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

Percentage Accurate: 59.6% → 91.1%

Time: 18.0s

Alternatives: 17

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% 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: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 5 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{a}{\frac{t\_2}{y + t}} + \frac{z}{\frac{t\_2}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ x y)) t_1) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 5e+241)))
     (+ (/ a (/ t_2 (+ y t))) (/ z (/ t_2 (+ x y))))
     (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (x + y)) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 5e+241)) {
		tmp = (a / (t_2 / (y + t))) + (z / (t_2 / (x + y)));
	} else {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 5e+241))
		tmp = Float64(Float64(a / Float64(t_2 / Float64(y + t))) + Float64(z / Float64(t_2 / Float64(x + y))));
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	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[(y + N[(x + 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] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 5e+241]], $MachinePrecision]], N[(N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $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 5.00000000000000025e241 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.0%

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

   3. Taylor expanded in z around inf 7.0%

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

      1. associate--l+ 7.0%

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

      2. associate-/l* 36.9%

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

      3. associate-+r+ 36.9%

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

      4. div-sub 36.9%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in z around inf 39.3%

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

      1. associate-/l* 81.3%

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

      2. +-commutative 81.3%

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

      3. associate-+r+ 81.3%

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

      4. associate-+r+ 81.3%

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

      5. +-commutative 81.3%

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

      6. associate-+r+ 81.3%

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

      7. +-commutative 81.3%

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

   8. Simplified 81.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000025e241

   1. Initial program 99.8%

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

      1. fma-def 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}} + \frac{z}{\frac{t\_1}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+241)))
     (+ (/ a (/ t_1 (+ y t))) (/ z (/ t_1 (+ x y))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+241)) {
		tmp = (a / (t_1 / (y + t))) + (z / (t_1 / (x + y)));
	} else {
		tmp = t_2;
	}
	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 tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+241)) {
		tmp = (a / (t_1 / (y + t))) + (z / (t_1 / (x + y)));
	} else {
		tmp = t_2;
	}
	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
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+241):
		tmp = (a / (t_1 / (y + t))) + (z / (t_1 / (x + y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+241))
		tmp = Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(z / Float64(t_1 / Float64(x + y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+241)))
		tmp = (a / (t_1 / (y + t))) + (z / (t_1 / (x + y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(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]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+241]], $MachinePrecision]], N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000025e241 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.0%

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

   3. Taylor expanded in z around inf 7.0%

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

      1. associate--l+ 7.0%

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

      2. associate-/l* 36.9%

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

      3. associate-+r+ 36.9%

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

      4. div-sub 36.9%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in z around inf 39.3%

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

      1. associate-/l* 81.3%

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

      2. +-commutative 81.3%

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

      3. associate-+r+ 81.3%

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

      4. associate-+r+ 81.3%

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

      5. +-commutative 81.3%

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

      6. associate-+r+ 81.3%

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

      7. +-commutative 81.3%

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

   8. Simplified 81.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000025e241

   1. Initial program 99.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+301}\right):\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}} + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+301)))
     (+ (/ a (/ t_1 (+ y t))) (- z b))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+301)) {
		tmp = (a / (t_1 / (y + t))) + (z - b);
	} else {
		tmp = t_2;
	}
	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 tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+301)) {
		tmp = (a / (t_1 / (y + t))) + (z - b);
	} else {
		tmp = t_2;
	}
	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
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+301):
		tmp = (a / (t_1 / (y + t))) + (z - b)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+301))
		tmp = Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(z - b));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+301)))
		tmp = (a / (t_1 / (y + t))) + (z - b);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(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]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+301]], $MachinePrecision]], N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z - b), $MachinePrecision]), $MachinePrecision], t$95$2]]]

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 1.00000000000000005e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

   3. Taylor expanded in z around inf 5.4%

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

      1. associate--l+ 5.4%

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

      2. associate-/l* 35.8%

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

      3. associate-+r+ 35.8%

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

      4. div-sub 35.8%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around inf 79.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000005e301

