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

Percentage Accurate: 60.5% → 98.5%

Time: 13.4s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \frac{z - b}{\frac{t_1}{y}} + \left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + \frac{z}{\frac{t_1}{x}}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (+
    (/ (- z b) (/ t_1 y))
    (+ (* a (+ (/ y t_1) (/ t t_1))) (/ z (/ t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	return ((z - b) / (t_1 / y)) + ((a * ((y / t_1) + (t / t_1))) + (z / (t_1 / x)));
}

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
    t_1 = y + (x + t)
    code = ((z - b) / (t_1 / y)) + ((a * ((y / t_1) + (t / t_1))) + (z / (t_1 / x)))
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);
	return ((z - b) / (t_1 / y)) + ((a * ((y / t_1) + (t / t_1))) + (z / (t_1 / x)));
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	return ((z - b) / (t_1 / y)) + ((a * ((y / t_1) + (t / t_1))) + (z / (t_1 / x)))

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	return Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(z / Float64(t_1 / x))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = ((z - b) / (t_1 / y)) + ((a * ((y / t_1) + (t / t_1))) + (z / (t_1 / x)));
end

Wolfram

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

Derivation

1. Initial program 64.5%

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

3. Simplified 64.7%

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

4. Taylor expanded in a around 0 76.1%

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

   1. associate-/l* 88.9%

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

   2. +-commutative 88.9%

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

   3. +-commutative 88.9%

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

   4. +-commutative 88.9%

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

   5. +-commutative 88.9%

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

   6. +-commutative 88.9%

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

   7. +-commutative 88.9%

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

   8. +-commutative 88.9%

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

   9. associate-/l* 99.2%

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

   10. +-commutative 99.2%

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

   11. +-commutative 99.2%

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

6. Simplified 99.2%

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

7. Final simplification 99.2%

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

Alternative 2: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \left(x + y\right)\\ t_3 := \frac{\left(t_2 + a \cdot \left(t + y\right)\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+201} \lor \neg \left(t_3 \leq 2 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(a + \frac{z}{\frac{t_1}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{t_1} + \left(\frac{a}{\frac{t_1}{t}} + \frac{y \cdot \left(a - b\right)}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* z (+ x y)))
        (t_3 (/ (- (+ t_2 (* a (+ t y))) (* b y)) t_1)))
   (if (or (<= t_3 -1e+201) (not (<= t_3 2e+245)))
     (+ (/ (- z b) (/ t_1 y)) (+ a (/ z (/ t_1 x))))
     (+ (/ t_2 t_1) (+ (/ a (/ t_1 t)) (/ (* y (- a b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x + y);
	double t_3 = ((t_2 + (a * (t + y))) - (b * y)) / t_1;
	double tmp;
	if ((t_3 <= -1e+201) || !(t_3 <= 2e+245)) {
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)));
	} else {
		tmp = (t_2 / t_1) + ((a / (t_1 / t)) + ((y * (a - b)) / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * (x + y)
    t_3 = ((t_2 + (a * (t + y))) - (b * y)) / t_1
    if ((t_3 <= (-1d+201)) .or. (.not. (t_3 <= 2d+245))) then
        tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)))
    else
        tmp = (t_2 / t_1) + ((a / (t_1 / t)) + ((y * (a - b)) / 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 = y + (x + t);
	double t_2 = z * (x + y);
	double t_3 = ((t_2 + (a * (t + y))) - (b * y)) / t_1;
	double tmp;
	if ((t_3 <= -1e+201) || !(t_3 <= 2e+245)) {
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)));
	} else {
		tmp = (t_2 / t_1) + ((a / (t_1 / t)) + ((y * (a - b)) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * (x + y)
	t_3 = ((t_2 + (a * (t + y))) - (b * y)) / t_1
	tmp = 0
	if (t_3 <= -1e+201) or not (t_3 <= 2e+245):
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)))
	else:
		tmp = (t_2 / t_1) + ((a / (t_1 / t)) + ((y * (a - b)) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(x + y))
	t_3 = Float64(Float64(Float64(t_2 + Float64(a * Float64(t + y))) - Float64(b * y)) / t_1)
	tmp = 0.0
	if ((t_3 <= -1e+201) || !(t_3 <= 2e+245))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(a + Float64(z / Float64(t_1 / x))));
	else
		tmp = Float64(Float64(t_2 / t_1) + Float64(Float64(a / Float64(t_1 / t)) + Float64(Float64(y * Float64(a - b)) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * (x + y);
	t_3 = ((t_2 + (a * (t + y))) - (b * y)) / t_1;
	tmp = 0.0;
	if ((t_3 <= -1e+201) || ~((t_3 <= 2e+245)))
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)));
	else
		tmp = (t_2 / t_1) + ((a / (t_1 / t)) + ((y * (a - b)) / t_1));
	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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$3, -1e+201], N[Not[LessEqual[t$95$3, 2e+245]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 / t$95$1), $MachinePrecision] + N[(N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $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)) < -1.00000000000000004e201 or 2.00000000000000009e245 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 21.4%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in a around 0 47.1%

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

      1. associate-/l* 77.2%

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

      2. +-commutative 77.2%

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

      3. +-commutative 77.2%

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

      4. +-commutative 77.2%

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

      5. +-commutative 77.2%

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

      6. +-commutative 77.2%

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

      7. +-commutative 77.2%

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

      8. +-commutative 77.2%

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

      9. associate-/l* 100.0%

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

      10. +-commutative 100.0%

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

      11. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 92.4%

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

   if -1.00000000000000004e201 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000009e245

