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

Percentage Accurate: 59.5% → 86.0%

Time: 12.1s

Alternatives: 14

Speedup: 1.2×

Specification

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

Fortran

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: 59.5% 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: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;a \cdot \left(b \cdot \frac{\frac{z}{b} \cdot \frac{x + y}{t\_1} - \frac{y}{t\_1}}{a} + \frac{y + t}{t\_1}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

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))
     (*
      a
      (+
       (* b (/ (- (* (/ z b) (/ (+ x y) t_1)) (/ y t_1)) a))
       (/ (+ y t) t_1)))
     (if (<= t_2 5e+267) t_2 (- (+ z a) b)))))

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 = a * ((b * ((((z / b) * ((x + y) / t_1)) - (y / t_1)) / a)) + ((y + t) / t_1));
	} else if (t_2 <= 5e+267) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	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 = a * ((b * ((((z / b) * ((x + y) / t_1)) - (y / t_1)) / a)) + ((y + t) / t_1));
	} else if (t_2 <= 5e+267) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	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 = a * ((b * ((((z / b) * ((x + y) / t_1)) - (y / t_1)) / a)) + ((y + t) / t_1))
	elif t_2 <= 5e+267:
		tmp = t_2
	else:
		tmp = (z + a) - b
	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(a * Float64(Float64(b * Float64(Float64(Float64(Float64(z / b) * Float64(Float64(x + y) / t_1)) - Float64(y / t_1)) / a)) + Float64(Float64(y + t) / t_1)));
	elseif (t_2 <= 5e+267)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + a) - b);
	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 = a * ((b * ((((z / b) * ((x + y) / t_1)) - (y / t_1)) / a)) + ((y + t) / t_1));
	elseif (t_2 <= 5e+267)
		tmp = t_2;
	else
		tmp = (z + a) - b;
	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[(a * N[(N[(b * N[(N[(N[(N[(z / b), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+267], t$95$2, N[(N[(z + a), $MachinePrecision] - b), $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 6.5%

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

   3. Taylor expanded in b around inf 12.2%

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

      1. +-commutative 12.2%

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

      2. mul-1-neg 12.2%

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

      3. unsub-neg 12.2%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in a around -inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. mul-1-neg 67.2%

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

      3. fma-define 67.2%

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

      4. mul-1-neg 67.2%

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

      5. +-commutative 67.2%

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

      6. +-commutative 67.2%

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

      7. associate-+r+ 67.2%

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

      8. fmm-undef 67.2%

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

   8. Simplified 77.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e267

   1. Initial program 99.7%

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

   if 4.9999999999999999e267 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.0%

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

   3. Taylor expanded in y around inf 79.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a \cdot \left(b \cdot \frac{\frac{z}{b} \cdot \frac{x + y}{t + \left(x + y\right)} - \frac{y}{t + \left(x + y\right)}}{a} + \frac{y + t}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+302} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+267}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -2e+302) (not (<= t_1 5e+267))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -2e+302) || !(t_1 <= 5e+267)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-2d+302)) .or. (.not. (t_1 <= 5d+267))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -2e+302) || !(t_1 <= 5e+267)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -2e+302) or not (t_1 <= 5e+267):
		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(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -2e+302) || !(t_1 <= 5e+267))
		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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -2e+302) || ~((t_1 <= 5e+267)))
		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[(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[Or[LessEqual[t$95$1, -2e+302], N[Not[LessEqual[t$95$1, 5e+267]], $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)) < -2.0000000000000002e302 or 4.9999999999999999e267 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.2%

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

   3. Taylor expanded in y around inf 76.5%

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

   if -2.0000000000000002e302 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e267

