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

Percentage Accurate: 61.1% → 88.7%

Time: 13.5s

Alternatives: 12

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+279}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 5e+279))) (- (+ 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 <= 5e+279)) {
		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 <= 5e+279)) {
		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 <= 5e+279):
		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 <= 5e+279))
		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 <= 5e+279)))
		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, 5e+279]], $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 5.0000000000000002e279 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.9%

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

   3. Taylor expanded in y around inf 76.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e279

   1. Initial program 99.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+279}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+156}:\\ \;\;\;\;z + a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* z (+ (/ y t) (/ x t))))))
   (if (<= t -2.4e+61)
     t_1
     (if (<= t 5.2e-32)
       (- (+ z a) b)
       (if (<= t 5.2e+156) (+ z (* a (/ t (+ x t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * ((y / t) + (x / t)));
	double tmp;
	if (t <= -2.4e+61) {
		tmp = t_1;
	} else if (t <= 5.2e-32) {
		tmp = (z + a) - b;
	} else if (t <= 5.2e+156) {
		tmp = z + (a * (t / (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 = a + (z * ((y / t) + (x / t)))
    if (t <= (-2.4d+61)) then
        tmp = t_1
    else if (t <= 5.2d-32) then
        tmp = (z + a) - b
    else if (t <= 5.2d+156) then
        tmp = z + (a * (t / (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 = a + (z * ((y / t) + (x / t)));
	double tmp;
	if (t <= -2.4e+61) {
		tmp = t_1;
	} else if (t <= 5.2e-32) {
		tmp = (z + a) - b;
	} else if (t <= 5.2e+156) {
		tmp = z + (a * (t / (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z * ((y / t) + (x / t)))
	tmp = 0
	if t <= -2.4e+61:
		tmp = t_1
	elif t <= 5.2e-32:
		tmp = (z + a) - b
	elif t <= 5.2e+156:
		tmp = z + (a * (t / (x + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z * Float64(Float64(y / t) + Float64(x / t))))
	tmp = 0.0
	if (t <= -2.4e+61)
		tmp = t_1;
	elseif (t <= 5.2e-32)
		tmp = Float64(Float64(z + a) - b);
	elseif (t <= 5.2e+156)
		tmp = Float64(z + Float64(a * Float64(t / Float64(x + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z * ((y / t) + (x / t)));
	tmp = 0.0;
	if (t <= -2.4e+61)
		tmp = t_1;
	elseif (t <= 5.2e-32)
		tmp = (z + a) - b;
	elseif (t <= 5.2e+156)
		tmp = z + (a * (t / (x + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(N[(y / t), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+61], t$95$1, If[LessEqual[t, 5.2e-32], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t, 5.2e+156], N[(z + N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3999999999999999e61 or 5.20000000000000037e156 < t

   1. Initial program 50.5%

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

   3. Taylor expanded in t around inf 64.6%

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

      1. associate--l+ 65.7%

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

      2. associate-/l* 64.7%

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

      3. associate-/l* 68.5%

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

      4. +-commutative 68.5%

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

      5. associate-/l* 81.0%

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

      6. +-commutative 81.0%

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

      7. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in z around inf 74.5%

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

      1. +-commutative 74.5%

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

   8. Simplified 74.5%

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

   if -2.3999999999999999e61 < t < 5.1999999999999995e-32

   1. Initial program 63.8%

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

   3. Taylor expanded in y around inf 64.5%

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

   if 5.1999999999999995e-32 < t < 5.20000000000000037e156

   1. Initial program 61.2%

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

   3. Taylor expanded in b around -inf 56.3%

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

      1. associate-*r* 56.3%

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

      2. neg-mul-1 56.3%

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

      3. fma-define 56.3%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in y around 0 46.0%

