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

Percentage Accurate: 60.9% → 87.0%

Time: 13.2s

Alternatives: 15

Speedup: 0.8×

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: 60.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{t\_2} + \frac{y}{t\_2}, \frac{t\_1 - y \cdot b}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ x (+ y t)))
        (t_3 (/ (- (+ (* z (+ x y)) t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+231)))
     (- (+ z a) b)
     (fma z (+ (/ x t_2) (/ y t_2)) (/ (- t_1 (* y b)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = x + (y + t);
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = fma(z, ((x / t_2) + (y / t_2)), ((t_1 - (y * b)) / t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+231))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = fma(z, Float64(Float64(x / t_2) + Float64(y / t_2)), Float64(Float64(t_1 - Float64(y * b)) / t_2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+231]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $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)) < -inf.0 or 2.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e231

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. fma-define 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

      7. div-sub 99.8%

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

      8. +-commutative 99.8%

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

      9. *-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+r+ 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{x + \left(y + t\right)} + \frac{y}{x + \left(y + t\right)}, \frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + t\_1\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2} + z \cdot \left(\frac{x}{t\_2} + \frac{y}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ x (+ y t)))
        (t_3 (/ (- (+ (* z (+ x y)) t_1) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+231)))
     (- (+ z a) b)
     (+ (/ (- t_1 (* y b)) t_2) (* z (+ (/ x t_2) (/ y t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = x + (y + t);
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t_1 - (y * b)) / t_2) + (z * ((x / t_2) + (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 * (y + t);
	double t_2 = x + (y + t);
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t_1 - (y * b)) / t_2) + (z * ((x / t_2) + (y / t_2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = x + (y + t)
	t_3 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 2e+231):
		tmp = (z + a) - b
	else:
		tmp = ((t_1 - (y * b)) / t_2) + (z * ((x / t_2) + (y / t_2)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+231))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t_1 - Float64(y * b)) / t_2) + Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = x + (y + t);
	t_3 = (((z * (x + y)) + t_1) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 2e+231)))
		tmp = (z + a) - b;
	else
		tmp = ((t_1 - (y * b)) / t_2) + (z * ((x / t_2) + (y / t_2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+231]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $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)) < -inf.0 or 2.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e231

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. div-sub 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+r+ 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)} + z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{y}{x + \left(y + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+231)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) 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)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+231)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+231)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+231):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+231))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / 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)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+231)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / 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[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+231]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $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 2.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e231

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-159}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.5e+142)
     t_1
     (if (<= y -1e-198)
       (+ z a)
       (if (<= y 2.9e-159)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 4.8e-37) (/ (- (* x z) (* y b)) (+ y (+ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= -1e-198) {
		tmp = z + a;
	} else if (y <= 2.9e-159) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.8e-37) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-7.5d+142)) then
        tmp = t_1
    else if (y <= (-1d-198)) then
        tmp = z + a
    else if (y <= 2.9d-159) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4.8d-37) then
        tmp = ((x * z) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= -1e-198) {
		tmp = z + a;
	} else if (y <= 2.9e-159) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.8e-37) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -7.5e+142:
		tmp = t_1
	elif y <= -1e-198:
		tmp = z + a
	elif y <= 2.9e-159:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4.8e-37:
		tmp = ((x * z) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= -1e-198)
		tmp = Float64(z + a);
	elseif (y <= 2.9e-159)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4.8e-37)
		tmp = Float64(Float64(Float64(x * z) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= -1e-198)
		tmp = z + a;
	elseif (y <= 2.9e-159)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4.8e-37)
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.5e+142], t$95$1, If[LessEqual[y, -1e-198], N[(z + a), $MachinePrecision], If[LessEqual[y, 2.9e-159], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-37], N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5000000000000002e142 or 4.79999999999999982e-37 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -7.5000000000000002e142 < y < -9.9999999999999991e-199