   1. Initial program 99.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+302} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+267}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-8}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1550000:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t\_1}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+114}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (/ (+ y t) (+ x (+ y t))))))
   (if (<= a -7.5e+76)
     t_2
     (if (<= a -4.9e-8)
       (- (+ z a) b)
       (if (<= a 1550000.0)
         (/ (- (* z (+ x y)) (* y b)) t_1)
         (if (<= a 4.1e+114) (/ (- (* a (+ y t)) (* y b)) t_1) 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 = a * ((y + t) / (x + (y + t)));
	double tmp;
	if (a <= -7.5e+76) {
		tmp = t_2;
	} else if (a <= -4.9e-8) {
		tmp = (z + a) - b;
	} else if (a <= 1550000.0) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (a <= 4.1e+114) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((y + t) / (x + (y + t)))
    if (a <= (-7.5d+76)) then
        tmp = t_2
    else if (a <= (-4.9d-8)) then
        tmp = (z + a) - b
    else if (a <= 1550000.0d0) then
        tmp = ((z * (x + y)) - (y * b)) / t_1
    else if (a <= 4.1d+114) then
        tmp = ((a * (y + t)) - (y * b)) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / (x + (y + t)));
	double tmp;
	if (a <= -7.5e+76) {
		tmp = t_2;
	} else if (a <= -4.9e-8) {
		tmp = (z + a) - b;
	} else if (a <= 1550000.0) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (a <= 4.1e+114) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((y + t) / (x + (y + t)))
	tmp = 0
	if a <= -7.5e+76:
		tmp = t_2
	elif a <= -4.9e-8:
		tmp = (z + a) - b
	elif a <= 1550000.0:
		tmp = ((z * (x + y)) - (y * b)) / t_1
	elif a <= 4.1e+114:
		tmp = ((a * (y + t)) - (y * b)) / t_1
	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(a * Float64(Float64(y + t) / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (a <= -7.5e+76)
		tmp = t_2;
	elseif (a <= -4.9e-8)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 1550000.0)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_1);
	elseif (a <= 4.1e+114)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1);
	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 = a * ((y + t) / (x + (y + t)));
	tmp = 0.0;
	if (a <= -7.5e+76)
		tmp = t_2;
	elseif (a <= -4.9e-8)
		tmp = (z + a) - b;
	elseif (a <= 1550000.0)
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	elseif (a <= 4.1e+114)
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	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[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+76], t$95$2, If[LessEqual[a, -4.9e-8], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 1550000.0], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[a, 4.1e+114], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.4999999999999995e76 or 4.1000000000000001e114 < a

   1. Initial program 43.7%

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

   3. Taylor expanded in a around inf 32.2%

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

      1. associate-/l* 77.2%

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

      2. +-commutative 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-+r+ 77.2%

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

   5. Simplified 77.2%

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

   if -7.4999999999999995e76 < a < -4.9000000000000002e-8

   1. Initial program 40.6%

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

   3. Taylor expanded in y around inf 81.6%

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

   if -4.9000000000000002e-8 < a < 1.55e6

   1. Initial program 79.4%

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

   3. Taylor expanded in a around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if 1.55e6 < a < 4.1000000000000001e114