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

      1. associate-/l* 60.6%

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

      2. +-commutative 60.6%

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

      3. associate-/l* 72.4%

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

      4. +-commutative 72.4%

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

   8. Simplified 72.4%

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

   9. Taylor expanded in x around inf 66.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+156}:\\ \;\;\;\;z + a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+43} \lor \neg \left(y \leq 7 \cdot 10^{-15}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + x \cdot \frac{z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.7e+43) (not (<= y 7e-15)))
   (- (+ z a) b)
   (+ (* a (/ t (+ x t))) (* x (/ z (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+43) || !(y <= 7e-15)) {
		tmp = (z + a) - b;
	} else {
		tmp = (a * (t / (x + t))) + (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 <= (-1.7d+43)) .or. (.not. (y <= 7d-15))) then
        tmp = (z + a) - b
    else
        tmp = (a * (t / (x + t))) + (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 <= -1.7e+43) || !(y <= 7e-15)) {
		tmp = (z + a) - b;
	} else {
		tmp = (a * (t / (x + t))) + (x * (z / (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.7e+43) or not (y <= 7e-15):
		tmp = (z + a) - b
	else:
		tmp = (a * (t / (x + t))) + (x * (z / (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.7e+43) || !(y <= 7e-15))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(a * Float64(t / Float64(x + t))) + Float64(x * Float64(z / Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.7e+43) || ~((y <= 7e-15)))
		tmp = (z + a) - b;
	else
		tmp = (a * (t / (x + t))) + (x * (z / (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.7e+43], N[Not[LessEqual[y, 7e-15]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000006e43 or 7.0000000000000001e-15 < y

   1. Initial program 37.9%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -1.70000000000000006e43 < y < 7.0000000000000001e-15

   1. Initial program 75.1%

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

   3. Taylor expanded in b around -inf 66.2%

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

      1. associate-*r* 66.2%

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

      2. neg-mul-1 66.2%

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

      3. fma-define 66.2%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around 0 54.9%

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

      1. associate-/l* 67.4%

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

      2. +-commutative 67.4%

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

      3. associate-/l* 72.6%

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

      4. +-commutative 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+43} \lor \neg \left(y \leq 7 \cdot 10^{-15}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t} + x \cdot \frac{z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-179}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;z + a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -9.5e-166)
     t_1
     (if (<= y 2.9e-179)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 7.5e+116) (+ z (* a (/ t (+ 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 <= -9.5e-166) {
		tmp = t_1;
	} else if (y <= 2.9e-179) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7.5e+116) {
		tmp = z + (a * (t / (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 <= (-9.5d-166)) then
        tmp = t_1
    else if (y <= 2.9d-179) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 7.5d+116) then
        tmp = z + (a * (t / (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 <= -9.5e-166) {
		tmp = t_1;
	} else if (y <= 2.9e-179) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7.5e+116) {
		tmp = z + (a * (t / (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 <= -9.5e-166:
		tmp = t_1
	elif y <= 2.9e-179:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 7.5e+116:
		tmp = z + (a * (t / (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 <= -9.5e-166)
		tmp = t_1;
	elseif (y <= 2.9e-179)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 7.5e+116)
		tmp = Float64(z + Float64(a * Float64(t / 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 <= -9.5e-166)
		tmp = t_1;
	elseif (y <= 2.9e-179)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 7.5e+116)
		tmp = z + (a * (t / (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, -9.5e-166], t$95$1, If[LessEqual[y, 2.9e-179], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+116], N[(z + N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000046e-166 or 7.5e116 < y

   1. Initial program 46.2%

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

   3. Taylor expanded in y around inf 68.7%

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

   if -9.50000000000000046e-166 < y < 2.8999999999999999e-179

   1. Initial program 82.5%

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

   3. Taylor expanded in y around 0 72.5%

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

   if 2.8999999999999999e-179 < y < 7.5e116

   1. Initial program 64.1%

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

   3. Taylor expanded in b around -inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. neg-mul-1 57.3%

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

      3. fma-define 57.3%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. associate-/l* 58.1%

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

      2. +-commutative 58.1%

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

      3. associate-/l* 66.3%

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

      4. +-commutative 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in x around inf 64.7%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-179}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;z + a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+77} \lor \neg \left(y \leq 6.2 \cdot 10^{+116}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e+77) (not (<= y 6.2e+116)))
   (- (+ z a) b)
   (+ z (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e+77) || !(y <= 6.2e+116)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * (t / (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 <= (-1.75d+77)) .or. (.not. (y <= 6.2d+116))) then
        tmp = (z + a) - b
    else
        tmp = z + (a * (t / (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 <= -1.75e+77) || !(y <= 6.2e+116)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * (t / (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e+77) or not (y <= 6.2e+116):
		tmp = (z + a) - b
	else:
		tmp = z + (a * (t / (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e+77) || !(y <= 6.2e+116))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(a * Float64(t / Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.75e+77) || ~((y <= 6.2e+116)))
		tmp = (z + a) - b;
	else
		tmp = z + (a * (t / (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.75e+77], N[Not[LessEqual[y, 6.2e+116]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e77 or 6.19999999999999992e116 < y