   1. Initial program 99.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+301}\right):\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \frac{z}{\frac{y + t}{y}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+206}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (/ z (/ (+ y t) y)))) (t_2 (- (+ z a) b)))
   (if (<= x -2.45e+206)
     z
     (if (<= x -4.1e-116)
       t_2
       (if (<= x 5.3e-20)
         t_1
         (if (<= x 1.05e+54)
           t_2
           (if (<= x 1.2e+133) t_1 (* z (/ x (+ x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((y + t) / y));
	double t_2 = (z + a) - b;
	double tmp;
	if (x <= -2.45e+206) {
		tmp = z;
	} else if (x <= -4.1e-116) {
		tmp = t_2;
	} else if (x <= 5.3e-20) {
		tmp = t_1;
	} else if (x <= 1.05e+54) {
		tmp = t_2;
	} else if (x <= 1.2e+133) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z / ((y + t) / y))
    t_2 = (z + a) - b
    if (x <= (-2.45d+206)) then
        tmp = z
    else if (x <= (-4.1d-116)) then
        tmp = t_2
    else if (x <= 5.3d-20) then
        tmp = t_1
    else if (x <= 1.05d+54) then
        tmp = t_2
    else if (x <= 1.2d+133) then
        tmp = t_1
    else
        tmp = 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 t_1 = a + (z / ((y + t) / y));
	double t_2 = (z + a) - b;
	double tmp;
	if (x <= -2.45e+206) {
		tmp = z;
	} else if (x <= -4.1e-116) {
		tmp = t_2;
	} else if (x <= 5.3e-20) {
		tmp = t_1;
	} else if (x <= 1.05e+54) {
		tmp = t_2;
	} else if (x <= 1.2e+133) {
		tmp = t_1;
	} else {
		tmp = z * (x / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z / ((y + t) / y))
	t_2 = (z + a) - b
	tmp = 0
	if x <= -2.45e+206:
		tmp = z
	elif x <= -4.1e-116:
		tmp = t_2
	elif x <= 5.3e-20:
		tmp = t_1
	elif x <= 1.05e+54:
		tmp = t_2
	elif x <= 1.2e+133:
		tmp = t_1
	else:
		tmp = z * (x / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z / Float64(Float64(y + t) / y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= -2.45e+206)
		tmp = z;
	elseif (x <= -4.1e-116)
		tmp = t_2;
	elseif (x <= 5.3e-20)
		tmp = t_1;
	elseif (x <= 1.05e+54)
		tmp = t_2;
	elseif (x <= 1.2e+133)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z / ((y + t) / y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (x <= -2.45e+206)
		tmp = z;
	elseif (x <= -4.1e-116)
		tmp = t_2;
	elseif (x <= 5.3e-20)
		tmp = t_1;
	elseif (x <= 1.05e+54)
		tmp = t_2;
	elseif (x <= 1.2e+133)
		tmp = t_1;
	else
		tmp = z * (x / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[x, -2.45e+206], z, If[LessEqual[x, -4.1e-116], t$95$2, If[LessEqual[x, 5.3e-20], t$95$1, If[LessEqual[x, 1.05e+54], t$95$2, If[LessEqual[x, 1.2e+133], t$95$1, N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.45e206

   1. Initial program 50.4%

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

   3. Taylor expanded in x around inf 80.7%

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

   if -2.45e206 < x < -4.0999999999999999e-116 or 5.3000000000000002e-20 < x < 1.04999999999999993e54

   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. Add Preprocessing

   3. Taylor expanded in y around inf 65.6%

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

   if -4.0999999999999999e-116 < x < 5.3000000000000002e-20 or 1.04999999999999993e54 < x < 1.1999999999999999e133

   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 69.1%

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

      1. associate--l+ 69.1%

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

      2. associate-/l* 79.0%

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

      3. associate-+r+ 79.0%

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

      4. div-sub 79.0%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 67.8%

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

      1. associate-/l* 79.4%

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

      2. +-commutative 79.4%

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

      3. associate-+r+ 79.4%

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

      4. associate-+r+ 79.4%

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

      5. +-commutative 79.4%

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

      6. associate-+r+ 79.4%

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

      7. +-commutative 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in t around inf 76.1%

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

   10. Taylor expanded in x around 0 73.3%

       \[\leadsto \frac{a}{1} + \frac{z}{\color{blue}{\frac{t + y}{y}}} \]
   11. Step-by-step derivation

       1. +-commutative 73.3%

          \[\leadsto \frac{a}{1} + \frac{z}{\frac{\color{blue}{y + t}}{y}} \]

   12. Simplified 73.3%

       \[\leadsto \frac{a}{1} + \frac{z}{\color{blue}{\frac{y + t}{y}}} \]