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. *-commutative 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-8}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1550000:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+114}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{y \cdot t\_1}{y + \left(x + t\right)}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ (* y t_1) (+ y (+ x t)))))
   (if (<= y -2e+86)
     t_1
     (if (<= y -5.5e-85)
       t_2
       (if (<= y 4.2e-84)
         (* z (+ (/ x (+ x (+ y t))) (/ a z)))
         (if (<= y 6.6e+56) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = (y * t_1) / (y + (x + t));
	double tmp;
	if (y <= -2e+86) {
		tmp = t_1;
	} else if (y <= -5.5e-85) {
		tmp = t_2;
	} else if (y <= 4.2e-84) {
		tmp = z * ((x / (x + (y + t))) + (a / z));
	} else if (y <= 6.6e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = (y * t_1) / (y + (x + t))
    if (y <= (-2d+86)) then
        tmp = t_1
    else if (y <= (-5.5d-85)) then
        tmp = t_2
    else if (y <= 4.2d-84) then
        tmp = z * ((x / (x + (y + t))) + (a / z))
    else if (y <= 6.6d+56) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = (y * t_1) / (y + (x + t));
	double tmp;
	if (y <= -2e+86) {
		tmp = t_1;
	} else if (y <= -5.5e-85) {
		tmp = t_2;
	} else if (y <= 4.2e-84) {
		tmp = z * ((x / (x + (y + t))) + (a / z));
	} else if (y <= 6.6e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = (y * t_1) / (y + (x + t))
	tmp = 0
	if y <= -2e+86:
		tmp = t_1
	elif y <= -5.5e-85:
		tmp = t_2
	elif y <= 4.2e-84:
		tmp = z * ((x / (x + (y + t))) + (a / z))
	elif y <= 6.6e+56:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (y <= -2e+86)
		tmp = t_1;
	elseif (y <= -5.5e-85)
		tmp = t_2;
	elseif (y <= 4.2e-84)
		tmp = Float64(z * Float64(Float64(x / Float64(x + Float64(y + t))) + Float64(a / z)));
	elseif (y <= 6.6e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = (y * t_1) / (y + (x + t));
	tmp = 0.0;
	if (y <= -2e+86)
		tmp = t_1;
	elseif (y <= -5.5e-85)
		tmp = t_2;
	elseif (y <= 4.2e-84)
		tmp = z * ((x / (x + (y + t))) + (a / z));
	elseif (y <= 6.6e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+86], t$95$1, If[LessEqual[y, -5.5e-85], t$95$2, If[LessEqual[y, 4.2e-84], N[(z * N[(N[(x / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+56], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e86 or 6.60000000000000004e56 < 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 81.8%

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

   if -2e86 < y < -5.4999999999999997e-85 or 4.19999999999999996e-84 < y < 6.60000000000000004e56

   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 y around inf 67.5%

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

   if -5.4999999999999997e-85 < y < 4.19999999999999996e-84

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. +-commutative 73.1%

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

      3. associate-+r+ 73.1%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in t around inf 66.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+86}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-288}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-69}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.65e-85)
     t_1
     (if (<= y 5.2e-288)
       (* z (+ (/ x (+ x (+ y t))) (/ a z)))
       (if (<= y 2.05e-69) (/ (+ (* t a) (* x z)) (+ x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.65e-85) {
		tmp = t_1;
	} else if (y <= 5.2e-288) {
		tmp = z * ((x / (x + (y + t))) + (a / z));
	} else if (y <= 2.05e-69) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.65d-85)) then
        tmp = t_1
    else if (y <= 5.2d-288) then
        tmp = z * ((x / (x + (y + t))) + (a / z))
    else if (y <= 2.05d-69) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.65e-85) {
		tmp = t_1;
	} else if (y <= 5.2e-288) {
		tmp = z * ((x / (x + (y + t))) + (a / z));
	} else if (y <= 2.05e-69) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.65e-85:
		tmp = t_1
	elif y <= 5.2e-288:
		tmp = z * ((x / (x + (y + t))) + (a / z))
	elif y <= 2.05e-69:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.65e-85)
		tmp = t_1;
	elseif (y <= 5.2e-288)
		tmp = Float64(z * Float64(Float64(x / Float64(x + Float64(y + t))) + Float64(a / z)));
	elseif (y <= 2.05e-69)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.65e-85)
		tmp = t_1;
	elseif (y <= 5.2e-288)
		tmp = z * ((x / (x + (y + t))) + (a / z));
	elseif (y <= 2.05e-69)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.65e-85], t$95$1, If[LessEqual[y, 5.2e-288], N[(z * N[(N[(x / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-69], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.64999999999999986e-85 or 2.04999999999999995e-69 < y