   1. Initial program 54.2%

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

   3. Taylor expanded in b around 0 47.1%

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

   4. Taylor expanded in y around inf 62.6%

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

   if -9.9999999999999991e-199 < y < 2.8999999999999999e-159

   1. Initial program 71.3%

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

   3. Taylor expanded in y around 0 61.5%

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

   if 2.8999999999999999e-159 < y < 4.79999999999999982e-37

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in y around 0 60.9%

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

      1. *-commutative 60.9%

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

   8. Simplified 60.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-159}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-95}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5.6e+145)
     t_1
     (if (<= y -3.7e-198)
       (+ z a)
       (if (<= y 4e-95)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 7e-31) (* z (/ (+ x y) (+ x (+ y t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e+145) {
		tmp = t_1;
	} else if (y <= -3.7e-198) {
		tmp = z + a;
	} else if (y <= 4e-95) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7e-31) {
		tmp = z * ((x + y) / (x + (y + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-5.6d+145)) then
        tmp = t_1
    else if (y <= (-3.7d-198)) then
        tmp = z + a
    else if (y <= 4d-95) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 7d-31) then
        tmp = z * ((x + y) / (x + (y + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e+145) {
		tmp = t_1;
	} else if (y <= -3.7e-198) {
		tmp = z + a;
	} else if (y <= 4e-95) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7e-31) {
		tmp = z * ((x + y) / (x + (y + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5.6e+145:
		tmp = t_1
	elif y <= -3.7e-198:
		tmp = z + a
	elif y <= 4e-95:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 7e-31:
		tmp = z * ((x + y) / (x + (y + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.6e+145)
		tmp = t_1;
	elseif (y <= -3.7e-198)
		tmp = Float64(z + a);
	elseif (y <= 4e-95)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 7e-31)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(x + Float64(y + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.6e+145)
		tmp = t_1;
	elseif (y <= -3.7e-198)
		tmp = z + a;
	elseif (y <= 4e-95)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 7e-31)
		tmp = z * ((x + y) / (x + (y + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.6e+145], t$95$1, If[LessEqual[y, -3.7e-198], N[(z + a), $MachinePrecision], If[LessEqual[y, 4e-95], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-31], N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5999999999999997e145 or 6.99999999999999971e-31 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -5.5999999999999997e145 < y < -3.69999999999999971e-198