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. distribute-rgt-in 99.7%

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

      3. associate-+r+ 99.7%

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

      4. associate--l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-def 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-/l* 99.8%

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

      7. +-commutative 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -1 \cdot 10^{+201} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 2 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a + \frac{z}{\frac{y + \left(x + t\right)}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{y + \left(x + t\right)} + \left(\frac{a}{\frac{y + \left(x + t\right)}{t}} + \frac{y \cdot \left(a - b\right)}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 3: 80.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq \infty\right):\\ \;\;\;\;\left(a + \frac{z}{\frac{t_2}{x}}\right) + y \cdot \frac{z - b}{x + \left(t + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + \left(t_1 - b \cdot y\right)}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t y)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) t_2)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 INFINITY)))
     (+ (+ a (/ z (/ t_2 x))) (* y (/ (- z b) (+ x (+ t y)))))
     (/ (+ t_3 (- t_1 (* b y))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= ((double) INFINITY))) {
		tmp = (a + (z / (t_2 / x))) + (y * ((z - b) / (x + (t + y))));
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= Double.POSITIVE_INFINITY)) {
		tmp = (a + (z / (t_2 / x))) + (y * ((z - b) / (x + (t + y))));
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + y)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (b * y)) / t_2
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= math.inf):
		tmp = (a + (z / (t_2 / x))) + (y * ((z - b) / (x + (t + y))))
	else:
		tmp = (t_3 + (t_1 - (b * y))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= Inf))
		tmp = Float64(Float64(a + Float64(z / Float64(t_2 / x))) + Float64(y * Float64(Float64(z - b) / Float64(x + Float64(t + y)))));
	else
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * y))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + y);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= Inf)))
		tmp = (a + (z / (t_2 / x))) + (y * ((z - b) / (x + (t + y))));
	else
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, Infinity]], $MachinePrecision]], N[(N[(a + N[(z / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(z - b), $MachinePrecision] / N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $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)) < -inf.0 or +inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 3.8%

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

   3. Simplified 5.1%

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

   4. Taylor expanded in a around 0 33.0%

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

      1. associate-/l* 68.1%

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

      2. +-commutative 68.1%

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

      3. +-commutative 68.1%

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

      4. +-commutative 68.1%

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

      5. +-commutative 68.1%

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

      6. +-commutative 68.1%

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

      7. +-commutative 68.1%

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

      8. +-commutative 68.1%

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

      9. associate-/l* 100.0%

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

      10. +-commutative 100.0%

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

      11. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 87.8%

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

      1. associate-/r/ 87.7%

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

      2. associate-+l+ 87.7%

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

   9. Applied egg-rr 87.7%

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

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

   1. Initial program 78.2%

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

      1. associate--l+ 78.2%

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

      2. +-commutative 78.2%

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

      3. +-commutative 78.2%

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

      4. *-commutative 78.2%

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

   3. Applied egg-rr 78.2%

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

4. Final simplification 79.9%

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

Alternative 4: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+201} \lor \neg \left(t_4 \leq 2 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_2}{y}} + \left(a + \frac{z}{\frac{t_2}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + \left(t_1 - b \cdot y\right)}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t y)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) t_2)))
   (if (or (<= t_4 -1e+201) (not (<= t_4 2e+245)))
     (+ (/ (- z b) (/ t_2 y)) (+ a (/ z (/ t_2 x))))
     (/ (+ t_3 (- t_1 (* b y))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -1e+201) || !(t_4 <= 2e+245)) {
		tmp = ((z - b) / (t_2 / y)) + (a + (z / (t_2 / x)));
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (t + y)
    t_2 = y + (x + t)
    t_3 = z * (x + y)
    t_4 = ((t_3 + t_1) - (b * y)) / t_2
    if ((t_4 <= (-1d+201)) .or. (.not. (t_4 <= 2d+245))) then
        tmp = ((z - b) / (t_2 / y)) + (a + (z / (t_2 / x)))
    else
        tmp = (t_3 + (t_1 - (b * y))) / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -1e+201) || !(t_4 <= 2e+245)) {
		tmp = ((z - b) / (t_2 / y)) + (a + (z / (t_2 / x)));
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + y)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (b * y)) / t_2
	tmp = 0
	if (t_4 <= -1e+201) or not (t_4 <= 2e+245):
		tmp = ((z - b) / (t_2 / y)) + (a + (z / (t_2 / x)))
	else:
		tmp = (t_3 + (t_1 - (b * y))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if ((t_4 <= -1e+201) || !(t_4 <= 2e+245))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_2 / y)) + Float64(a + Float64(z / Float64(t_2 / x))));
	else
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * y))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + y);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if ((t_4 <= -1e+201) || ~((t_4 <= 2e+245)))
		tmp = ((z - b) / (t_2 / y)) + (a + (z / (t_2 / x)));
	else
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$4, -1e+201], N[Not[LessEqual[t$95$4, 2e+245]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $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)) < -1.00000000000000004e201 or 2.00000000000000009e245 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 21.4%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in a around 0 47.1%

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

      1. associate-/l* 77.2%

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

      2. +-commutative 77.2%

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

      3. +-commutative 77.2%

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

      4. +-commutative 77.2%

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

      5. +-commutative 77.2%

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

      6. +-commutative 77.2%

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

      7. +-commutative 77.2%

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

      8. +-commutative 77.2%

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

      9. associate-/l* 100.0%

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

      10. +-commutative 100.0%

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

      11. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 92.4%

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

   if -1.00000000000000004e201 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000009e245