   1. Initial program 55.7%

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

   3. Taylor expanded in y around inf 70.1%

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

   if -1.64999999999999986e-85 < y < 5.19999999999999979e-288

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate--l+ 74.0%

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

      2. +-commutative 74.0%

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

      3. associate-+r+ 74.0%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in t around inf 73.8%

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

   if 5.19999999999999979e-288 < y < 2.04999999999999995e-69

   1. Initial program 78.6%

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

   3. Taylor expanded in y around 0 63.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-85}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-288}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{a}{z}\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-69}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-170} \lor \neg \left(y \leq 4.4 \cdot 10^{-68}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e-170) (not (<= y 4.4e-68)))
   (- (+ 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 <= -1.55e-170) || !(y <= 4.4e-68)) {
		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 <= (-1.55d-170)) .or. (.not. (y <= 4.4d-68))) 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 <= -1.55e-170) || !(y <= 4.4e-68)) {
		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 <= -1.55e-170) or not (y <= 4.4e-68):
		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 <= -1.55e-170) || !(y <= 4.4e-68))
		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 <= -1.55e-170) || ~((y <= 4.4e-68)))
		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, -1.55e-170], N[Not[LessEqual[y, 4.4e-68]], $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 < -1.54999999999999993e-170 or 4.40000000000000005e-68 < y

   1. Initial program 56.4%

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

   3. Taylor expanded in y around inf 67.0%

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

   if -1.54999999999999993e-170 < y < 4.40000000000000005e-68

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0 68.6%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-170} \lor \neg \left(y \leq 4.4 \cdot 10^{-68}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+24} \lor \neg \left(x \leq 3.7 \cdot 10^{+112}\right):\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -4.6e+24) (not (<= x 3.7e+112)))
   (+ z (* y (- (/ a x) (/ b x))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.6e+24) || !(x <= 3.7e+112)) {
		tmp = z + (y * ((a / x) - (b / 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 <= (-4.6d+24)) .or. (.not. (x <= 3.7d+112))) then
        tmp = z + (y * ((a / x) - (b / 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 <= -4.6e+24) || !(x <= 3.7e+112)) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.6e+24) or not (x <= 3.7e+112):
		tmp = z + (y * ((a / x) - (b / x)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -4.6e+24) || !(x <= 3.7e+112))
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / 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 <= -4.6e+24) || ~((x <= 3.7e+112)))
		tmp = z + (y * ((a / x) - (b / x)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.6e+24], N[Not[LessEqual[x, 3.7e+112]], $MachinePrecision]], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999998e24 or 3.70000000000000004e112 < x

   1. Initial program 56.4%

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

   3. Taylor expanded in x around inf 58.2%

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

      1. associate--l+ 59.3%

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

      2. +-commutative 59.3%

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

      3. associate-/l* 58.4%

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

      4. associate-/l* 66.6%

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

      5. +-commutative 66.6%

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

      6. *-commutative 66.6%

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

      7. associate-/l* 70.0%

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

      8. +-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in y around inf 66.2%

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

   if -4.5999999999999998e24 < x < 3.70000000000000004e112

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 67.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+24} \lor \neg \left(x \leq 3.7 \cdot 10^{+112}\right):\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+16} \lor \neg \left(a \leq 13000000000\right):\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (or (<= a -3.2e+16) (not (<= a 13000000000.0)))
     (* a (/ (+ y t) t_1))
     (* z (/ (+ x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if ((a <= -3.2e+16) || !(a <= 13000000000.0)) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = z * ((x + y) / 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 = x + (y + t)
    if ((a <= (-3.2d+16)) .or. (.not. (a <= 13000000000.0d0))) then
        tmp = a * ((y + t) / t_1)
    else
        tmp = z * ((x + y) / 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 = x + (y + t);
	double tmp;
	if ((a <= -3.2e+16) || !(a <= 13000000000.0)) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = z * ((x + y) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if (a <= -3.2e+16) or not (a <= 13000000000.0):
		tmp = a * ((y + t) / t_1)
	else:
		tmp = z * ((x + y) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if ((a <= -3.2e+16) || !(a <= 13000000000.0))
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	else
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if ((a <= -3.2e+16) || ~((a <= 13000000000.0)))
		tmp = a * ((y + t) / t_1);
	else
		tmp = z * ((x + y) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -3.2e+16], N[Not[LessEqual[a, 13000000000.0]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2e16 or 1.3e10 < a

