqual[t, -1.9e-306], t$95$1, If[LessEqual[t, 4.6e-123], z, If[LessEqual[t, 4.4e+42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e91 or 4.4000000000000003e42 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in z around 0 37.9%

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

      1. *-commutative 37.9%

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

   5. Simplified 37.9%

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

   6. Taylor expanded in y around 0 33.8%

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

      1. associate-/l* 61.0%

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

      2. +-commutative 61.0%

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

   8. Simplified 61.0%

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

   if -2.7e91 < t < -1.9e-306 or 4.59999999999999973e-123 < t < 4.4000000000000003e42

   1. Initial program 61.1%

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

   3. Taylor expanded in y around inf 68.1%

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

   if -1.9e-306 < t < 4.59999999999999973e-123

   1. Initial program 70.9%

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

   3. Taylor expanded in x around inf 65.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-306}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-120}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -2.7e+91)
     (* a (/ t (+ x t)))
     (if (<= t -8.8e-307)
       t_1
       (if (<= t 8e-120) z (if (<= t 1.3e+183) t_1 (- a (/ (* y b) t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -2.7e+91) {
		tmp = a * (t / (x + t));
	} else if (t <= -8.8e-307) {
		tmp = t_1;
	} else if (t <= 8e-120) {
		tmp = z;
	} else if (t <= 1.3e+183) {
		tmp = t_1;
	} else {
		tmp = a - ((y * b) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-2.7d+91)) then
        tmp = a * (t / (x + t))
    else if (t <= (-8.8d-307)) then
        tmp = t_1
    else if (t <= 8d-120) then
        tmp = z
    else if (t <= 1.3d+183) then
        tmp = t_1
    else
        tmp = a - ((y * b) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -2.7e+91) {
		tmp = a * (t / (x + t));
	} else if (t <= -8.8e-307) {
		tmp = t_1;
	} else if (t <= 8e-120) {
		tmp = z;
	} else if (t <= 1.3e+183) {
		tmp = t_1;
	} else {
		tmp = a - ((y * b) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -2.7e+91:
		tmp = a * (t / (x + t))
	elif t <= -8.8e-307:
		tmp = t_1
	elif t <= 8e-120:
		tmp = z
	elif t <= 1.3e+183:
		tmp = t_1
	else:
		tmp = a - ((y * b) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -2.7e+91)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	elseif (t <= -8.8e-307)
		tmp = t_1;
	elseif (t <= 8e-120)
		tmp = z;
	elseif (t <= 1.3e+183)
		tmp = t_1;
	else
		tmp = Float64(a - Float64(Float64(y * b) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -2.7e+91)
		tmp = a * (t / (x + t));
	elseif (t <= -8.8e-307)
		tmp = t_1;
	elseif (t <= 8e-120)
		tmp = z;
	elseif (t <= 1.3e+183)
		tmp = t_1;
	else
		tmp = a - ((y * b) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -2.7e+91], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.8e-307], t$95$1, If[LessEqual[t, 8e-120], z, If[LessEqual[t, 1.3e+183], t$95$1, N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7e91