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

   3. Applied egg-rr 99.7%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -1 \cdot 10^{+201} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 2 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a + \frac{z}{\frac{y + \left(x + t\right)}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(t + y\right) - b \cdot y\right)}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 86.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+279}:\\ \;\;\;\;\frac{t_3 + \left(t_1 - b \cdot y\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t y)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) t_2)))
   (if (<= t_4 (- INFINITY))
     (+ z a)
     (if (<= t_4 2e+279) (/ (+ t_3 (- t_1 (* b y))) t_2) (+ (- z b) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = z + a;
	} else if (t_4 <= 2e+279) {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	} else {
		tmp = (z - b) + a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + y);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = z + a;
	} else if (t_4 <= 2e+279) {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	} else {
		tmp = (z - b) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + y)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (b * y)) / t_2
	tmp = 0
	if t_4 <= -math.inf:
		tmp = z + a
	elif t_4 <= 2e+279:
		tmp = (t_3 + (t_1 - (b * y))) / t_2
	else:
		tmp = (z - b) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(z + a);
	elseif (t_4 <= 2e+279)
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * y))) / t_2);
	else
		tmp = Float64(Float64(z - b) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + y);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = z + a;
	elseif (t_4 <= 2e+279)
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	else
		tmp = (z - b) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(z + a), $MachinePrecision], If[LessEqual[t$95$4, 2e+279], N[(N[(t$95$3 + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.2%

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

      1. *-commutative 6.2%

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

      2. distribute-rgt-in 5.9%

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

      3. associate-+r+ 5.9%

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

      4. associate--l+ 5.9%

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

      5. +-commutative 5.9%

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

      6. +-commutative 5.9%

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

      7. distribute-lft-out-- 5.9%

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

      8. fma-def 6.2%

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

      9. +-commutative 6.2%

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

      10. fma-def 6.2%

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

      11. associate-+l+ 6.2%

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

      12. +-commutative 6.2%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in y around inf 79.8%

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

      1. associate--l+ 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in b around 0 80.0%

      \[\leadsto \color{blue}{a + z} \]
   8. Step-by-step derivation

      1. +-commutative 80.0%

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

   9. Simplified 80.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000012e279

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

   3. Applied egg-rr 99.7%

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

   if 2.00000000000000012e279 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.1%

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

      1. *-commutative 7.1%

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

      2. distribute-rgt-in 7.1%

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

      3. associate-+r+ 7.1%

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

      4. associate--l+ 7.1%

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

      5. +-commutative 7.1%

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

      6. +-commutative 7.1%

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

      7. distribute-lft-out-- 7.4%

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

      8. fma-def 7.9%

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

      9. +-commutative 7.9%

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

      10. fma-def 8.1%

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

      11. associate-+l+ 8.1%

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

      12. +-commutative 8.1%

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

   3. Simplified 8.1%

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

   4. Taylor expanded in y around inf 74.6%

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

      1. associate--l+ 74.6%

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

   6. Simplified 74.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;z + a\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(t + y\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 2 \cdot 10^{+279}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(t + y\right) - b \cdot y\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \]

Alternative 6: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ t_2 := t_1 + \left(a + \frac{z \cdot x}{t}\right)\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-131}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+110}:\\ \;\;\;\;t_1 + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- z b) (/ (+ y (+ x t)) y)))
        (t_2 (+ t_1 (+ a (/ (* z x) t)))))
   (if (<= t -2.45e-28)
     t_2
     (if (<= t 6e-131)
       (+ (- z b) a)
       (if (<= t 1.08e+110) (+ t_1 (+ z a)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z - b) / ((y + (x + t)) / y);
	double t_2 = t_1 + (a + ((z * x) / t));
	double tmp;
	if (t <= -2.45e-28) {
		tmp = t_2;
	} else if (t <= 6e-131) {
		tmp = (z - b) + a;
	} else if (t <= 1.08e+110) {
		tmp = t_1 + (z + a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - b) / ((y + (x + t)) / y)
    t_2 = t_1 + (a + ((z * x) / t))
    if (t <= (-2.45d-28)) then
        tmp = t_2
    else if (t <= 6d-131) then
        tmp = (z - b) + a
    else if (t <= 1.08d+110) then
        tmp = t_1 + (z + a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z - b) / ((y + (x + t)) / y);
	double t_2 = t_1 + (a + ((z * x) / t));
	double tmp;
	if (t <= -2.45e-28) {
		tmp = t_2;
	} else if (t <= 6e-131) {
		tmp = (z - b) + a;
	} else if (t <= 1.08e+110) {
		tmp = t_1 + (z + a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z - b) / ((y + (x + t)) / y)
	t_2 = t_1 + (a + ((z * x) / t))
	tmp = 0
	if t <= -2.45e-28:
		tmp = t_2
	elif t <= 6e-131:
		tmp = (z - b) + a
	elif t <= 1.08e+110:
		tmp = t_1 + (z + a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z - b) / Float64(Float64(y + Float64(x + t)) / y))
	t_2 = Float64(t_1 + Float64(a + Float64(Float64(z * x) / t)))
	tmp = 0.0
	if (t <= -2.45e-28)
		tmp = t_2;
	elseif (t <= 6e-131)
		tmp = Float64(Float64(z - b) + a);
	elseif (t <= 1.08e+110)
		tmp = Float64(t_1 + Float64(z + a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z - b) / ((y + (x + t)) / y);
	t_2 = t_1 + (a + ((z * x) / t));
	tmp = 0.0;
	if (t <= -2.45e-28)
		tmp = t_2;
	elseif (t <= 6e-131)
		tmp = (z - b) + a;
	elseif (t <= 1.08e+110)
		tmp = t_1 + (z + a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z - b), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(a + N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e-28], t$95$2, If[LessEqual[t, 6e-131], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 1.08e+110], N[(t$95$1 + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45000000000000015e-28 or 1.08000000000000001e110 < t