   1. Initial program 30.6%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -1.7500000000000001e77 < y < 6.19999999999999992e116

   1. Initial program 71.6%

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

   3. Taylor expanded in b around -inf 63.8%

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

      1. associate-*r* 63.8%

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

      2. neg-mul-1 63.8%

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

      3. fma-define 63.8%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around 0 50.9%

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

      1. associate-/l* 63.8%

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

      2. +-commutative 63.8%

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

      3. associate-/l* 68.8%

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

      4. +-commutative 68.8%

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

   8. Simplified 68.8%

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

   9. Taylor expanded in x around inf 60.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+77} \lor \neg \left(y \leq 6.2 \cdot 10^{+116}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-252}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+162}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.6e+99) z (if (<= x 5.2e-252) a (if (<= x 5e+162) (- a b) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+99) {
		tmp = z;
	} else if (x <= 5.2e-252) {
		tmp = a;
	} else if (x <= 5e+162) {
		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 (x <= (-9.6d+99)) then
        tmp = z
    else if (x <= 5.2d-252) then
        tmp = a
    else if (x <= 5d+162) 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 (x <= -9.6e+99) {
		tmp = z;
	} else if (x <= 5.2e-252) {
		tmp = a;
	} else if (x <= 5e+162) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.6e+99:
		tmp = z
	elif x <= 5.2e-252:
		tmp = a
	elif x <= 5e+162:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.6e+99)
		tmp = z;
	elseif (x <= 5.2e-252)
		tmp = a;
	elseif (x <= 5e+162)
		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 (x <= -9.6e+99)
		tmp = z;
	elseif (x <= 5.2e-252)
		tmp = a;
	elseif (x <= 5e+162)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.6e+99], z, If[LessEqual[x, 5.2e-252], a, If[LessEqual[x, 5e+162], N[(a - b), $MachinePrecision], z]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.6000000000000005e99 or 4.9999999999999997e162 < x

   1. Initial program 49.6%

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

   3. Taylor expanded in x around inf 52.8%

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

   if -9.6000000000000005e99 < x < 5.1999999999999998e-252

   1. Initial program 62.4%

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

   3. Taylor expanded in t around inf 49.5%

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

   if 5.1999999999999998e-252 < x < 4.9999999999999997e162

   1. Initial program 63.0%

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

   3. Taylor expanded in z around 0 46.8%

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

      1. +-commutative 46.8%

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

      2. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around inf 50.2%

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

Alternative 7: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{+156} \lor \neg \left(t \leq 4.1 \cdot 10^{+120}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.62e+156) (not (<= t 4.1e+120)))
   (* a (/ t (+ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.62e+156) || !(t <= 4.1e+120)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.62d+156)) .or. (.not. (t <= 4.1d+120))) then
        tmp = a * (t / (x + t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.62e+156) || !(t <= 4.1e+120)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.62e+156) or not (t <= 4.1e+120):
		tmp = a * (t / (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.62e+156) || !(t <= 4.1e+120))
		tmp = Float64(a * Float64(t / Float64(x + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.62e+156) || ~((t <= 4.1e+120)))
		tmp = a * (t / (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.62e+156], N[Not[LessEqual[t, 4.1e+120]], $MachinePrecision]], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.62000000000000006e156 or 4.1e120 < t