   1. Initial program 53.5%

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

   3. Taylor expanded in z around 0 37.2%

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

      1. *-commutative 37.2%

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

   5. Simplified 37.2%

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

   6. Taylor expanded in y around 0 35.4%

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

      1. associate-/l* 65.3%

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

      2. +-commutative 65.3%

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

   8. Simplified 65.3%

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

   if -2.7e91 < t < -8.8e-307 or 7.99999999999999983e-120 < t < 1.3e183

   1. Initial program 61.7%

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

   3. Taylor expanded in y around inf 63.2%

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

   if -8.8e-307 < t < 7.99999999999999983e-120

   1. Initial program 70.9%

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

   3. Taylor expanded in x around inf 65.3%

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

   if 1.3e183 < t

   1. Initial program 41.2%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. associate-/l* 63.2%

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

      2. associate-/l* 70.9%

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

      3. +-commutative 70.9%

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

      4. associate-/l* 81.8%

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

      5. +-commutative 81.8%

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

      6. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in x around 0 70.7%

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

   7. Taylor expanded in z around 0 73.9%

      \[\leadsto \color{blue}{a - \frac{b \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-307}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-120}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+183}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -6.3 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(\frac{y}{x + y} + \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -6.3e+87)
     (* a (/ t (+ x t)))
     (if (<= t 3.5e-296)
       t_1
       (if (<= t 4.2e-22)
         (* a (+ (/ y (+ x y)) (/ z a)))
         (if (<= t 1.35e+183) t_1 (- a (/ (* y b) t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -6.3e+87) {
		tmp = a * (t / (x + t));
	} else if (t <= 3.5e-296) {
		tmp = t_1;
	} else if (t <= 4.2e-22) {
		tmp = a * ((y / (x + y)) + (z / a));
	} else if (t <= 1.35e+183) {
		tmp = t_1;
	} else {
		tmp = a - ((y * b) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-6.3d+87)) then
        tmp = a * (t / (x + t))
    else if (t <= 3.5d-296) then
        tmp = t_1
    else if (t <= 4.2d-22) then
        tmp = a * ((y / (x + y)) + (z / a))
    else if (t <= 1.35d+183) then
        tmp = t_1
    else
        tmp = a - ((y * b) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -6.3e+87) {
		tmp = a * (t / (x + t));
	} else if (t <= 3.5e-296) {
		tmp = t_1;
	} else if (t <= 4.2e-22) {
		tmp = a * ((y / (x + y)) + (z / a));
	} else if (t <= 1.35e+183) {
		tmp = t_1;
	} else {
		tmp = a - ((y * b) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -6.3e+87:
		tmp = a * (t / (x + t))
	elif t <= 3.5e-296:
		tmp = t_1
	elif t <= 4.2e-22:
		tmp = a * ((y / (x + y)) + (z / a))
	elif t <= 1.35e+183:
		tmp = t_1
	else:
		tmp = a - ((y * b) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -6.3e+87)
		tmp = Float64(a * Float64(t / Float64(x + t)));
	elseif (t <= 3.5e-296)
		tmp = t_1;
	elseif (t <= 4.2e-22)
		tmp = Float64(a * Float64(Float64(y / Float64(x + y)) + Float64(z / a)));
	elseif (t <= 1.35e+183)
		tmp = t_1;
	else
		tmp = Float64(a - Float64(Float64(y * b) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -6.3e+87)
		tmp = a * (t / (x + t));
	elseif (t <= 3.5e-296)
		tmp = t_1;
	elseif (t <= 4.2e-22)
		tmp = a * ((y / (x + y)) + (z / a));
	elseif (t <= 1.35e+183)
		tmp = t_1;
	else
		tmp = a - ((y * b) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -6.3e+87], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-296], t$95$1, If[LessEqual[t, 4.2e-22], N[(a * N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+183], t$95$1, N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.3e87

   1. Initial program 53.5%

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

   3. Taylor expanded in z around 0 37.2%

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

      1. *-commutative 37.2%

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

   5. Simplified 37.2%

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

   6. Taylor expanded in y around 0 35.4%

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

      1. associate-/l* 65.3%

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

      2. +-commutative 65.3%

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

   8. Simplified 65.3%

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

   if -6.3e87 < t < 3.4999999999999999e-296 or 4.20000000000000016e-22 < t < 1.34999999999999991e183

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 64.2%

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

   if 3.4999999999999999e-296 < t < 4.20000000000000016e-22

   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 a around inf 59.5%

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

      1. associate--l+ 59.5%

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

      2. +-commutative 59.5%

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

      3. +-commutative 59.5%

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

      4. associate-/l* 68.9%

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

      5. +-commutative 68.9%

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

      6. +-commutative 68.9%

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

      7. *-commutative 68.9%

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

      8. +-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in b around 0 54.5%

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

      1. associate-/l* 64.0%

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

      2. associate-/r* 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in t around 0 66.0%

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

       1. +-commutative 66.0%

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

   11. Simplified 66.0%

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

   if 1.34999999999999991e183 < t

   1. Initial program 41.2%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. associate-/l* 63.2%

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

      2. associate-/l* 70.9%

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

      3. +-commutative 70.9%

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

      4. associate-/l* 81.8%

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

      5. +-commutative 81.8%

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

      6. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in x around 0 70.7%

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

   7. Taylor expanded in z around 0 73.9%

      \[\leadsto \color{blue}{a - \frac{b \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-296}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(\frac{y}{x + y} + \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+183}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-10} \lor \neg \left(y \leq 115\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e-10) (not (<= y 115.0)))
   (- (+ z a) b)
   (/ (+ (* (+ x y) z) (* (+ y t) a)) (+ y (+ x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-10) || !(y <= 115.0)) {
		tmp = (z + a) - b;
	} else {
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t));
	}
	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 ((y <= (-1.35d-10)) .or. (.not. (y <= 115.0d0))) then
        tmp = (z + a) - b
    else
        tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t))
    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 ((y <= -1.35e-10) || !(y <= 115.0)) {
		tmp = (z + a) - b;
	} else {
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e-10) or not (y <= 115.0):
		tmp = (z + a) - b
	else:
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e-10) || !(y <= 115.0))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) / Float64(y + Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e-10) || ~((y <= 115.0)))
		tmp = (z + a) - b;
	else
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e-10], N[Not[LessEqual[y, 115.0]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-10 or 115 < y

