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

Percentage Accurate: 60.8% → 87.0%

Time: 13.3s

Alternatives: 14

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+60}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{x \cdot z}{t_1} + \left(y + t\right) \cdot \frac{a}{t_1}\right)\\ \mathbf{elif}\;t_2 \leq 10^{+253}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 -4e+60)
     (+ (/ (- z b) (/ t_1 y)) (+ (/ (* x z) t_1) (* (+ y t) (/ a t_1))))
     (if (<= t_2 1e+253) t_2 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -4e+60) {
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + ((y + t) * (a / t_1)));
	} else if (t_2 <= 1e+253) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
    if (t_2 <= (-4d+60)) then
        tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + ((y + t) * (a / t_1)))
    else if (t_2 <= 1d+253) then
        tmp = t_2
    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 t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -4e+60) {
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + ((y + t) * (a / t_1)));
	} else if (t_2 <= 1e+253) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -4e+60:
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + ((y + t) * (a / t_1)))
	elif t_2 <= 1e+253:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -4e+60)
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(Float64(x * z) / t_1) + Float64(Float64(y + t) * Float64(a / t_1))));
	elseif (t_2 <= 1e+253)
		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 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -4e+60)
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + ((y + t) * (a / t_1)));
	elseif (t_2 <= 1e+253)
		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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+60], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+253], 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)) < -3.9999999999999998e60

   1. Initial program 47.2%

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

   3. Simplified 47.2%

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

   4. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 67.4%

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

      2. +-commutative 67.4%

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

      3. associate-/l* 88.4%

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

   6. Simplified 88.4%

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

      1. associate-/r/ 88.4%

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

      2. +-commutative 88.4%

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

   8. Applied egg-rr 88.4%

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

   if -3.9999999999999998e60 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e252

   1. Initial program 99.7%

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

   if 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.4%

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

   2. Taylor expanded in y around inf 85.3%

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

      1. +-commutative 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -4 \cdot 10^{+60}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{x \cdot z}{y + \left(x + t\right)} + \left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 2: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;a + \frac{z - b}{\frac{t_1}{y}}\\ \mathbf{elif}\;t_2 \leq 10^{+253}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ a (/ (- z b) (/ t_1 y)))
     (if (<= t_2 1e+253) t_2 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = a + ((z - b) / (t_1 / y));
	} else if (t_2 <= 1e+253) {
		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 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = a + ((z - b) / (t_1 / y));
	} else if (t_2 <= 1e+253) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = a + ((z - b) / (t_1 / y))
	elif t_2 <= 1e+253:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(a + Float64(Float64(z - b) / Float64(t_1 / y)));
	elseif (t_2 <= 1e+253)
		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 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = a + ((z - b) / (t_1 / y));
	elseif (t_2 <= 1e+253)
		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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(a + N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+253], 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 7.4%

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

   3. Simplified 7.2%

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

   4. Taylor expanded in a around inf 7.4%

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

      1. associate-/l* 42.7%

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

      2. +-commutative 42.7%

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

      3. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in y around inf 75.0%

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

   8. Taylor expanded in a around inf 77.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e252

   1. Initial program 99.7%

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

   if 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.4%

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

   2. Taylor expanded in y around inf 85.3%

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

      1. +-commutative 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{x \cdot z}{t_1} + \frac{a}{1 + \frac{x}{t}}\right)\\ \mathbf{elif}\;t_2 \leq 10^{+253}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ (/ (- z b) (/ t_1 y)) (+ (/ (* x z) t_1) (/ a (+ 1.0 (/ x t)))))
     (if (<= t_2 1e+253) t_2 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (1.0 + (x / t))));
	} else if (t_2 <= 1e+253) {
		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 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (1.0 + (x / t))));
	} else if (t_2 <= 1e+253) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (1.0 + (x / t))))
	elif t_2 <= 1e+253:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(Float64(x * z) / t_1) + Float64(a / Float64(1.0 + Float64(x / t)))));
	elseif (t_2 <= 1e+253)
		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 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (1.0 + (x / t))));
	elseif (t_2 <= 1e+253)
		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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+253], 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 7.4%

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

   3. Simplified 7.2%

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

   4. Taylor expanded in a around inf 7.4%

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

      1. associate-/l* 42.7%

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

      2. +-commutative 42.7%

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

      3. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in t around inf 79.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e252