   1. Initial program 48.6%

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

   3. Taylor expanded in z around 0 41.5%

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

      1. +-commutative 41.5%

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

      2. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in y around 0 31.6%

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

      1. associate-/l* 67.5%

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

      2. +-commutative 67.5%

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

   8. Simplified 67.5%

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

   if -1.62000000000000006e156 < t < 4.1e120

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 62.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{+156} \lor \neg \left(t \leq 4.1 \cdot 10^{+120}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;a + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.1e+60)
   (+ a (* z (/ x t)))
   (if (<= t 1e+119) (- (+ z a) b) (* a (/ t (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+60) {
		tmp = a + (z * (x / t));
	} else if (t <= 1e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (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 (t <= (-3.1d+60)) then
        tmp = a + (z * (x / t))
    else if (t <= 1d+119) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (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 (t <= -3.1e+60) {
		tmp = a + (z * (x / t));
	} else if (t <= 1e+119) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.1e+60:
		tmp = a + (z * (x / t))
	elif t <= 1e+119:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.1e+60)
		tmp = Float64(a + Float64(z * Float64(x / t)));
	elseif (t <= 1e+119)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.1e+60)
		tmp = a + (z * (x / t));
	elseif (t <= 1e+119)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.1e+60], N[(a + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+119], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.1000000000000001e60

   1. Initial program 51.7%

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

   3. Taylor expanded in t around inf 62.7%

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

      1. associate--l+ 62.7%

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

      2. associate-/l* 62.8%

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

      3. associate-/l* 65.3%

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

      4. +-commutative 65.3%

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

      5. associate-/l* 77.8%

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

      6. +-commutative 77.8%

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

      7. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in z around inf 71.1%

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

      1. +-commutative 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in y around 0 66.5%

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

   if -3.1000000000000001e60 < t < 9.99999999999999944e118

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 62.7%

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

   if 9.99999999999999944e118 < t

   1. Initial program 49.7%

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

   3. Taylor expanded in z around 0 41.7%

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

      1. +-commutative 41.7%

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

      2. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around 0 32.8%

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

      1. associate-/l* 66.5%

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

      2. +-commutative 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;a + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 10^{+119}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+165}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.1e+165) a (if (<= t 1.16e+120) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+165) {
		tmp = a;
	} else if (t <= 1.16e+120) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.1d+165)) then
        tmp = a
    else if (t <= 1.16d+120) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+165) {
		tmp = a;
	} else if (t <= 1.16e+120) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.1e+165:
		tmp = a
	elif t <= 1.16e+120:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.1e+165)
		tmp = a;
	elseif (t <= 1.16e+120)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.1e+165)
		tmp = a;
	elseif (t <= 1.16e+120)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.1e+165], a, If[LessEqual[t, 1.16e+120], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1000000000000002e165 or 1.16000000000000003e120 < t

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf 59.9%

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

   if -3.1000000000000002e165 < t < 1.16000000000000003e120

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 62.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+165}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+63}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+64}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4e+63) a (if (<= t 4.2e+64) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+63) {
		tmp = a;
	} else if (t <= 4.2e+64) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4d+63)) then
        tmp = a
    else if (t <= 4.2d+64) then
        tmp = z - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+63) {
		tmp = a;
	} else if (t <= 4.2e+64) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+63:
		tmp = a
	elif t <= 4.2e+64:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+63)
		tmp = a;
	elseif (t <= 4.2e+64)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4e+63)
		tmp = a;
	elseif (t <= 4.2e+64)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+63], a, If[LessEqual[t, 4.2e+64], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000023e63 or 4.2000000000000001e64 < t

   1. Initial program 52.7%

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

   3. Taylor expanded in t around inf 56.3%

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

   if -4.00000000000000023e63 < t < 4.2000000000000001e64

   1. Initial program 63.7%

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

   3. Taylor expanded in a around 0 42.2%

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

      1. +-commutative 42.2%

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

      2. *-commutative 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in y around inf 50.7%

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

Alternative 11: 44.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+47}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.35e+97) z (if (<= x 4.2e+47) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e+97) {
		tmp = z;
	} else if (x <= 4.2e+47) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.35d+97)) then
        tmp = z
    else if (x <= 4.2d+47) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e+97) {
		tmp = z;
	} else if (x <= 4.2e+47) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.35e+97:
		tmp = z
	elif x <= 4.2e+47:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.35e+97)
		tmp = z;
	elseif (x <= 4.2e+47)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.35e+97)
		tmp = z;
	elseif (x <= 4.2e+47)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.35e+97], z, If[LessEqual[x, 4.2e+47], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.34999999999999997e97 or 4.2e47 < x

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf 46.4%

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

   if -1.34999999999999997e97 < x < 4.2e47

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf 50.2%

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

Alternative 12: 32.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 58.9%

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

3. Taylor expanded in t around inf 35.9%

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

Developer Target 1: 82.9% 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 2024145 
(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)))