   1. Initial program 60.9%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in a around 0 83.5%

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

      1. associate-/l* 94.2%

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

      2. +-commutative 94.2%

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

      3. +-commutative 94.2%

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

      4. +-commutative 94.2%

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

      5. +-commutative 94.2%

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

      6. +-commutative 94.2%

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

      7. +-commutative 94.2%

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

      8. +-commutative 94.2%

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

      9. associate-/l* 99.0%

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

      10. +-commutative 99.0%

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

      11. +-commutative 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in y around inf 94.2%

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

   8. Taylor expanded in t around inf 86.3%

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

   if -2.45000000000000015e-28 < t < 5.99999999999999992e-131

   1. Initial program 69.0%

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

      1. *-commutative 69.0%

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

      2. distribute-rgt-in 69.0%

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

      3. associate-+r+ 69.0%

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

      4. associate--l+ 69.0%

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

      5. +-commutative 69.0%

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

      6. +-commutative 69.0%

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

      7. distribute-lft-out-- 69.2%

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

      8. fma-def 69.4%

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

      9. +-commutative 69.4%

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

      10. fma-def 69.4%

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

      11. associate-+l+ 69.4%

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

      12. +-commutative 69.4%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate--l+ 74.3%

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

   6. Simplified 74.3%

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

   if 5.99999999999999992e-131 < t < 1.08000000000000001e110

   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. Step-by-step derivation

   3. Simplified 63.9%

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

   4. Taylor expanded in a around 0 70.3%

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

      1. associate-/l* 80.0%

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

      2. +-commutative 80.0%

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

      3. +-commutative 80.0%

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

      4. +-commutative 80.0%

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

      5. +-commutative 80.0%

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

      6. +-commutative 80.0%

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

      7. +-commutative 80.0%

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

      8. +-commutative 80.0%

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

      9. associate-/l* 100.0%

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

      10. +-commutative 100.0%

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

      11. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 85.1%

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

   8. Taylor expanded in x around inf 70.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-28}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a + \frac{z \cdot x}{t}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-131}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+110}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(a + \frac{z \cdot x}{t}\right)\\ \end{array} \]

Alternative 7: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{x + \left(t + y\right)}{t + y}}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.96 \cdot 10^{+98}:\\ \;\;\;\;\frac{\left(z - b\right) \cdot y}{t + y}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+45}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (/ (+ x (+ t y)) (+ t y)))))
   (if (<= t -2.75e+153)
     t_1
     (if (<= t -1.96e+98)
       (/ (* (- z b) y) (+ t y))
       (if (<= t -3.9e+45)
         (/ (+ (* z x) (* t a)) (+ x t))
         (if (<= t 8.5e+175) (+ (- z b) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((x + (t + y)) / (t + y));
	double tmp;
	if (t <= -2.75e+153) {
		tmp = t_1;
	} else if (t <= -1.96e+98) {
		tmp = ((z - b) * y) / (t + y);
	} else if (t <= -3.9e+45) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else if (t <= 8.5e+175) {
		tmp = (z - b) + a;
	} 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 / ((x + (t + y)) / (t + y))
    if (t <= (-2.75d+153)) then
        tmp = t_1
    else if (t <= (-1.96d+98)) then
        tmp = ((z - b) * y) / (t + y)
    else if (t <= (-3.9d+45)) then
        tmp = ((z * x) + (t * a)) / (x + t)
    else if (t <= 8.5d+175) then
        tmp = (z - b) + a
    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 / ((x + (t + y)) / (t + y));
	double tmp;
	if (t <= -2.75e+153) {
		tmp = t_1;
	} else if (t <= -1.96e+98) {
		tmp = ((z - b) * y) / (t + y);
	} else if (t <= -3.9e+45) {
		tmp = ((z * x) + (t * a)) / (x + t);
	} else if (t <= 8.5e+175) {
		tmp = (z - b) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / ((x + (t + y)) / (t + y))
	tmp = 0
	if t <= -2.75e+153:
		tmp = t_1
	elif t <= -1.96e+98:
		tmp = ((z - b) * y) / (t + y)
	elif t <= -3.9e+45:
		tmp = ((z * x) + (t * a)) / (x + t)
	elif t <= 8.5e+175:
		tmp = (z - b) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(Float64(x + Float64(t + y)) / Float64(t + y)))
	tmp = 0.0
	if (t <= -2.75e+153)
		tmp = t_1;
	elseif (t <= -1.96e+98)
		tmp = Float64(Float64(Float64(z - b) * y) / Float64(t + y));
	elseif (t <= -3.9e+45)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(x + t));
	elseif (t <= 8.5e+175)
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / ((x + (t + y)) / (t + y));
	tmp = 0.0;
	if (t <= -2.75e+153)
		tmp = t_1;
	elseif (t <= -1.96e+98)
		tmp = ((z - b) * y) / (t + y);
	elseif (t <= -3.9e+45)
		tmp = ((z * x) + (t * a)) / (x + t);
	elseif (t <= 8.5e+175)
		tmp = (z - b) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.75e+153], t$95$1, If[LessEqual[t, -1.96e+98], N[(N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e+45], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+175], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7500000000000001e153 or 8.50000000000000034e175 < t