   if 1.1999999999999999e133 < x

   1. Initial program 33.6%

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

   3. Taylor expanded in y around 0 30.8%

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

   4. Taylor expanded in a around 0 23.1%

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

      1. associate-/l* 52.8%

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

      2. associate-/r/ 63.5%

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

      3. +-commutative 63.5%

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

   6. Simplified 63.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+206}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-116}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;a + \frac{z}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+133}:\\ \;\;\;\;a + \frac{z}{\frac{y + t}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{z}{\frac{t\_1}{x + y}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1350000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-144}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ z (/ t_1 (+ x y)))))
   (if (<= z -7e+136)
     t_2
     (if (<= z -1350000000000.0)
       (- (+ z a) b)
       (if (<= z -2e-144)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= z 8.5e+29) (/ a (/ t_1 (+ y t))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z / (t_1 / (x + y));
	double tmp;
	if (z <= -7e+136) {
		tmp = t_2;
	} else if (z <= -1350000000000.0) {
		tmp = (z + a) - b;
	} else if (z <= -2e-144) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (z <= 8.5e+29) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z / (t_1 / (x + y))
    if (z <= (-7d+136)) then
        tmp = t_2
    else if (z <= (-1350000000000.0d0)) then
        tmp = (z + a) - b
    else if (z <= (-2d-144)) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (z <= 8.5d+29) then
        tmp = a / (t_1 / (y + t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z / (t_1 / (x + y));
	double tmp;
	if (z <= -7e+136) {
		tmp = t_2;
	} else if (z <= -1350000000000.0) {
		tmp = (z + a) - b;
	} else if (z <= -2e-144) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (z <= 8.5e+29) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z / (t_1 / (x + y))
	tmp = 0
	if z <= -7e+136:
		tmp = t_2
	elif z <= -1350000000000.0:
		tmp = (z + a) - b
	elif z <= -2e-144:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif z <= 8.5e+29:
		tmp = a / (t_1 / (y + t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z / Float64(t_1 / Float64(x + y)))
	tmp = 0.0
	if (z <= -7e+136)
		tmp = t_2;
	elseif (z <= -1350000000000.0)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= -2e-144)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (z <= 8.5e+29)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z / (t_1 / (x + y));
	tmp = 0.0;
	if (z <= -7e+136)
		tmp = t_2;
	elseif (z <= -1350000000000.0)
		tmp = (z + a) - b;
	elseif (z <= -2e-144)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (z <= 8.5e+29)
		tmp = a / (t_1 / (y + t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+136], t$95$2, If[LessEqual[z, -1350000000000.0], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, -2e-144], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+29], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.00000000000000002e136 or 8.5000000000000006e29 < z

   1. Initial program 45.7%

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

   3. Taylor expanded in z around inf 36.6%

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

      1. associate-/l* 75.1%

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

      2. associate-+r+ 75.1%

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

      3. +-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -7.00000000000000002e136 < z < -1.35e12

   1. Initial program 51.3%

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

   3. Taylor expanded in y around inf 80.3%

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

   if -1.35e12 < z < -1.9999999999999999e-144

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 60.5%

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

   if -1.9999999999999999e-144 < z < 8.5000000000000006e29

   1. Initial program 63.7%

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

   3. Taylor expanded in a around inf 41.2%

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

      1. associate-/l* 66.3%

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

      2. associate-+r+ 66.3%

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

   5. Simplified 66.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;z \leq -1350000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-144}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+205} \lor \neg \left(x \leq 6.2 \cdot 10^{+55}\right):\\ \;\;\;\;z + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{\frac{y + t}{z - b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (/ (+ y (+ x t)) (+ y t)))))
   (if (or (<= x -4.8e+205) (not (<= x 6.2e+55)))
     (+ z t_1)
     (+ t_1 (/ y (/ (+ y t) (- z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((y + (x + t)) / (y + t));
	double tmp;
	if ((x <= -4.8e+205) || !(x <= 6.2e+55)) {
		tmp = z + t_1;
	} else {
		tmp = t_1 + (y / ((y + t) / (z - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / ((y + (x + t)) / (y + t))
    if ((x <= (-4.8d+205)) .or. (.not. (x <= 6.2d+55))) then
        tmp = z + t_1
    else
        tmp = t_1 + (y / ((y + t) / (z - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((y + (x + t)) / (y + t));
	double tmp;
	if ((x <= -4.8e+205) || !(x <= 6.2e+55)) {
		tmp = z + t_1;
	} else {
		tmp = t_1 + (y / ((y + t) / (z - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / ((y + (x + t)) / (y + t))
	tmp = 0
	if (x <= -4.8e+205) or not (x <= 6.2e+55):
		tmp = z + t_1
	else:
		tmp = t_1 + (y / ((y + t) / (z - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t)))
	tmp = 0.0
	if ((x <= -4.8e+205) || !(x <= 6.2e+55))
		tmp = Float64(z + t_1);
	else
		tmp = Float64(t_1 + Float64(y / Float64(Float64(y + t) / Float64(z - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / ((y + (x + t)) / (y + t));
	tmp = 0.0;
	if ((x <= -4.8e+205) || ~((x <= 6.2e+55)))
		tmp = z + t_1;
	else
		tmp = t_1 + (y / ((y + t) / (z - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -4.8e+205], N[Not[LessEqual[x, 6.2e+55]], $MachinePrecision]], N[(z + t$95$1), $MachinePrecision], N[(t$95$1 + N[(y / N[(N[(y + t), $MachinePrecision] / N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999972e205 or 6.19999999999999987e55 < x

   1. Initial program 45.7%

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

   3. Taylor expanded in z around inf 45.8%

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

      1. associate--l+ 45.8%

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

      2. associate-/l* 54.7%

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

      3. associate-+r+ 54.7%

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

      4. div-sub 54.7%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in z around inf 50.1%

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

      1. associate-/l* 91.4%

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

      2. +-commutative 91.4%

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

      3. associate-+r+ 91.4%

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

      4. associate-+r+ 91.4%

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

      5. +-commutative 91.4%

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

      6. associate-+r+ 91.4%

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

      7. +-commutative 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in t around 0 86.4%

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

   if -4.79999999999999972e205 < x < 6.19999999999999987e55

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. associate-/l* 78.6%

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

      3. associate-+r+ 78.6%

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

      4. div-sub 78.6%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in x around 0 70.1%