   1. Initial program 99.7%

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

   if 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.4%

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

   2. Taylor expanded in y around inf 85.3%

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

      1. +-commutative 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{x \cdot z}{y + \left(x + t\right)} + \frac{a}{1 + \frac{x}{t}}\right)\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 4: 86.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1} \leq 10^{+253}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{x \cdot z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1) 1e+253)
     (+ (/ (- z b) (/ t_1 y)) (+ (/ a (/ t_1 (+ y t))) (/ (* x z) t_1)))
     (- (+ z a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1) <= 1e+253) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1) <= 1d+253) then
        tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
    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 t_1 = y + (x + t);
	double tmp;
	if ((((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1) <= 1e+253) {
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1) <= 1e+253:
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1) <= 1e+253)
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(x * z) / t_1)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1) <= 1e+253)
		tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 1e+253], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]

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)) < 9.9999999999999994e252

   1. Initial program 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in a around inf 79.6%

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

      1. associate-/l* 85.9%

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

      2. +-commutative 85.9%

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

      3. associate-/l* 93.5%

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

   6. Simplified 93.5%

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

   if 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.4%

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

   2. Taylor expanded in y around inf 85.3%

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

      1. +-commutative 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 71.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-159} \lor \neg \left(y \leq 1.36 \cdot 10^{-138}\right):\\ \;\;\;\;a + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.06e-159) (not (<= y 1.36e-138)))
   (+ a (/ (- z b) (/ (+ y (+ x t)) y)))
   (/ (+ (* x z) (* t a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.06e-159) || !(y <= 1.36e-138)) {
		tmp = a + ((z - b) / ((y + (x + t)) / y));
	} else {
		tmp = ((x * z) + (t * a)) / (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 <= (-1.06d-159)) .or. (.not. (y <= 1.36d-138))) then
        tmp = a + ((z - b) / ((y + (x + t)) / y))
    else
        tmp = ((x * z) + (t * a)) / (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 <= -1.06e-159) || !(y <= 1.36e-138)) {
		tmp = a + ((z - b) / ((y + (x + t)) / y));
	} else {
		tmp = ((x * z) + (t * a)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.06e-159) or not (y <= 1.36e-138):
		tmp = a + ((z - b) / ((y + (x + t)) / y))
	else:
		tmp = ((x * z) + (t * a)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.06e-159) || !(y <= 1.36e-138))
		tmp = Float64(a + Float64(Float64(z - b) / Float64(Float64(y + Float64(x + t)) / y)));
	else
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.06e-159) || ~((y <= 1.36e-138)))
		tmp = a + ((z - b) / ((y + (x + t)) / y));
	else
		tmp = ((x * z) + (t * a)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.06e-159], N[Not[LessEqual[y, 1.36e-138]], $MachinePrecision]], N[(a + N[(N[(z - b), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e-159 or 1.36e-138 < 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. Step-by-step derivation

   3. Simplified 56.7%

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

   4. Taylor expanded in a around inf 56.4%

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

      1. associate-/l* 73.3%

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

      2. +-commutative 73.3%

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

      3. associate-/l* 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in y around inf 81.2%

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

   8. Taylor expanded in a around inf 80.3%

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

   if -1.06e-159 < y < 1.36e-138

   1. Initial program 85.1%

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

   2. Taylor expanded in y around 0 78.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-159} \lor \neg \left(y \leq 1.36 \cdot 10^{-138}\right):\\ \;\;\;\;a + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \end{array} \]

Alternative 6: 58.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-159} \lor \neg \left(y \leq 1.15 \cdot 10^{-139}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e-159) (not (<= y 1.15e-139)))
   (- (+ z a) b)
   (* z (/ (+ x y) (+ y (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e-159) || !(y <= 1.15e-139)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.2d-159)) .or. (.not. (y <= 1.15d-139))) then
        tmp = (z + a) - b
    else
        tmp = z * ((x + y) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e-159) || !(y <= 1.15e-139)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.2e-159) or not (y <= 1.15e-139):
		tmp = (z + a) - b
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.2e-159) || !(y <= 1.15e-139))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.2e-159) || ~((y <= 1.15e-139)))
		tmp = (z + a) - b;
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.2e-159], N[Not[LessEqual[y, 1.15e-139]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999998e-159 or 1.15000000000000006e-139 < 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. Taylor expanded in y around inf 66.4%