   1. Initial program 56.2%

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

      1. *-commutative 56.2%

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

      2. distribute-rgt-in 56.1%

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

      3. associate-+r+ 56.1%

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

      4. associate--l+ 56.1%

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

      5. +-commutative 56.1%

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

      6. +-commutative 56.1%

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

      7. distribute-lft-out-- 56.1%

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

      8. fma-def 56.2%

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

      9. +-commutative 56.2%

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

      10. fma-def 56.4%

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

      11. associate-+l+ 56.4%

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

      12. +-commutative 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in a around inf 40.0%

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

      1. *-un-lft-identity 40.0%

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

      2. associate-/l* 72.9%

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

      3. +-commutative 72.9%

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

      4. +-commutative 72.9%

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

      5. associate-+l+ 72.9%

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

      6. +-commutative 72.9%

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

   6. Applied egg-rr 72.9%

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

   if -2.7500000000000001e153 < t < -1.95999999999999986e98

   1. Initial program 71.9%

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

   2. Taylor expanded in a around 0 72.9%

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

      1. div-inv 72.7%

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

      2. *-commutative 72.7%

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

      3. +-commutative 72.7%

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

      4. *-commutative 72.7%

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

      5. associate-+l+ 72.7%

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

   4. Applied egg-rr 72.7%

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

   5. Taylor expanded in x around 0 67.3%

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

      1. distribute-lft-out-- 67.3%

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

   7. Simplified 67.3%

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

   if -1.95999999999999986e98 < t < -3.8999999999999999e45

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-in 99.6%

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

      3. associate-+r+ 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. fma-def 99.6%

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

      9. +-commutative 99.6%

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

      10. fma-def 99.6%

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

      11. associate-+l+ 99.6%

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

      12. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 75.1%

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

   if -3.8999999999999999e45 < t < 8.50000000000000034e175

   1. Initial program 66.1%

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

      1. *-commutative 66.1%

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

      2. distribute-rgt-in 66.1%

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

      3. associate-+r+ 66.1%

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

      4. associate--l+ 66.1%

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

      5. +-commutative 66.1%

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

      6. +-commutative 66.1%

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

      7. distribute-lft-out-- 66.2%

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

      8. fma-def 66.4%

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

      9. +-commutative 66.4%

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

      10. fma-def 66.5%

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

      11. associate-+l+ 66.5%

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

      12. +-commutative 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in y around inf 69.6%

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

      1. associate--l+ 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+153}:\\ \;\;\;\;\frac{a}{\frac{x + \left(t + y\right)}{t + y}}\\ \mathbf{elif}\;t \leq -1.96 \cdot 10^{+98}:\\ \;\;\;\;\frac{\left(z - b\right) \cdot y}{t + y}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+45}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{x + t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + \left(t + y\right)}{t + y}}\\ \end{array} \]

Alternative 8: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+184}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= x -4.8e+93)
     (/ z (/ t_1 (+ x y)))
     (if (<= x 2e+184)
       (+ (/ (- z b) (/ t_1 y)) (+ z a))
       (/ z (/ (+ x t) x))))))

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 <= -4.8e+93) {
		tmp = z / (t_1 / (x + y));
	} else if (x <= 2e+184) {
		tmp = ((z - b) / (t_1 / y)) + (z + a);
	} else {
		tmp = z / ((x + t) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (x <= (-4.8d+93)) then
        tmp = z / (t_1 / (x + y))
    else if (x <= 2d+184) then
        tmp = ((z - b) / (t_1 / y)) + (z + a)
    else
        tmp = z / ((x + t) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -4.8e+93) {
		tmp = z / (t_1 / (x + y));
	} else if (x <= 2e+184) {
		tmp = ((z - b) / (t_1 / y)) + (z + a);
	} else {
		tmp = z / ((x + t) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if x <= -4.8e+93:
		tmp = z / (t_1 / (x + y))
	elif x <= 2e+184:
		tmp = ((z - b) / (t_1 / y)) + (z + a)
	else:
		tmp = z / ((x + t) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (x <= -4.8e+93)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif (x <= 2e+184)
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(z + a));
	else
		tmp = Float64(z / Float64(Float64(x + t) / x));
	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 <= -4.8e+93)
		tmp = z / (t_1 / (x + y));
	elseif (x <= 2e+184)
		tmp = ((z - b) / (t_1 / y)) + (z + a);
	else
		tmp = z / ((x + t) / x);
	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[x, -4.8e+93], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+184], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.80000000000000021e93

   1. Initial program 57.2%

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

   2. Taylor expanded in a around 0 50.3%

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

   3. Taylor expanded in z around inf 43.1%

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

      1. *-commutative 43.1%

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

      2. +-commutative 43.1%

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

      3. +-commutative 43.1%

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

      4. +-commutative 43.1%

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

      5. associate-+r+ 43.1%

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

      6. associate-/l* 74.9%

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

      7. associate-+r+ 74.9%

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

      8. +-commutative 74.9%

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

      9. +-commutative 74.9%

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

      10. +-commutative 74.9%

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

   5. Simplified 74.9%

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

   if -4.80000000000000021e93 < x < 2.00000000000000003e184

   1. Initial program 68.5%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in a around 0 81.4%

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

      1. associate-/l* 97.4%

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

      2. +-commutative 97.4%

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

      3. +-commutative 97.4%

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

      4. +-commutative 97.4%

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

      5. +-commutative 97.4%

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

      6. +-commutative 97.4%

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

      7. +-commutative 97.4%

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

      8. +-commutative 97.4%

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

      9. associate-/l* 99.4%

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

      10. +-commutative 99.4%

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

      11. +-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in y around inf 94.7%

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

   8. Taylor expanded in x around inf 66.3%

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

   if 2.00000000000000003e184 < x

   1. Initial program 44.3%

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

   2. Taylor expanded in a around 0 40.6%

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

   3. Taylor expanded in z around inf 37.1%

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

      1. *-commutative 37.1%

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

      2. +-commutative 37.1%

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

      3. +-commutative 37.1%

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

      4. +-commutative 37.1%

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

      5. associate-+r+ 37.1%

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

      6. associate-/l* 80.2%

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

      7. associate-+r+ 80.2%

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

      8. +-commutative 80.2%

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

      9. +-commutative 80.2%

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

      10. +-commutative 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around 0 37.1%