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

      1. associate-/l* 83.3%

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

      2. +-commutative 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+205} \lor \neg \left(x \leq 6.2 \cdot 10^{+55}\right):\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{y}{\frac{y + t}{z - b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+161} \lor \neg \left(t \leq -5.2 \cdot 10^{+97} \lor \neg \left(t \leq -6.5 \cdot 10^{+59}\right) \land t \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.1e+161)
         (not (or (<= t -5.2e+97) (and (not (<= t -6.5e+59)) (<= t 9.5e+38)))))
   (+ a (/ z (/ t (+ x y))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.1e+161) || !((t <= -5.2e+97) || (!(t <= -6.5e+59) && (t <= 9.5e+38)))) {
		tmp = a + (z / (t / (x + y)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.1d+161)) .or. (.not. (t <= (-5.2d+97)) .or. (.not. (t <= (-6.5d+59))) .and. (t <= 9.5d+38))) then
        tmp = a + (z / (t / (x + y)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.1e+161) || !((t <= -5.2e+97) || (!(t <= -6.5e+59) && (t <= 9.5e+38)))) {
		tmp = a + (z / (t / (x + y)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.1e+161) or not ((t <= -5.2e+97) or (not (t <= -6.5e+59) and (t <= 9.5e+38))):
		tmp = a + (z / (t / (x + y)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.1e+161) || !((t <= -5.2e+97) || (!(t <= -6.5e+59) && (t <= 9.5e+38))))
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.1e+161) || ~(((t <= -5.2e+97) || (~((t <= -6.5e+59)) && (t <= 9.5e+38)))))
		tmp = a + (z / (t / (x + y)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.1e+161], N[Not[Or[LessEqual[t, -5.2e+97], And[N[Not[LessEqual[t, -6.5e+59]], $MachinePrecision], LessEqual[t, 9.5e+38]]]], $MachinePrecision]], N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e161 or -5.2e97 < t < -6.50000000000000021e59 or 9.4999999999999995e38 < t

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 55.8%

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

      1. associate--l+ 55.8%

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

      2. associate-/l* 78.8%

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

      3. associate-+r+ 78.8%

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

      4. div-sub 78.8%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in z around inf 73.2%

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

      1. associate-/l* 89.0%

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

      2. +-commutative 89.0%

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

      3. associate-+r+ 89.0%

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

      4. associate-+r+ 89.0%

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

      5. +-commutative 89.0%

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

      6. associate-+r+ 89.0%

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

      7. +-commutative 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in t around inf 81.1%

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

   10. Taylor expanded in t around inf 69.3%

       \[\leadsto \frac{a}{1} + \frac{z}{\frac{\color{blue}{t}}{y + x}} \]

   if -1.1e161 < t < -5.2e97 or -6.50000000000000021e59 < t < 9.4999999999999995e38

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 64.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+161} \lor \neg \left(t \leq -5.2 \cdot 10^{+97} \lor \neg \left(t \leq -6.5 \cdot 10^{+59}\right) \land t \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-27}:\\ \;\;\;\;a + \frac{z}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+22}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ a (/ (+ y (+ x t)) (+ y t))))))
   (if (<= x -9.6e-120)
     t_1
     (if (<= x 1.95e-27)
       (+ a (/ z (/ (+ y t) y)))
       (if (<= x 1.9e+22) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((y + (x + t)) / (y + t)));
	double tmp;
	if (x <= -9.6e-120) {
		tmp = t_1;
	} else if (x <= 1.95e-27) {
		tmp = a + (z / ((y + t) / y));
	} else if (x <= 1.9e+22) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a / ((y + (x + t)) / (y + t)))
    if (x <= (-9.6d-120)) then
        tmp = t_1
    else if (x <= 1.95d-27) then
        tmp = a + (z / ((y + t) / y))
    else if (x <= 1.9d+22) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((y + (x + t)) / (y + t)));
	double tmp;
	if (x <= -9.6e-120) {
		tmp = t_1;
	} else if (x <= 1.95e-27) {
		tmp = a + (z / ((y + t) / y));
	} else if (x <= 1.9e+22) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a / ((y + (x + t)) / (y + t)))
	tmp = 0
	if x <= -9.6e-120:
		tmp = t_1
	elif x <= 1.95e-27:
		tmp = a + (z / ((y + t) / y))
	elif x <= 1.9e+22:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t))))
	tmp = 0.0
	if (x <= -9.6e-120)
		tmp = t_1;
	elseif (x <= 1.95e-27)
		tmp = Float64(a + Float64(z / Float64(Float64(y + t) / y)));
	elseif (x <= 1.9e+22)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a / ((y + (x + t)) / (y + t)));
	tmp = 0.0;
	if (x <= -9.6e-120)
		tmp = t_1;
	elseif (x <= 1.95e-27)
		tmp = a + (z / ((y + t) / y));
	elseif (x <= 1.9e+22)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e-120], t$95$1, If[LessEqual[x, 1.95e-27], N[(a + N[(z / N[(N[(y + t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+22], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5999999999999998e-120 or 1.9000000000000002e22 < x