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

      1. +-commutative 66.4%

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

   4. Simplified 66.4%

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

   if -4.1999999999999998e-159 < y < 1.15000000000000006e-139

   1. Initial program 84.2%

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

   2. Taylor expanded in z around inf 46.1%

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

      1. associate-/l* 45.2%

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

   4. Simplified 45.2%

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

      1. associate-/r/ 53.9%

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

      2. +-commutative 53.9%

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

      3. +-commutative 53.9%

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

   6. Applied egg-rr 53.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-159} \lor \neg \left(y \leq 1.15 \cdot 10^{-139}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7: 63.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-160} \lor \neg \left(y \leq 9.5 \cdot 10^{-141}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e-160) (not (<= y 9.5e-141)))
   (- (+ z a) b)
   (/ (+ (* x z) (* t a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e-160) || !(y <= 9.5e-141)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((x * z) + (t * a)) / (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 <= (-4.6d-160)) .or. (.not. (y <= 9.5d-141))) then
        tmp = (z + a) - b
    else
        tmp = ((x * z) + (t * a)) / (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 <= -4.6e-160) || !(y <= 9.5e-141)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((x * z) + (t * a)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.6e-160) or not (y <= 9.5e-141):
		tmp = (z + a) - b
	else:
		tmp = ((x * z) + (t * a)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e-160) || !(y <= 9.5e-141))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.6e-160) || ~((y <= 9.5e-141)))
		tmp = (z + a) - b;
	else
		tmp = ((x * z) + (t * a)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e-160], N[Not[LessEqual[y, 9.5e-141]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999997e-160 or 9.49999999999999996e-141 < y

   1. Initial program 56.1%

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

   2. Taylor expanded in y around inf 66.0%

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

      1. +-commutative 66.0%

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

   4. Simplified 66.0%

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

   if -4.5999999999999997e-160 < y < 9.49999999999999996e-141

   1. Initial program 86.4%

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

   2. Taylor expanded in y around 0 79.3%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-160} \lor \neg \left(y \leq 9.5 \cdot 10^{-141}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \end{array} \]

Alternative 8: 57.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+225} \lor \neg \left(b \leq 9.5 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{y}{y + \left(x + t\right)} \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.15e+225) (not (<= b 9.5e+135)))
   (* (/ y (+ y (+ x t))) (- b))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.15e+225) || !(b <= 9.5e+135)) {
		tmp = (y / (y + (x + t))) * -b;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.15d+225)) .or. (.not. (b <= 9.5d+135))) then
        tmp = (y / (y + (x + t))) * -b
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.15e+225) || !(b <= 9.5e+135)) {
		tmp = (y / (y + (x + t))) * -b;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.15e+225) or not (b <= 9.5e+135):
		tmp = (y / (y + (x + t))) * -b
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.15e+225) || !(b <= 9.5e+135))
		tmp = Float64(Float64(y / Float64(y + Float64(x + t))) * Float64(-b));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.15e+225) || ~((b <= 9.5e+135)))
		tmp = (y / (y + (x + t))) * -b;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.15e+225], N[Not[LessEqual[b, 9.5e+135]], $MachinePrecision]], N[(N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-b)), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1500000000000001e225 or 9.50000000000000036e135 < b