   1. Initial program 51.1%

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

   3. Taylor expanded in a around inf 34.7%

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

      1. associate-/l* 70.6%

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

      2. +-commutative 70.6%

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

      3. +-commutative 70.6%

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

      4. associate-+r+ 70.6%

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

   5. Simplified 70.6%

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

   if -3.2e16 < a < 1.3e10

   1. Initial program 77.0%

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

   3. Taylor expanded in z around inf 44.9%

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

      1. associate-/l* 60.1%

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

      2. +-commutative 60.1%

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

      3. +-commutative 60.1%

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

      4. associate-+r+ 60.1%

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

   5. Simplified 60.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+16} \lor \neg \left(a \leq 13000000000\right):\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+25} \lor \neg \left(x \leq 5.9 \cdot 10^{+109}\right):\\ \;\;\;\;z - b \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.7e+25) (not (<= x 5.9e+109)))
   (- z (* b (/ y x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.7e+25) || !(x <= 5.9e+109)) {
		tmp = z - (b * (y / 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 <= (-1.7d+25)) .or. (.not. (x <= 5.9d+109))) then
        tmp = z - (b * (y / 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 <= -1.7e+25) || !(x <= 5.9e+109)) {
		tmp = z - (b * (y / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.7e+25) or not (x <= 5.9e+109):
		tmp = z - (b * (y / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.7e+25) || !(x <= 5.9e+109))
		tmp = Float64(z - Float64(b * Float64(y / 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 <= -1.7e+25) || ~((x <= 5.9e+109)))
		tmp = z - (b * (y / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.7e+25], N[Not[LessEqual[x, 5.9e+109]], $MachinePrecision]], N[(z - N[(b * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999992e25 or 5.8999999999999997e109 < x

   1. Initial program 56.4%

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

   3. Taylor expanded in x around inf 58.2%

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

      1. associate--l+ 59.3%

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

      2. +-commutative 59.3%

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

      3. associate-/l* 58.4%

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

      4. associate-/l* 66.6%

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

      5. +-commutative 66.6%

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

      6. *-commutative 66.6%

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

      7. associate-/l* 70.0%

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

      8. +-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in y around inf 66.2%

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

   7. Taylor expanded in a around 0 53.5%

      \[\leadsto z + \color{blue}{-1 \cdot \frac{b \cdot y}{x}} \]
   8. Step-by-step derivation

      1. mul-1-neg 53.5%

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

      2. associate-/l* 56.4%

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

   9. Simplified 56.4%

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

   if -1.69999999999999992e25 < x < 5.8999999999999997e109

   1. Initial program 67.4%

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

   3. Taylor expanded in y around inf 67.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+25} \lor \neg \left(x \leq 5.9 \cdot 10^{+109}\right):\\ \;\;\;\;z - b \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+144} \lor \neg \left(x \leq 4.4 \cdot 10^{+118}\right):\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -4.2e+144) (not (<= x 4.4e+118)))
   (+ z (* y (/ a x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -4.2e+144) || !(x <= 4.4e+118)) {
		tmp = z + (y * (a / 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 <= (-4.2d+144)) .or. (.not. (x <= 4.4d+118))) then
        tmp = z + (y * (a / 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 <= -4.2e+144) || !(x <= 4.4e+118)) {
		tmp = z + (y * (a / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.2e+144) or not (x <= 4.4e+118):
		tmp = z + (y * (a / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -4.2e+144) || !(x <= 4.4e+118))
		tmp = Float64(z + Float64(y * Float64(a / 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 <= -4.2e+144) || ~((x <= 4.4e+118)))
		tmp = z + (y * (a / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.2e+144], N[Not[LessEqual[x, 4.4e+118]], $MachinePrecision]], N[(z + N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999993e144 or 4.39999999999999972e118 < x