   1. Initial program 52.2%

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

   3. Taylor expanded in z around inf 52.2%

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

      1. associate--l+ 52.2%

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

      2. associate-/l* 66.9%

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

      3. associate-+r+ 66.9%

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

      4. div-sub 66.9%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in z around inf 62.0%

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

      1. associate-/l* 86.4%

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

      2. +-commutative 86.4%

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

      3. associate-+r+ 86.4%

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

      4. associate-+r+ 86.4%

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

      5. +-commutative 86.4%

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

      6. associate-+r+ 86.4%

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

      7. +-commutative 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in t around 0 76.9%

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

   if -9.5999999999999998e-120 < x < 1.94999999999999986e-27

   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. Add Preprocessing

   3. Taylor expanded in z around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. associate-/l* 79.9%

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

      3. associate-+r+ 79.9%

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

      4. div-sub 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in z around inf 68.4%

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

      1. associate-/l* 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-+r+ 78.4%

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

      4. associate-+r+ 78.4%

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

      5. +-commutative 78.4%

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

      6. associate-+r+ 78.4%

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

      7. +-commutative 78.4%

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

   8. Simplified 78.4%

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

   9. Taylor expanded in t around inf 76.5%

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

   10. Taylor expanded in x around 0 74.1%

       \[\leadsto \frac{a}{1} + \frac{z}{\color{blue}{\frac{t + y}{y}}} \]
   11. Step-by-step derivation

       1. +-commutative 74.1%

          \[\leadsto \frac{a}{1} + \frac{z}{\frac{\color{blue}{y + t}}{y}} \]

   12. Simplified 74.1%

       \[\leadsto \frac{a}{1} + \frac{z}{\color{blue}{\frac{y + t}{y}}} \]

   if 1.94999999999999986e-27 < x < 1.9000000000000002e22

   1. Initial program 53.2%

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

   3. Taylor expanded in y around inf 92.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-27}:\\ \;\;\;\;a + \frac{z}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+22}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+205}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-219}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= x -4.8e+205)
     z
     (if (<= x -2.5e-195)
       t_1
       (if (<= x -9e-219)
         (+ a (/ (* x (- z a)) t))
         (if (<= x 2.8e+138) t_1 (* z (/ x (+ x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= -4.8e+205) {
		tmp = z;
	} else if (x <= -2.5e-195) {
		tmp = t_1;
	} else if (x <= -9e-219) {
		tmp = a + ((x * (z - a)) / t);
	} else if (x <= 2.8e+138) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (x <= (-4.8d+205)) then
        tmp = z
    else if (x <= (-2.5d-195)) then
        tmp = t_1
    else if (x <= (-9d-219)) then
        tmp = a + ((x * (z - a)) / t)
    else if (x <= 2.8d+138) then
        tmp = t_1
    else
        tmp = 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 t_1 = (z + a) - b;
	double tmp;
	if (x <= -4.8e+205) {
		tmp = z;
	} else if (x <= -2.5e-195) {
		tmp = t_1;
	} else if (x <= -9e-219) {
		tmp = a + ((x * (z - a)) / t);
	} else if (x <= 2.8e+138) {
		tmp = t_1;
	} else {
		tmp = z * (x / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if x <= -4.8e+205:
		tmp = z
	elif x <= -2.5e-195:
		tmp = t_1
	elif x <= -9e-219:
		tmp = a + ((x * (z - a)) / t)
	elif x <= 2.8e+138:
		tmp = t_1
	else:
		tmp = z * (x / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= -4.8e+205)
		tmp = z;
	elseif (x <= -2.5e-195)
		tmp = t_1;
	elseif (x <= -9e-219)
		tmp = Float64(a + Float64(Float64(x * Float64(z - a)) / t));
	elseif (x <= 2.8e+138)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (x <= -4.8e+205)
		tmp = z;
	elseif (x <= -2.5e-195)
		tmp = t_1;
	elseif (x <= -9e-219)
		tmp = a + ((x * (z - a)) / t);
	elseif (x <= 2.8e+138)
		tmp = t_1;
	else
		tmp = z * (x / (x + t));
	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[x, -4.8e+205], z, If[LessEqual[x, -2.5e-195], t$95$1, If[LessEqual[x, -9e-219], N[(a + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+138], t$95$1, N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.79999999999999972e205

   1. Initial program 50.4%

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

   3. Taylor expanded in x around inf 80.7%

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

   if -4.79999999999999972e205 < x < -2.50000000000000004e-195 or -9.00000000000000029e-219 < x < 2.8000000000000001e138