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

      1. associate-/l* 80.2%

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

   8. Simplified 80.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+184}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \end{array} \]

Alternative 9: 59.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+93} \lor \neg \left(x \leq 1.9 \cdot 10^{+148}\right):\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5e+93) (not (<= x 1.9e+148)))
   (/ z (/ (+ y (+ x t)) (+ x y)))
   (+ (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5e+93) || !(x <= 1.9e+148)) {
		tmp = z / ((y + (x + t)) / (x + y));
	} else {
		tmp = (z - b) + 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 ((x <= (-5d+93)) .or. (.not. (x <= 1.9d+148))) then
        tmp = z / ((y + (x + t)) / (x + y))
    else
        tmp = (z - b) + 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 ((x <= -5e+93) || !(x <= 1.9e+148)) {
		tmp = z / ((y + (x + t)) / (x + y));
	} else {
		tmp = (z - b) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5e+93) or not (x <= 1.9e+148):
		tmp = z / ((y + (x + t)) / (x + y))
	else:
		tmp = (z - b) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5e+93) || !(x <= 1.9e+148))
		tmp = Float64(z / Float64(Float64(y + Float64(x + t)) / Float64(x + y)));
	else
		tmp = Float64(Float64(z - b) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5e+93) || ~((x <= 1.9e+148)))
		tmp = z / ((y + (x + t)) / (x + y));
	else
		tmp = (z - b) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5e+93], N[Not[LessEqual[x, 1.9e+148]], $MachinePrecision]], N[(z / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000001e93 or 1.8999999999999999e148 < x

   1. Initial program 53.0%

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

   2. Taylor expanded in a around 0 46.3%

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

   3. Taylor expanded in z around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. +-commutative 39.5%

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

      3. +-commutative 39.5%

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

      4. +-commutative 39.5%

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

      5. associate-+r+ 39.5%

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

      6. associate-/l* 74.4%

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

      7. associate-+r+ 74.4%

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

      8. +-commutative 74.4%

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

      9. +-commutative 74.4%

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

      10. +-commutative 74.4%

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

   5. Simplified 74.4%

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

   if -5.0000000000000001e93 < x < 1.8999999999999999e148

   1. Initial program 68.6%

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

      1. *-commutative 68.6%

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

      2. distribute-rgt-in 68.6%

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

      3. associate-+r+ 68.6%

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

      4. associate--l+ 68.6%

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

      5. +-commutative 68.6%

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

      6. +-commutative 68.6%

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

      7. distribute-lft-out-- 68.6%

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

      8. fma-def 68.7%

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

      9. +-commutative 68.7%

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

      10. fma-def 68.8%

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

      11. associate-+l+ 68.8%

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

      12. +-commutative 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

   6. Simplified 64.7%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+93} \lor \neg \left(x \leq 1.9 \cdot 10^{+148}\right):\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \]

Alternative 10: 54.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+173}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-224}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-252}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+187}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.52e+173)
   a
   (if (<= t -2.9e-224)
     (+ z a)
     (if (<= t 2.1e-252) (- z b) (if (<= t 2.6e+187) (+ z a) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.52e+173) {
		tmp = a;
	} else if (t <= -2.9e-224) {
		tmp = z + a;
	} else if (t <= 2.1e-252) {
		tmp = z - b;
	} else if (t <= 2.6e+187) {
		tmp = z + a;
	} 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 <= (-1.52d+173)) then
        tmp = a
    else if (t <= (-2.9d-224)) then
        tmp = z + a
    else if (t <= 2.1d-252) then
        tmp = z - b
    else if (t <= 2.6d+187) then
        tmp = z + a
    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 <= -1.52e+173) {
		tmp = a;
	} else if (t <= -2.9e-224) {
		tmp = z + a;
	} else if (t <= 2.1e-252) {
		tmp = z - b;
	} else if (t <= 2.6e+187) {
		tmp = z + a;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.52e+173:
		tmp = a
	elif t <= -2.9e-224:
		tmp = z + a
	elif t <= 2.1e-252:
		tmp = z - b
	elif t <= 2.6e+187:
		tmp = z + a
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.52e+173)
		tmp = a;
	elseif (t <= -2.9e-224)
		tmp = Float64(z + a);
	elseif (t <= 2.1e-252)
		tmp = Float64(z - b);
	elseif (t <= 2.6e+187)
		tmp = Float64(z + a);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.52e+173)
		tmp = a;
	elseif (t <= -2.9e-224)
		tmp = z + a;
	elseif (t <= 2.1e-252)
		tmp = z - b;
	elseif (t <= 2.6e+187)
		tmp = z + a;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.52e+173], a, If[LessEqual[t, -2.9e-224], N[(z + a), $MachinePrecision], If[LessEqual[t, 2.1e-252], N[(z - b), $MachinePrecision], If[LessEqual[t, 2.6e+187], N[(z + a), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.51999999999999988e173 or 2.5999999999999999e187 < t