   1. Initial program 46.9%

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

   2. Taylor expanded in b around inf 30.3%

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

      1. neg-mul-1 30.3%

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

      2. distribute-rgt-neg-in 30.3%

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

   4. Simplified 30.3%

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

      1. *-un-lft-identity 30.3%

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

      2. associate-/l* 62.8%

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

      3. +-commutative 62.8%

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

      4. +-commutative 62.8%

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

      5. +-commutative 62.8%

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

   6. Applied egg-rr 62.8%

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

      1. *-lft-identity 62.8%

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

      2. associate-/r/ 65.5%

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

   8. Simplified 65.5%

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

   if -2.1500000000000001e225 < b < 9.50000000000000036e135

   1. Initial program 68.7%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. +-commutative 62.6%

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

   4. Simplified 62.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+225} \lor \neg \left(b \leq 9.5 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{y}{y + \left(x + t\right)} \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 57.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+225}:\\ \;\;\;\;\frac{-y}{\frac{t_1}{b}}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+134}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t_1} \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= b -1.2e+225)
     (/ (- y) (/ t_1 b))
     (if (<= b 3.3e+134) (- (+ z a) b) (* (/ y t_1) (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (b <= -1.2e+225) {
		tmp = -y / (t_1 / b);
	} else if (b <= 3.3e+134) {
		tmp = (z + a) - b;
	} else {
		tmp = (y / t_1) * -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) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (b <= (-1.2d+225)) then
        tmp = -y / (t_1 / b)
    else if (b <= 3.3d+134) then
        tmp = (z + a) - b
    else
        tmp = (y / t_1) * -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 t_1 = y + (x + t);
	double tmp;
	if (b <= -1.2e+225) {
		tmp = -y / (t_1 / b);
	} else if (b <= 3.3e+134) {
		tmp = (z + a) - b;
	} else {
		tmp = (y / t_1) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if b <= -1.2e+225:
		tmp = -y / (t_1 / b)
	elif b <= 3.3e+134:
		tmp = (z + a) - b
	else:
		tmp = (y / t_1) * -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (b <= -1.2e+225)
		tmp = Float64(Float64(-y) / Float64(t_1 / b));
	elseif (b <= 3.3e+134)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(y / t_1) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (b <= -1.2e+225)
		tmp = -y / (t_1 / b);
	elseif (b <= 3.3e+134)
		tmp = (z + a) - b;
	else
		tmp = (y / t_1) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+225], N[((-y) / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+134], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(y / t$95$1), $MachinePrecision] * (-b)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2e225

   1. Initial program 41.1%

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

   2. Taylor expanded in b around inf 28.5%

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

      1. mul-1-neg 28.5%

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

      2. associate-/l* 72.4%

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

      3. distribute-neg-frac 72.4%

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

   4. Simplified 72.4%

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

   if -1.2e225 < b < 3.3e134

   1. Initial program 68.7%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. +-commutative 62.6%

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

   4. Simplified 62.6%

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

   if 3.3e134 < b

   1. Initial program 50.0%

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

   2. Taylor expanded in b around inf 31.2%

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

      1. neg-mul-1 31.2%

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

      2. distribute-rgt-neg-in 31.2%

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

   4. Simplified 31.2%

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

      1. *-un-lft-identity 31.2%

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

      2. associate-/l* 57.7%

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

      3. +-commutative 57.7%

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

      4. +-commutative 57.7%

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

      5. +-commutative 57.7%

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

   6. Applied egg-rr 57.7%

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

      1. *-lft-identity 57.7%

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

      2. associate-/r/ 64.2%

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

   8. Simplified 64.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+225}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(x + t\right)}{b}}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+134}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + \left(x + t\right)} \cdot \left(-b\right)\\ \end{array} \]

Alternative 10: 59.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+180} \lor \neg \left(t \leq 1.35 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e+180) (not (<= t 1.35e+176)))
   (/ a (/ (+ x t) t))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+180) || !(t <= 1.35e+176)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2d+180)) .or. (.not. (t <= 1.35d+176))) then
        tmp = a / ((x + t) / t)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+180) || !(t <= 1.35e+176)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e+180) or not (t <= 1.35e+176):
		tmp = a / ((x + t) / t)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e+180) || !(t <= 1.35e+176))
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2e+180) || ~((t <= 1.35e+176)))
		tmp = a / ((x + t) / t);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e+180], N[Not[LessEqual[t, 1.35e+176]], $MachinePrecision]], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2e180 or 1.3499999999999999e176 < t

   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. Taylor expanded in a around inf 29.8%