   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 y around inf 60.9%

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

   if -2.50000000000000004e-195 < x < -9.00000000000000029e-219

   1. Initial program 75.1%

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

   3. Taylor expanded in y around 0 77.7%

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

   4. Taylor expanded in t around -inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

      3. distribute-lft-out-- 89.7%

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

      4. mul-1-neg 89.7%

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

      5. *-commutative 89.7%

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

      6. distribute-lft-out-- 89.7%

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

   6. Simplified 89.7%

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

   if 2.8000000000000001e138 < x

   1. Initial program 35.8%

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

   3. Taylor expanded in y around 0 32.8%

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

   4. Taylor expanded in a around 0 24.4%

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

      1. associate-/l* 51.5%

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

      2. associate-/r/ 63.2%

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

      3. +-commutative 63.2%

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

   6. Simplified 63.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+205}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-195}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-219}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-86}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-154}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-164}:\\ \;\;\;\;-b\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.65e+58)
   z
   (if (<= z -4e-86)
     a
     (if (<= z -1.2e-154)
       z
       (if (<= z -2.35e-164) (- b) (if (<= z 21.0) a z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e+58) {
		tmp = z;
	} else if (z <= -4e-86) {
		tmp = a;
	} else if (z <= -1.2e-154) {
		tmp = z;
	} else if (z <= -2.35e-164) {
		tmp = -b;
	} else if (z <= 21.0) {
		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 <= (-1.65d+58)) then
        tmp = z
    else if (z <= (-4d-86)) then
        tmp = a
    else if (z <= (-1.2d-154)) then
        tmp = z
    else if (z <= (-2.35d-164)) then
        tmp = -b
    else if (z <= 21.0d0) 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 <= -1.65e+58) {
		tmp = z;
	} else if (z <= -4e-86) {
		tmp = a;
	} else if (z <= -1.2e-154) {
		tmp = z;
	} else if (z <= -2.35e-164) {
		tmp = -b;
	} else if (z <= 21.0) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.65e+58:
		tmp = z
	elif z <= -4e-86:
		tmp = a
	elif z <= -1.2e-154:
		tmp = z
	elif z <= -2.35e-164:
		tmp = -b
	elif z <= 21.0:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e+58)
		tmp = z;
	elseif (z <= -4e-86)
		tmp = a;
	elseif (z <= -1.2e-154)
		tmp = z;
	elseif (z <= -2.35e-164)
		tmp = Float64(-b);
	elseif (z <= 21.0)
		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 <= -1.65e+58)
		tmp = z;
	elseif (z <= -4e-86)
		tmp = a;
	elseif (z <= -1.2e-154)
		tmp = z;
	elseif (z <= -2.35e-164)
		tmp = -b;
	elseif (z <= 21.0)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e+58], z, If[LessEqual[z, -4e-86], a, If[LessEqual[z, -1.2e-154], z, If[LessEqual[z, -2.35e-164], (-b), If[LessEqual[z, 21.0], a, z]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999991e58 or -4.00000000000000034e-86 < z < -1.19999999999999993e-154 or 21 < z

   1. Initial program 50.0%

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

   3. Taylor expanded in x around inf 53.1%

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

   if -1.64999999999999991e58 < z < -4.00000000000000034e-86 or -2.3499999999999998e-164 < z < 21

   1. Initial program 68.7%

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

   3. Taylor expanded in t around inf 53.0%

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

   if -1.19999999999999993e-154 < z < -2.3499999999999998e-164

   1. Initial program 42.7%

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

   3. Taylor expanded in x around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. neg-mul-1 61.2%

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

   8. Simplified 61.2%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-86}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-154}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-164}:\\ \;\;\;\;-b\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+42} \lor \neg \left(a \leq 480000000000\right):\\ \;\;\;\;z + \frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{t\_1}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= a -8.8e+42) (not (<= a 480000000000.0)))
     (+ z (/ a (/ t_1 (+ y t))))
     (+ a (/ z (/ t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((a <= -8.8e+42) || !(a <= 480000000000.0)) {
		tmp = z + (a / (t_1 / (y + t)));
	} else {
		tmp = a + (z / (t_1 / (x + y)));
	}
	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 ((a <= (-8.8d+42)) .or. (.not. (a <= 480000000000.0d0))) then
        tmp = z + (a / (t_1 / (y + t)))
    else
        tmp = a + (z / (t_1 / (x + y)))
    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 ((a <= -8.8e+42) || !(a <= 480000000000.0)) {
		tmp = z + (a / (t_1 / (y + t)));
	} else {
		tmp = a + (z / (t_1 / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (a <= -8.8e+42) or not (a <= 480000000000.0):
		tmp = z + (a / (t_1 / (y + t)))
	else:
		tmp = a + (z / (t_1 / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((a <= -8.8e+42) || !(a <= 480000000000.0))
		tmp = Float64(z + Float64(a / Float64(t_1 / Float64(y + t))));
	else
		tmp = Float64(a + Float64(z / Float64(t_1 / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((a <= -8.8e+42) || ~((a <= 480000000000.0)))
		tmp = z + (a / (t_1 / (y + t)));
	else
		tmp = a + (z / (t_1 / (x + y)));
	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[Or[LessEqual[a, -8.8e+42], N[Not[LessEqual[a, 480000000000.0]], $MachinePrecision]], N[(z + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.8000000000000005e42 or 4.8e11 < a