   1. Initial program 58.0%

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

   3. Taylor expanded in x around inf 62.4%

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

      1. associate--l+ 63.7%

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

      2. +-commutative 63.7%

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

      3. associate-/l* 62.6%

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

      4. associate-/l* 72.3%

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

      5. +-commutative 72.3%

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

      6. *-commutative 72.3%

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

      7. associate-/l* 76.5%

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

      8. +-commutative 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in y around inf 69.3%

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

   7. Taylor expanded in a around inf 57.9%

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

   if -4.19999999999999993e144 < x < 4.39999999999999972e118

   1. Initial program 65.8%

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

   3. Taylor expanded in y around inf 65.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+144} \lor \neg \left(x \leq 4.4 \cdot 10^{+118}\right):\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 950000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.05e+17) a (if (<= a 950000000000.0) z (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e+17) {
		tmp = a;
	} else if (a <= 950000000000.0) {
		tmp = z;
	} else {
		tmp = 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 (a <= (-1.05d+17)) then
        tmp = a
    else if (a <= 950000000000.0d0) then
        tmp = z
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e+17) {
		tmp = a;
	} else if (a <= 950000000000.0) {
		tmp = z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.05e+17:
		tmp = a
	elif a <= 950000000000.0:
		tmp = z
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.05e+17)
		tmp = a;
	elseif (a <= 950000000000.0)
		tmp = z;
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.05e+17)
		tmp = a;
	elseif (a <= 950000000000.0)
		tmp = z;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.05e+17], a, If[LessEqual[a, 950000000000.0], z, N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05e17

   1. Initial program 53.3%

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

   3. Taylor expanded in t around inf 57.0%

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

   if -1.05e17 < a < 9.5e11

   1. Initial program 77.0%

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

   3. Taylor expanded in x around inf 45.7%

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

   if 9.5e11 < a

   1. Initial program 49.1%

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

   3. Taylor expanded in z around 0 45.5%

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

      1. +-commutative 45.5%

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

      2. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in y around inf 57.6%

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

Alternative 12: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+16}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5100000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.6e+16) a (if (<= a 5100000.0) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.6e+16) {
		tmp = a;
	} else if (a <= 5100000.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.6d+16)) then
        tmp = a
    else if (a <= 5100000.0d0) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.6e+16) {
		tmp = a;
	} else if (a <= 5100000.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.6e+16:
		tmp = a
	elif a <= 5100000.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.6e+16)
		tmp = a;
	elseif (a <= 5100000.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.6e+16)
		tmp = a;
	elseif (a <= 5100000.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.6e+16], a, If[LessEqual[a, 5100000.0], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -5.6e16 or 5.1e6 < a

   1. Initial program 51.1%

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

   3. Taylor expanded in t around inf 53.7%

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

   if -5.6e16 < a < 5.1e6

   1. Initial program 77.0%

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

   3. Taylor expanded in x around inf 45.7%

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

Alternative 13: 56.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1.8e+77) z (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+77) {
		tmp = z;
	} 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 <= (-1.8d+77)) then
        tmp = z
    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 <= -1.8e+77) {
		tmp = z;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.8e+77:
		tmp = z
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.8e+77)
		tmp = z;
	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 <= -1.8e+77)
		tmp = z;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.8e+77], z, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e77

   1. Initial program 58.4%

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

   3. Taylor expanded in x around inf 46.1%

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

   if -1.7999999999999999e77 < x

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 61.6%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.8% 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 63.6%

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

3. Taylor expanded in t around inf 33.2%

   \[\leadsto \color{blue}{a} \]
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 2024157 
(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)))