   1. Initial program 34.9%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -1.35e-10 < y < 115

   1. Initial program 81.2%

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

   3. Taylor expanded in b around 0 75.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-10} \lor \neg \left(y \leq 115\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+123}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+65} \lor \neg \left(x \leq 5.2 \cdot 10^{+156}\right) \land x \leq 10^{+179}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.45e+123)
   z
   (if (or (<= x 7.8e+65) (and (not (<= x 5.2e+156)) (<= x 1e+179)))
     (- (+ z a) b)
     z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.45e+123) {
		tmp = z;
	} else if ((x <= 7.8e+65) || (!(x <= 5.2e+156) && (x <= 1e+179))) {
		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 <= (-2.45d+123)) then
        tmp = z
    else if ((x <= 7.8d+65) .or. (.not. (x <= 5.2d+156)) .and. (x <= 1d+179)) 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 <= -2.45e+123) {
		tmp = z;
	} else if ((x <= 7.8e+65) || (!(x <= 5.2e+156) && (x <= 1e+179))) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.45e+123:
		tmp = z
	elif (x <= 7.8e+65) or (not (x <= 5.2e+156) and (x <= 1e+179)):
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.45e+123)
		tmp = z;
	elseif ((x <= 7.8e+65) || (!(x <= 5.2e+156) && (x <= 1e+179)))
		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 <= -2.45e+123)
		tmp = z;
	elseif ((x <= 7.8e+65) || (~((x <= 5.2e+156)) && (x <= 1e+179)))
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.45e+123], z, If[Or[LessEqual[x, 7.8e+65], And[N[Not[LessEqual[x, 5.2e+156]], $MachinePrecision], LessEqual[x, 1e+179]]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.44999999999999988e123 or 7.7999999999999996e65 < x < 5.20000000000000037e156 or 9.9999999999999998e178 < x

   1. Initial program 53.5%

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

   3. Taylor expanded in x around inf 60.6%

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

   if -2.44999999999999988e123 < x < 7.7999999999999996e65 or 5.20000000000000037e156 < x < 9.9999999999999998e178

   1. Initial program 62.2%

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

   3. Taylor expanded in y around inf 66.1%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+123}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+65} \lor \neg \left(x \leq 5.2 \cdot 10^{+156}\right) \land x \leq 10^{+179}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-26} \lor \neg \left(y \leq 1.8 \cdot 10^{-26}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e-26) (not (<= y 1.8e-26)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e-26) || !(y <= 1.8e-26)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	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 ((y <= (-2.6d-26)) .or. (.not. (y <= 1.8d-26))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (x * z)) / (x + t)
    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 ((y <= -2.6e-26) || !(y <= 1.8e-26)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e-26) or not (y <= 1.8e-26):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e-26) || !(y <= 1.8e-26))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.6e-26) || ~((y <= 1.8e-26)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e-26], N[Not[LessEqual[y, 1.8e-26]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6000000000000001e-26 or 1.8000000000000001e-26 < y

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf 78.5%

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

   if -2.6000000000000001e-26 < y < 1.8000000000000001e-26

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 70.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-26} \lor \neg \left(y \leq 1.8 \cdot 10^{-26}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -108000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -108000000.0) z (if (<= z 1.2e+14) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -108000000.0) {
		tmp = z;
	} else if (z <= 1.2e+14) {
		tmp = 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 (z <= (-108000000.0d0)) then
        tmp = z
    else if (z <= 1.2d+14) then
        tmp = 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 (z <= -108000000.0) {
		tmp = z;
	} else if (z <= 1.2e+14) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -108000000.0:
		tmp = z
	elif z <= 1.2e+14:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -108000000.0)
		tmp = z;
	elseif (z <= 1.2e+14)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -108000000.0)
		tmp = z;
	elseif (z <= 1.2e+14)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -108000000.0], z, If[LessEqual[z, 1.2e+14], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08e8 or 1.2e14 < z

   1. Initial program 46.7%

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

   3. Taylor expanded in x around inf 56.2%

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

   if -1.08e8 < z < 1.2e14

   1. Initial program 71.3%

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

   3. Taylor expanded in z around 0 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in y around inf 48.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -108000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2250000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2250000.0) z (if (<= z 4.6e+14) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2250000.0) {
		tmp = z;
	} else if (z <= 4.6e+14) {
		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 (z <= (-2250000.0d0)) then
        tmp = z
    else if (z <= 4.6d+14) 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 (z <= -2250000.0) {
		tmp = z;
	} else if (z <= 4.6e+14) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2250000.0:
		tmp = z
	elif z <= 4.6e+14:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2250000.0)
		tmp = z;
	elseif (z <= 4.6e+14)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2250000.0)
		tmp = z;
	elseif (z <= 4.6e+14)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2250000.0], z, If[LessEqual[z, 4.6e+14], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e6 or 4.6e14 < z

   1. Initial program 46.7%

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

   3. Taylor expanded in x around inf 56.2%

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

   if -2.25e6 < z < 4.6e14

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 47.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2250000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.4% 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 59.5%

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

3. Taylor expanded in t around inf 33.5%

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

4. Final simplification 33.5%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (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)))