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf 43.9%

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

      1. associate--l+ 43.9%

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

      2. associate-/l* 72.2%

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

      3. associate-+r+ 72.2%

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

      4. div-sub 72.2%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. associate-/l* 88.0%

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

      2. +-commutative 88.0%

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

      3. associate-+r+ 88.0%

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

      4. associate-+r+ 88.0%

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

      5. +-commutative 88.0%

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

      6. associate-+r+ 88.0%

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

      7. +-commutative 88.0%

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

   8. Simplified 88.0%

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

   9. Taylor expanded in t around 0 83.9%

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

   if -8.8000000000000005e42 < a < 4.8e11

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. associate-/l* 70.8%

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

      3. associate-+r+ 70.8%

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

      4. div-sub 70.8%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around inf 58.1%

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

      1. associate-/l* 77.6%

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

      2. +-commutative 77.6%

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

      3. associate-+r+ 77.6%

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

      4. associate-+r+ 77.6%

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

      5. +-commutative 77.6%

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

      6. associate-+r+ 77.6%

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

      7. +-commutative 77.6%

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

   8. Simplified 77.6%

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

   9. Taylor expanded in t around inf 73.6%

      \[\leadsto \frac{a}{\color{blue}{1}} + \frac{z}{\frac{\left(t + x\right) + y}{y + x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+42} \lor \neg \left(a \leq 480000000000\right):\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{if}\;a \leq -5 \cdot 10^{+41}:\\ \;\;\;\;t\_2 + \left(z - b\right)\\ \mathbf{elif}\;a \leq 120000000000:\\ \;\;\;\;a + \frac{z}{\frac{t\_1}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;z + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ a (/ t_1 (+ y t)))))
   (if (<= a -5e+41)
     (+ t_2 (- z b))
     (if (<= a 120000000000.0) (+ a (/ z (/ t_1 (+ x y)))) (+ z t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double tmp;
	if (a <= -5e+41) {
		tmp = t_2 + (z - b);
	} else if (a <= 120000000000.0) {
		tmp = a + (z / (t_1 / (x + y)));
	} else {
		tmp = z + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a / (t_1 / (y + t))
    if (a <= (-5d+41)) then
        tmp = t_2 + (z - b)
    else if (a <= 120000000000.0d0) then
        tmp = a + (z / (t_1 / (x + y)))
    else
        tmp = z + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double tmp;
	if (a <= -5e+41) {
		tmp = t_2 + (z - b);
	} else if (a <= 120000000000.0) {
		tmp = a + (z / (t_1 / (x + y)));
	} else {
		tmp = z + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a / (t_1 / (y + t))
	tmp = 0
	if a <= -5e+41:
		tmp = t_2 + (z - b)
	elif a <= 120000000000.0:
		tmp = a + (z / (t_1 / (x + y)))
	else:
		tmp = z + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	tmp = 0.0
	if (a <= -5e+41)
		tmp = Float64(t_2 + Float64(z - b));
	elseif (a <= 120000000000.0)
		tmp = Float64(a + Float64(z / Float64(t_1 / Float64(x + y))));
	else
		tmp = Float64(z + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a / (t_1 / (y + t));
	tmp = 0.0;
	if (a <= -5e+41)
		tmp = t_2 + (z - b);
	elseif (a <= 120000000000.0)
		tmp = a + (z / (t_1 / (x + y)));
	else
		tmp = z + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+41], N[(t$95$2 + N[(z - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 120000000000.0], N[(a + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.00000000000000022e41

   1. Initial program 43.3%

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

   3. Taylor expanded in z around inf 43.3%

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

      1. associate--l+ 43.3%

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

      2. associate-/l* 69.7%

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

      3. associate-+r+ 69.7%

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

      4. div-sub 69.7%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in y around inf 85.8%

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

   if -5.00000000000000022e41 < a < 1.2e11

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. associate--l+ 70.8%

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

      2. associate-/l* 70.8%

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

      3. associate-+r+ 70.8%

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

      4. div-sub 70.8%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around inf 58.1%

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

      1. associate-/l* 77.6%

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

      2. +-commutative 77.6%

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

      3. associate-+r+ 77.6%

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

      4. associate-+r+ 77.6%

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

      5. +-commutative 77.6%

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

      6. associate-+r+ 77.6%

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

      7. +-commutative 77.6%

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

   8. Simplified 77.6%

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

   9. Taylor expanded in t around inf 73.6%

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

   if 1.2e11 < a

   1. Initial program 44.4%

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

   3. Taylor expanded in z around inf 44.4%

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

      1. associate--l+ 44.4%

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

      2. associate-/l* 74.5%

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

      3. associate-+r+ 74.5%

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

      4. div-sub 74.5%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around inf 68.7%