   1. Initial program 54.2%

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

   3. Taylor expanded in b around 0 47.1%

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

   4. Taylor expanded in y around inf 62.6%

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

   if -3.69999999999999971e-198 < y < 3.99999999999999996e-95

   1. Initial program 74.7%

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

   3. Taylor expanded in y around 0 59.4%

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

   if 3.99999999999999996e-95 < y < 6.99999999999999971e-31

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 38.3%

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

      1. associate-/l* 60.5%

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

      2. +-commutative 60.5%

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

      3. +-commutative 60.5%

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

      4. associate-+r+ 60.4%

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

   5. Simplified 60.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+145}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-95}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.06 \cdot 10^{-116}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (- (+ z a) b)))
   (if (<= y -9.6e+142)
     t_2
     (if (<= y -2.06e-116)
       (+ z a)
       (if (<= y 3.7e-268)
         (* a (/ (+ y t) t_1))
         (if (<= y 1.3e-38) (* z (/ (+ x y) t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -9.6e+142) {
		tmp = t_2;
	} else if (y <= -2.06e-116) {
		tmp = z + a;
	} else if (y <= 3.7e-268) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= 1.3e-38) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = (z + a) - b
    if (y <= (-9.6d+142)) then
        tmp = t_2
    else if (y <= (-2.06d-116)) then
        tmp = z + a
    else if (y <= 3.7d-268) then
        tmp = a * ((y + t) / t_1)
    else if (y <= 1.3d-38) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -9.6e+142) {
		tmp = t_2;
	} else if (y <= -2.06e-116) {
		tmp = z + a;
	} else if (y <= 3.7e-268) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= 1.3e-38) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -9.6e+142:
		tmp = t_2
	elif y <= -2.06e-116:
		tmp = z + a
	elif y <= 3.7e-268:
		tmp = a * ((y + t) / t_1)
	elif y <= 1.3e-38:
		tmp = z * ((x + y) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9.6e+142)
		tmp = t_2;
	elseif (y <= -2.06e-116)
		tmp = Float64(z + a);
	elseif (y <= 3.7e-268)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (y <= 1.3e-38)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9.6e+142)
		tmp = t_2;
	elseif (y <= -2.06e-116)
		tmp = z + a;
	elseif (y <= 3.7e-268)
		tmp = a * ((y + t) / t_1);
	elseif (y <= 1.3e-38)
		tmp = z * ((x + y) / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.6e+142], t$95$2, If[LessEqual[y, -2.06e-116], N[(z + a), $MachinePrecision], If[LessEqual[y, 3.7e-268], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-38], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5999999999999996e142 or 1.30000000000000005e-38 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -9.5999999999999996e142 < y < -2.06000000000000011e-116

   1. Initial program 47.8%

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

   3. Taylor expanded in b around 0 42.8%

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

   4. Taylor expanded in y around inf 68.5%

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

   if -2.06000000000000011e-116 < y < 3.70000000000000018e-268

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 63.5%

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

      2. +-commutative 63.5%

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

      3. +-commutative 63.5%

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

      4. associate-+r+ 63.5%

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

   5. Simplified 63.5%

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

   if 3.70000000000000018e-268 < y < 1.30000000000000005e-38

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf 33.7%

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

      1. associate-/l* 50.1%

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

      2. +-commutative 50.1%

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

      3. +-commutative 50.1%

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

      4. associate-+r+ 50.0%

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

   5. Simplified 50.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.06 \cdot 10^{-116}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \frac{x + y}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6.4e+154)
     t_1
     (if (<= y -2.85e-117)
       (+ z a)
       (if (<= y 6e-269)
         (* a (/ (+ y t) (+ x (+ y t))))
         (if (<= y 1.7e-64) (* z (/ (+ x y) (+ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.4e+154) {
		tmp = t_1;
	} else if (y <= -2.85e-117) {
		tmp = z + a;
	} else if (y <= 6e-269) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else if (y <= 1.7e-64) {
		tmp = z * ((x + y) / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-6.4d+154)) then
        tmp = t_1
    else if (y <= (-2.85d-117)) then
        tmp = z + a
    else if (y <= 6d-269) then
        tmp = a * ((y + t) / (x + (y + t)))
    else if (y <= 1.7d-64) then
        tmp = z * ((x + y) / (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.4e+154) {
		tmp = t_1;
	} else if (y <= -2.85e-117) {
		tmp = z + a;
	} else if (y <= 6e-269) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else if (y <= 1.7e-64) {
		tmp = z * ((x + y) / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6.4e+154:
		tmp = t_1
	elif y <= -2.85e-117:
		tmp = z + a
	elif y <= 6e-269:
		tmp = a * ((y + t) / (x + (y + t)))
	elif y <= 1.7e-64:
		tmp = z * ((x + y) / (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.4e+154)
		tmp = t_1;
	elseif (y <= -2.85e-117)
		tmp = Float64(z + a);
	elseif (y <= 6e-269)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(x + Float64(y + t))));
	elseif (y <= 1.7e-64)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.4e+154)
		tmp = t_1;
	elseif (y <= -2.85e-117)
		tmp = z + a;
	elseif (y <= 6e-269)
		tmp = a * ((y + t) / (x + (y + t)));
	elseif (y <= 1.7e-64)
		tmp = z * ((x + y) / (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.4e+154], t$95$1, If[LessEqual[y, -2.85e-117], N[(z + a), $MachinePrecision], If[LessEqual[y, 6e-269], N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-64], N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4e154 or 1.70000000000000006e-64 < y