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

      1. +-commutative 29.8%

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

      2. associate-*l/ 50.6%

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

   4. Applied egg-rr 50.6%

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

   5. Taylor expanded in y around 0 29.0%

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

      1. associate-/l* 60.2%

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

   7. Simplified 60.2%

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

   if -2e180 < t < 1.3499999999999999e176

   1. Initial program 67.1%

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

   2. Taylor expanded in y around inf 62.7%

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

      1. +-commutative 62.7%

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

   4. Simplified 62.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+180} \lor \neg \left(t \leq 1.35 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 41.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -60:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 10^{-233}:\\ \;\;\;\;-b\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -60.0)
   a
   (if (<= t 5.4e-297) z (if (<= t 1e-233) (- b) (if (<= t 2.2e+44) z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -60.0) {
		tmp = a;
	} else if (t <= 5.4e-297) {
		tmp = z;
	} else if (t <= 1e-233) {
		tmp = -b;
	} else if (t <= 2.2e+44) {
		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 (t <= (-60.0d0)) then
        tmp = a
    else if (t <= 5.4d-297) then
        tmp = z
    else if (t <= 1d-233) then
        tmp = -b
    else if (t <= 2.2d+44) 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 (t <= -60.0) {
		tmp = a;
	} else if (t <= 5.4e-297) {
		tmp = z;
	} else if (t <= 1e-233) {
		tmp = -b;
	} else if (t <= 2.2e+44) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -60.0:
		tmp = a
	elif t <= 5.4e-297:
		tmp = z
	elif t <= 1e-233:
		tmp = -b
	elif t <= 2.2e+44:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -60.0)
		tmp = a;
	elseif (t <= 5.4e-297)
		tmp = z;
	elseif (t <= 1e-233)
		tmp = Float64(-b);
	elseif (t <= 2.2e+44)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -60.0)
		tmp = a;
	elseif (t <= 5.4e-297)
		tmp = z;
	elseif (t <= 1e-233)
		tmp = -b;
	elseif (t <= 2.2e+44)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -60.0], a, If[LessEqual[t, 5.4e-297], z, If[LessEqual[t, 1e-233], (-b), If[LessEqual[t, 2.2e+44], z, a]]]]

Derivation

1. Split input into 3 regimes

2. if t < -60 or 2.19999999999999996e44 < t

   1. Initial program 58.5%

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

   2. Taylor expanded in t around inf 44.1%

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

   if -60 < t < 5.4000000000000002e-297 or 9.99999999999999958e-234 < t < 2.19999999999999996e44

   1. Initial program 66.2%

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

   2. Taylor expanded in x around inf 55.5%

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

   if 5.4000000000000002e-297 < t < 9.99999999999999958e-234

   1. Initial program 80.8%

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

   2. Taylor expanded in b around inf 40.1%

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

      1. neg-mul-1 40.1%

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

      2. distribute-rgt-neg-in 40.1%

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

   4. Simplified 40.1%

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

   5. Taylor expanded in y around inf 44.3%

      \[\leadsto \color{blue}{-1 \cdot b} \]
   6. Step-by-step derivation

      1. neg-mul-1 44.3%

         \[\leadsto \color{blue}{-b} \]

   7. Simplified 44.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -60:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 10^{-233}:\\ \;\;\;\;-b\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12: 57.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+210}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.6e+210) z (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.6e+210) {
		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 <= (-2.6d+210)) 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 <= -2.6e+210) {
		tmp = z;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.6e+210:
		tmp = z
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.6e+210)
		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 <= -2.6e+210)
		tmp = z;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.6e+210], z, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e210

   1. Initial program 60.6%

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

   2. Taylor expanded in x around inf 64.0%

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

   if -2.5999999999999999e210 < x

   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. Taylor expanded in y around inf 60.0%

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

      1. +-commutative 60.0%

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

   4. Simplified 60.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+210}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 13: 43.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-11}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.65e-11) a (if (<= t 2.1e+44) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e-11) {
		tmp = a;
	} else if (t <= 2.1e+44) {
		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 (t <= (-1.65d-11)) then
        tmp = a
    else if (t <= 2.1d+44) 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 (t <= -1.65e-11) {
		tmp = a;
	} else if (t <= 2.1e+44) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.65e-11:
		tmp = a
	elif t <= 2.1e+44:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.65e-11)
		tmp = a;
	elseif (t <= 2.1e+44)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.65e-11)
		tmp = a;
	elseif (t <= 2.1e+44)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.65e-11], a, If[LessEqual[t, 2.1e+44], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6500000000000001e-11 or 2.09999999999999987e44 < t

   1. Initial program 58.5%

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

   2. Taylor expanded in t around inf 44.1%

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

   if -1.6500000000000001e-11 < t < 2.09999999999999987e44

   1. Initial program 67.7%

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

   2. Taylor expanded in x around inf 51.4%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-11}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 32.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Taylor expanded in t around inf 30.1%

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

3. Final simplification 30.1%

   \[\leadsto a \]

Developer target: 82.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023194 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))