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

      1. associate-/l* 87.5%

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

      2. +-commutative 87.5%

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

      3. associate-+r+ 87.5%

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

      4. associate-+r+ 87.5%

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

      5. +-commutative 87.5%

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

      6. associate-+r+ 87.5%

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

      7. +-commutative 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in t around 0 84.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \left(z - b\right)\\ \mathbf{elif}\;a \leq 120000000000:\\ \;\;\;\;a + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+139}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.1e+206)
   z
   (if (<= x 6.2e+139) (- (+ z a) b) (* z (/ x (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e+206) {
		tmp = z;
	} else if (x <= 6.2e+139) {
		tmp = (z + a) - b;
	} else {
		tmp = 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 (x <= (-1.1d+206)) then
        tmp = z
    else if (x <= 6.2d+139) then
        tmp = (z + a) - b
    else
        tmp = 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 (x <= -1.1e+206) {
		tmp = z;
	} else if (x <= 6.2e+139) {
		tmp = (z + a) - b;
	} else {
		tmp = z * (x / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.1e+206:
		tmp = z
	elif x <= 6.2e+139:
		tmp = (z + a) - b
	else:
		tmp = z * (x / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.1e+206)
		tmp = z;
	elseif (x <= 6.2e+139)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = 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 (x <= -1.1e+206)
		tmp = z;
	elseif (x <= 6.2e+139)
		tmp = (z + a) - b;
	else
		tmp = z * (x / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.1e+206], z, If[LessEqual[x, 6.2e+139], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000001e206

   1. Initial program 50.4%

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

   3. Taylor expanded in x around inf 80.7%

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

   if -1.10000000000000001e206 < x < 6.2e139

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf 59.6%

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

   if 6.2e139 < x

   1. Initial program 35.8%

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

   3. Taylor expanded in y around 0 32.8%

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

   4. Taylor expanded in a around 0 24.4%

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

      1. associate-/l* 51.5%

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

      2. associate-/r/ 63.2%

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

      3. +-commutative 63.2%

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

   6. Simplified 63.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+139}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+206}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+197}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.45e+206) z (if (<= x 4e+197) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.45e+206) {
		tmp = z;
	} else if (x <= 4e+197) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.45d+206)) then
        tmp = z
    else if (x <= 4d+197) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.45e+206) {
		tmp = z;
	} else if (x <= 4e+197) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.45e+206:
		tmp = z
	elif x <= 4e+197:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.45e+206)
		tmp = z;
	elseif (x <= 4e+197)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.45e+206)
		tmp = z;
	elseif (x <= 4e+197)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.45e+206], z, If[LessEqual[x, 4e+197], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e206 or 3.9999999999999998e197 < x

   1. Initial program 43.0%

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

   3. Taylor expanded in x around inf 75.0%

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

   if -2.45e206 < x < 3.9999999999999998e197

   1. Initial program 61.8%

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

   3. Taylor expanded in y around inf 58.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+206}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+197}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 13.5:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.25e+58) z (if (<= z 13.5) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.25e+58) {
		tmp = z;
	} else if (z <= 13.5) {
		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 <= (-2.25d+58)) then
        tmp = z
    else if (z <= 13.5d0) 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 <= -2.25e+58) {
		tmp = z;
	} else if (z <= 13.5) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.25e+58:
		tmp = z
	elif z <= 13.5:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.25e+58)
		tmp = z;
	elseif (z <= 13.5)
		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 <= -2.25e+58)
		tmp = z;
	elseif (z <= 13.5)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.25e+58], z, If[LessEqual[z, 13.5], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999999e58 or 13.5 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in x around inf 54.9%

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

   if -2.2499999999999999e58 < z < 13.5

   1. Initial program 67.1%

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

   3. Taylor expanded in t around inf 48.5%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 13.5:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1350000:\\ \;\;\;\;z - b\\ \mathbf{elif}\;z \leq 0.21:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1350000.0) (- z b) (if (<= z 0.21) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1350000.0) {
		tmp = z - b;
	} else if (z <= 0.21) {
		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 <= (-1350000.0d0)) then
        tmp = z - b
    else if (z <= 0.21d0) 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 <= -1350000.0) {
		tmp = z - b;
	} else if (z <= 0.21) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1350000.0:
		tmp = z - b
	elif z <= 0.21:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1350000.0)
		tmp = Float64(z - b);
	elseif (z <= 0.21)
		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 <= -1350000.0)
		tmp = z - b;
	elseif (z <= 0.21)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1350000.0], N[(z - b), $MachinePrecision], If[LessEqual[z, 0.21], a, z]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e6

   1. Initial program 42.8%

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

   3. Taylor expanded in z around inf 33.0%

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

      1. +-commutative 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in y around inf 56.6%

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

   if -1.35e6 < z < 0.209999999999999992

   1. Initial program 67.8%

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

   3. Taylor expanded in t around inf 49.3%

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

   if 0.209999999999999992 < z

   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. Add Preprocessing

   3. Taylor expanded in x around inf 51.0%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1350000:\\ \;\;\;\;z - b\\ \mathbf{elif}\;z \leq 0.21:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.6% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.5%

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

3. Taylor expanded in t around inf 34.5%

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

4. Final simplification 34.5%

   \[\leadsto a \]
5. Add Preprocessing

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 2024040 
(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)))