   1. Initial program 33.9%

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

   3. Taylor expanded in y around inf 85.8%

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

   if -6.4e154 < y < -2.85e-117

   1. Initial program 47.8%

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

   3. Taylor expanded in b around 0 42.8%

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

   4. Taylor expanded in y around inf 68.5%

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

   if -2.85e-117 < y < 5.9999999999999997e-269

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 63.5%

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

      2. +-commutative 63.5%

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

      3. +-commutative 63.5%

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

      4. associate-+r+ 63.5%

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

   5. Simplified 63.5%

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

   if 5.9999999999999997e-269 < y < 1.70000000000000006e-64

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 32.2%

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

      1. associate-/l* 49.9%

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

      2. +-commutative 49.9%

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

      3. +-commutative 49.9%

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

      4. associate-+r+ 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around 0 49.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \frac{x + y}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+109} \lor \neg \left(y \leq 4.5 \cdot 10^{-29}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{x + t} + z \cdot \frac{x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e+109) (not (<= y 4.5e-29)))
   (- (+ z a) b)
   (+ (/ (* t a) (+ x t)) (* z (/ x (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+109) || !(y <= 4.5e-29)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) / (x + t)) + (z * (x / (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d+109)) .or. (.not. (y <= 4.5d-29))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) / (x + t)) + (z * (x / (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+109) || !(y <= 4.5e-29)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) / (x + t)) + (z * (x / (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e+109) or not (y <= 4.5e-29):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) / (x + t)) + (z * (x / (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e+109) || !(y <= 4.5e-29))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) / Float64(x + t)) + Float64(z * Float64(x / Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e+109) || ~((y <= 4.5e-29)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) / (x + t)) + (z * (x / (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e+109], N[Not[LessEqual[y, 4.5e-29]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000001e109 or 4.4999999999999998e-29 < y

   1. Initial program 31.7%

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

   3. Taylor expanded in y around inf 85.8%

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

   if -1.35000000000000001e109 < y < 4.4999999999999998e-29

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. +-commutative 75.8%

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

      3. associate-+r+ 75.8%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around 0 59.0%

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

      1. associate-/l* 63.5%

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

      2. associate-/r* 61.5%

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

   8. Simplified 61.5%

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

   9. Taylor expanded in z around 0 48.9%

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

       1. +-commutative 48.9%

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

       2. +-commutative 48.9%

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

       3. *-commutative 48.9%

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

       4. associate-*r/ 64.5%

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

   11. Simplified 64.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+109} \lor \neg \left(y \leq 4.5 \cdot 10^{-29}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{x + t} + z \cdot \frac{x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-279}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \frac{x + y}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.5e+148)
     t_1
     (if (<= y 1.22e-279)
       (+ z a)
       (if (<= y 8.5e-64) (* z (/ (+ x y) (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.5e+148) {
		tmp = t_1;
	} else if (y <= 1.22e-279) {
		tmp = z + a;
	} else if (y <= 8.5e-64) {
		tmp = z * ((x + y) / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.5d+148)) then
        tmp = t_1
    else if (y <= 1.22d-279) then
        tmp = z + a
    else if (y <= 8.5d-64) then
        tmp = z * ((x + y) / (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.5e+148) {
		tmp = t_1;
	} else if (y <= 1.22e-279) {
		tmp = z + a;
	} else if (y <= 8.5e-64) {
		tmp = z * ((x + y) / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.5e+148:
		tmp = t_1
	elif y <= 1.22e-279:
		tmp = z + a
	elif y <= 8.5e-64:
		tmp = z * ((x + y) / (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.5e+148)
		tmp = t_1;
	elseif (y <= 1.22e-279)
		tmp = Float64(z + a);
	elseif (y <= 8.5e-64)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.5e+148)
		tmp = t_1;
	elseif (y <= 1.22e-279)
		tmp = z + a;
	elseif (y <= 8.5e-64)
		tmp = z * ((x + y) / (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.5e+148], t$95$1, If[LessEqual[y, 1.22e-279], N[(z + a), $MachinePrecision], If[LessEqual[y, 8.5e-64], N[(z * N[(N[(x + y), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999994e148 or 8.49999999999999996e-64 < y