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. distribute-rgt-in 55.6%

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

      3. associate-+r+ 55.6%

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

      4. associate--l+ 55.6%

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

      5. +-commutative 55.6%

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

      6. +-commutative 55.6%

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

      7. distribute-lft-out-- 55.6%

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

      8. fma-def 55.8%

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

      9. +-commutative 55.8%

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

      10. fma-def 55.9%

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

      11. associate-+l+ 55.9%

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

      12. +-commutative 55.9%

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

   3. Simplified 55.9%

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

   4. Taylor expanded in t around inf 71.6%

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

   if -1.51999999999999988e173 < t < -2.9e-224 or 2.1e-252 < t < 2.5999999999999999e187

   1. Initial program 69.6%

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

      1. *-commutative 69.6%

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

      2. distribute-rgt-in 69.6%

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

      3. associate-+r+ 69.6%

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

      4. associate--l+ 69.6%

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

      5. +-commutative 69.6%

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

      6. +-commutative 69.6%

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

      7. distribute-lft-out-- 69.6%

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

      8. fma-def 69.8%

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

      9. +-commutative 69.8%

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

      10. fma-def 69.8%

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

      11. associate-+l+ 69.8%

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

      12. +-commutative 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. associate--l+ 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in b around 0 58.2%

      \[\leadsto \color{blue}{a + z} \]
   8. Step-by-step derivation

      1. +-commutative 58.2%

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

   9. Simplified 58.2%

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

   if -2.9e-224 < t < 2.1e-252

   1. Initial program 53.9%

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

   2. Taylor expanded in a around 0 48.3%

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

      1. div-inv 48.1%

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

      2. *-commutative 48.1%

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

      3. +-commutative 48.1%

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

      4. *-commutative 48.1%

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

      5. associate-+l+ 48.1%

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

   4. Applied egg-rr 48.1%

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

   5. Taylor expanded in y around inf 84.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+173}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-224}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-252}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+187}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 11: 59.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+93} \lor \neg \left(x \leq 6.8 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -3.6e+93) (not (<= x 6.8e+146)))
   (/ z (/ (+ x t) x))
   (+ (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.6e+93) || !(x <= 6.8e+146)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z - b) + 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 ((x <= (-3.6d+93)) .or. (.not. (x <= 6.8d+146))) then
        tmp = z / ((x + t) / x)
    else
        tmp = (z - b) + 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 ((x <= -3.6e+93) || !(x <= 6.8e+146)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z - b) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -3.6e+93) or not (x <= 6.8e+146):
		tmp = z / ((x + t) / x)
	else:
		tmp = (z - b) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -3.6e+93) || !(x <= 6.8e+146))
		tmp = Float64(z / Float64(Float64(x + t) / x));
	else
		tmp = Float64(Float64(z - b) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -3.6e+93) || ~((x <= 6.8e+146)))
		tmp = z / ((x + t) / x);
	else
		tmp = (z - b) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -3.6e+93], N[Not[LessEqual[x, 6.8e+146]], $MachinePrecision]], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999999e93 or 6.79999999999999981e146 < x

   1. Initial program 53.0%

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

   2. Taylor expanded in a around 0 46.3%

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

   3. Taylor expanded in z around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. +-commutative 39.5%

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

      3. +-commutative 39.5%

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

      4. +-commutative 39.5%

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

      5. associate-+r+ 39.5%

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

      6. associate-/l* 74.4%

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

      7. associate-+r+ 74.4%

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

      8. +-commutative 74.4%

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

      9. +-commutative 74.4%

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

      10. +-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in y around 0 39.5%

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

      1. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

   if -3.5999999999999999e93 < x < 6.79999999999999981e146

   1. Initial program 68.6%

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

      1. *-commutative 68.6%

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

      2. distribute-rgt-in 68.6%

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

      3. associate-+r+ 68.6%

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

      4. associate--l+ 68.6%

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

      5. +-commutative 68.6%

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

      6. +-commutative 68.6%

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

      7. distribute-lft-out-- 68.6%

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

      8. fma-def 68.7%

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

      9. +-commutative 68.7%

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

      10. fma-def 68.8%

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

      11. associate-+l+ 68.8%

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

      12. +-commutative 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in y around inf 64.7%

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

      1. associate--l+ 64.7%

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

   6. Simplified 64.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+93} \lor \neg \left(x \leq 6.8 \cdot 10^{+146}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \]

Alternative 12: 59.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+172}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+174}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.08e+172) a (if (<= t 1.35e+174) (+ (- z b) a) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.08e+172) {
		tmp = a;
	} else if (t <= 1.35e+174) {
		tmp = (z - b) + a;
	} 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 <= (-1.08d+172)) then
        tmp = a
    else if (t <= 1.35d+174) then
        tmp = (z - b) + a
    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 <= -1.08e+172) {
		tmp = a;
	} else if (t <= 1.35e+174) {
		tmp = (z - b) + a;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.08e+172:
		tmp = a
	elif t <= 1.35e+174:
		tmp = (z - b) + a
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.08e+172)
		tmp = a;
	elseif (t <= 1.35e+174)
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.08e+172)
		tmp = a;
	elseif (t <= 1.35e+174)
		tmp = (z - b) + a;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.08e+172], a, If[LessEqual[t, 1.35e+174], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0799999999999999e172 or 1.35e174 < t