   1. Initial program 33.9%

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

   3. Taylor expanded in y around inf 85.8%

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

   if -4.49999999999999994e148 < y < 1.22000000000000002e-279

   1. Initial program 62.8%

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

   3. Taylor expanded in b around 0 57.2%

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

   4. Taylor expanded in y around inf 62.5%

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

   if 1.22000000000000002e-279 < y < 8.49999999999999996e-64

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf 32.0%

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

      1. associate-/l* 48.4%

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

      2. +-commutative 48.4%

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

      3. +-commutative 48.4%

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

      4. associate-+r+ 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around 0 47.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+148}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-279}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \frac{x + y}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-142}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.5e+142)
     t_1
     (if (<= y 3.25e-142)
       (+ z a)
       (if (<= y 1.25e-38) (* z (/ x (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= 3.25e-142) {
		tmp = z + a;
	} else if (y <= 1.25e-38) {
		tmp = z * (x / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-7.5d+142)) then
        tmp = t_1
    else if (y <= 3.25d-142) then
        tmp = z + a
    else if (y <= 1.25d-38) then
        tmp = z * (x / (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= 3.25e-142) {
		tmp = z + a;
	} else if (y <= 1.25e-38) {
		tmp = z * (x / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -7.5e+142:
		tmp = t_1
	elif y <= 3.25e-142:
		tmp = z + a
	elif y <= 1.25e-38:
		tmp = z * (x / (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= 3.25e-142)
		tmp = Float64(z + a);
	elseif (y <= 1.25e-38)
		tmp = Float64(z * Float64(x / Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= 3.25e-142)
		tmp = z + a;
	elseif (y <= 1.25e-38)
		tmp = z * (x / (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.5e+142], t$95$1, If[LessEqual[y, 3.25e-142], N[(z + a), $MachinePrecision], If[LessEqual[y, 1.25e-38], N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000002e142 or 1.25000000000000008e-38 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -7.5000000000000002e142 < y < 3.25000000000000013e-142

   1. Initial program 64.5%

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

   3. Taylor expanded in b around 0 57.5%

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

   4. Taylor expanded in y around inf 55.9%

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

   if 3.25000000000000013e-142 < y < 1.25000000000000008e-38

   1. Initial program 76.9%

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

   3. Taylor expanded in a around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around 0 36.4%

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

      1. associate-/l* 47.8%

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

      2. +-commutative 47.8%

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

   8. Simplified 47.8%

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

   9. Taylor expanded in z around 0 36.4%

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

       1. +-commutative 36.4%

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

       2. *-commutative 36.4%

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

       3. associate-*r/ 55.4%

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

   11. Simplified 55.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-142}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-143}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.5e+142)
     t_1
     (if (<= y 5.3e-143)
       (+ z a)
       (if (<= y 3.5e-62) (* x (/ z (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= 5.3e-143) {
		tmp = z + a;
	} else if (y <= 3.5e-62) {
		tmp = x * (z / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-7.5d+142)) then
        tmp = t_1
    else if (y <= 5.3d-143) then
        tmp = z + a
    else if (y <= 3.5d-62) then
        tmp = x * (z / (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= 5.3e-143) {
		tmp = z + a;
	} else if (y <= 3.5e-62) {
		tmp = x * (z / (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -7.5e+142:
		tmp = t_1
	elif y <= 5.3e-143:
		tmp = z + a
	elif y <= 3.5e-62:
		tmp = x * (z / (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= 5.3e-143)
		tmp = Float64(z + a);
	elseif (y <= 3.5e-62)
		tmp = Float64(x * Float64(z / Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= 5.3e-143)
		tmp = z + a;
	elseif (y <= 3.5e-62)
		tmp = x * (z / (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.5e+142], t$95$1, If[LessEqual[y, 5.3e-143], N[(z + a), $MachinePrecision], If[LessEqual[y, 3.5e-62], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000002e142 or 3.5000000000000001e-62 < y

   1. Initial program 33.9%

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

   3. Taylor expanded in y around inf 85.8%

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

   if -7.5000000000000002e142 < y < 5.29999999999999997e-143

   1. Initial program 64.5%

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

   3. Taylor expanded in b around 0 57.5%

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

   4. Taylor expanded in y around inf 55.9%

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

   if 5.29999999999999997e-143 < y < 3.5000000000000001e-62

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 34.7%

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

      1. associate-/l* 57.2%

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

      2. +-commutative 57.2%

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

      3. +-commutative 57.2%

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

      4. associate-+r+ 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-/l* 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-143}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+142} \lor \neg \left(y \leq 1.45 \cdot 10^{-64}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.8e+142) (not (<= y 1.45e-64))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.8e+142) || !(y <= 1.45e-64)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + 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 ((y <= (-7.8d+142)) .or. (.not. (y <= 1.45d-64))) then
        tmp = (z + a) - b
    else
        tmp = z + 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 ((y <= -7.8e+142) || !(y <= 1.45e-64)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.8e+142) or not (y <= 1.45e-64):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.8e+142) || !(y <= 1.45e-64))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.8e+142) || ~((y <= 1.45e-64)))
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.8e+142], N[Not[LessEqual[y, 1.45e-64]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8000000000000001e142 or 1.4499999999999999e-64 < y

   1. Initial program 34.5%

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

   3. Taylor expanded in y around inf 85.1%

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

   if -7.8000000000000001e142 < y < 1.4499999999999999e-64

   1. Initial program 65.4%

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

   3. Taylor expanded in b around 0 55.9%

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

   4. Taylor expanded in y around inf 52.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+142} \lor \neg \left(y \leq 1.45 \cdot 10^{-64}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-47}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.2e-47) z (if (<= z 1.7e-24) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.2e-47) {
		tmp = z;
	} else if (z <= 1.7e-24) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.2d-47)) then
        tmp = z
    else if (z <= 1.7d-24) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.2e-47) {
		tmp = z;
	} else if (z <= 1.7e-24) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.2e-47:
		tmp = z
	elif z <= 1.7e-24:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.2e-47)
		tmp = z;
	elseif (z <= 1.7e-24)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.2e-47)
		tmp = z;
	elseif (z <= 1.7e-24)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.2e-47], z, If[LessEqual[z, 1.7e-24], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e-47 or 1.69999999999999996e-24 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in x around inf 52.1%

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

   if -5.2e-47 < z < 1.69999999999999996e-24

   1. Initial program 58.7%

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

   3. Taylor expanded in t around inf 50.0%

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

Alternative 14: 51.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+168}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t -8.5e+168) a (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e+168) {
		tmp = a;
	} else {
		tmp = z + 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 <= (-8.5d+168)) then
        tmp = a
    else
        tmp = z + 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 <= -8.5e+168) {
		tmp = a;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.5e+168:
		tmp = a
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.5e+168)
		tmp = a;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.5e+168)
		tmp = a;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.5e+168], a, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000069e168

   1. Initial program 29.4%

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

   3. Taylor expanded in t around inf 48.6%

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

   if -8.50000000000000069e168 < t

   1. Initial program 54.4%

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

   3. Taylor expanded in b around 0 45.7%

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

   4. Taylor expanded in y around inf 63.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+168}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.7% 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 51.2%

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

3. Taylor expanded in t around inf 35.0%

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

Developer Target 1: 81.8% 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 2024132 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

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