   1. Initial program 56.3%

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

      1. *-commutative 56.3%

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

      2. distribute-rgt-in 56.2%

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

      3. associate-+r+ 56.2%

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

      4. associate--l+ 56.2%

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

      5. +-commutative 56.2%

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

      6. +-commutative 56.2%

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

      7. distribute-lft-out-- 56.2%

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

      8. fma-def 56.3%

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

      9. +-commutative 56.3%

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

      10. fma-def 56.5%

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

      11. associate-+l+ 56.5%

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

      12. +-commutative 56.5%

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

   3. Simplified 56.5%

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

   4. Taylor expanded in t around inf 70.2%

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

   if -1.0799999999999999e172 < t < 1.35e174

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. associate-+r+ 67.5%

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

      4. associate--l+ 67.5%

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

      5. +-commutative 67.5%

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

      6. +-commutative 67.5%

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

      7. distribute-lft-out-- 67.6%

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

      8. fma-def 67.8%

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

      9. +-commutative 67.8%

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

      10. fma-def 67.8%

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

      11. associate-+l+ 67.8%

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

      12. +-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in y around inf 66.5%

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

      1. associate--l+ 66.5%

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

   6. Simplified 66.5%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+172}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+174}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 54.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+171}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+188}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.22e+171) a (if (<= t 2.55e+188) (+ z a) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e+171) {
		tmp = a;
	} else if (t <= 2.55e+188) {
		tmp = z + a;
	} 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 <= (-1.22d+171)) then
        tmp = a
    else if (t <= 2.55d+188) then
        tmp = z + a
    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 <= -1.22e+171) {
		tmp = a;
	} else if (t <= 2.55e+188) {
		tmp = z + a;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.22e+171:
		tmp = a
	elif t <= 2.55e+188:
		tmp = z + a
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.22e+171)
		tmp = a;
	elseif (t <= 2.55e+188)
		tmp = Float64(z + a);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.22e+171)
		tmp = a;
	elseif (t <= 2.55e+188)
		tmp = z + a;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.22e+171], a, If[LessEqual[t, 2.55e+188], N[(z + a), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2200000000000001e171 or 2.5500000000000001e188 < t

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. distribute-rgt-in 55.6%

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

      3. associate-+r+ 55.6%

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

      4. associate--l+ 55.6%

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

      5. +-commutative 55.6%

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

      6. +-commutative 55.6%

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

      7. distribute-lft-out-- 55.6%

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

      8. fma-def 55.8%

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

      9. +-commutative 55.8%

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

      10. fma-def 55.9%

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

      11. associate-+l+ 55.9%

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

      12. +-commutative 55.9%

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

   3. Simplified 55.9%

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

   4. Taylor expanded in t around inf 71.6%

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

   if -1.2200000000000001e171 < t < 2.5500000000000001e188

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. associate-+r+ 67.5%

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

      4. associate--l+ 67.5%

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

      5. +-commutative 67.5%

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

      6. +-commutative 67.5%

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

      7. distribute-lft-out-- 67.6%

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

      8. fma-def 67.8%

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

      9. +-commutative 67.8%

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

      10. fma-def 67.8%

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

      11. associate-+l+ 67.8%

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

      12. +-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in y around inf 66.1%

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

      1. associate--l+ 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in b around 0 57.0%

      \[\leadsto \color{blue}{a + z} \]
   8. Step-by-step derivation

      1. +-commutative 57.0%

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

   9. Simplified 57.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+171}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+188}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 43.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-28}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.95e-28) a (if (<= t 2.2e+133) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.95e-28) {
		tmp = a;
	} else if (t <= 2.2e+133) {
		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 <= (-2.95d-28)) then
        tmp = a
    else if (t <= 2.2d+133) 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 <= -2.95e-28) {
		tmp = a;
	} else if (t <= 2.2e+133) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.95e-28:
		tmp = a
	elif t <= 2.2e+133:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.95e-28)
		tmp = a;
	elseif (t <= 2.2e+133)
		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 <= -2.95e-28)
		tmp = a;
	elseif (t <= 2.2e+133)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.95e-28], a, If[LessEqual[t, 2.2e+133], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9500000000000001e-28 or 2.2e133 < t

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

      2. distribute-rgt-in 60.4%

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

      3. associate-+r+ 60.4%

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

      4. associate--l+ 60.4%

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

      5. +-commutative 60.4%

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

      6. +-commutative 60.4%

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

      7. distribute-lft-out-- 60.4%

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

      8. fma-def 60.7%

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

      9. +-commutative 60.7%

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

      10. fma-def 60.8%

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

      11. associate-+l+ 60.8%

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

      12. +-commutative 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in t around inf 57.1%

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

   if -2.9500000000000001e-28 < t < 2.2e133

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. associate-+r+ 67.5%

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

      4. associate--l+ 67.5%

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

      5. +-commutative 67.5%

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

      6. +-commutative 67.5%

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

      7. distribute-lft-out-- 67.6%

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

      8. fma-def 67.8%

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

      9. +-commutative 67.8%

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

      10. fma-def 67.8%

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

      11. associate-+l+ 67.8%

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

      12. +-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in x around inf 51.2%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-28}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 33.7% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.5%

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

   1. *-commutative 64.5%

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

   2. distribute-rgt-in 64.5%

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

   3. associate-+r+ 64.5%

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

   4. associate--l+ 64.5%

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

   5. +-commutative 64.5%

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

   6. +-commutative 64.5%

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

   7. distribute-lft-out-- 64.6%

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

   8. fma-def 64.8%

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

   9. +-commutative 64.8%

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

   10. fma-def 64.8%

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

   11. associate-+l+ 64.8%

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

   12. +-commutative 64.8%

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

3. Simplified 64.8%

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

4. Taylor expanded in t around inf 37.3%

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

5. Final simplification 37.3%

   \[\leadsto a \]

Developer target: 82.5% 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 2023215 
(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)))