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

Percentage Accurate: 61.3% → 91.5%

Time: 14.3s

Alternatives: 16

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.3% 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: 91.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 2 \cdot 10^{+255}\right):\\ \;\;\;\;a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + \frac{z}{\frac{t_2}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+255)))
     (+ (* a (+ (/ y t_1) (/ t t_1))) (/ z (/ t_2 (+ x y))))
     t_3)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+255)) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / (t_2 / (x + y)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 2e+255)) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / (t_2 / (x + y)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = y + (x + t)
	t_3 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 2e+255):
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / (t_2 / (x + y)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+255))
		tmp = Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(z / Float64(t_2 / Float64(x + y))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = y + (x + t);
	t_3 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 2e+255)))
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / (t_2 / (x + y)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+255]], $MachinePrecision]], N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$2 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]

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 1.99999999999999998e255 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.5%

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

   2. Taylor expanded in a around 0 35.8%

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

      1. associate--l+ 35.8%

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

      2. +-commutative 35.8%

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

      3. +-commutative 35.8%

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

      4. +-commutative 35.8%

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

      5. div-sub 35.8%

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

      6. +-commutative 35.8%

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

      7. *-commutative 35.8%

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

      8. +-commutative 35.8%

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

   4. Simplified 35.8%

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

   5. Taylor expanded in z around inf 39.4%

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

      1. associate-/l* 85.1%

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

      2. +-commutative 85.1%

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

      3. +-commutative 85.1%

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

      4. +-commutative 85.1%

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

      5. associate-+r+ 85.1%

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

      6. +-commutative 85.1%

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

   7. Simplified 85.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999998e255

   1. Initial program 99.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+255}\right):\\ \;\;\;\;a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right) + \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+278}\right):\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+278)))
     (+ a (/ z (+ 1.0 (/ t (+ x y)))))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+278)) {
		tmp = a + (z / (1.0 + (t / (x + y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+278)) {
		tmp = a + (z / (1.0 + (t / (x + y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+278):
		tmp = a + (z / (1.0 + (t / (x + y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+278))
		tmp = Float64(a + Float64(z / Float64(1.0 + Float64(t / Float64(x + y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+278)))
		tmp = a + (z / (1.0 + (t / (x + y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+278]], $MachinePrecision]], N[(a + N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999964e277 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.0%

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

   2. Taylor expanded in a around 0 33.3%

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

      1. associate--l+ 33.3%

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

      2. +-commutative 33.3%

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

      3. +-commutative 33.3%

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

      4. +-commutative 33.3%

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

      5. div-sub 33.3%

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

      6. +-commutative 33.3%

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

      7. *-commutative 33.3%

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

      8. +-commutative 33.3%

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

   4. Simplified 33.3%

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

   5. Taylor expanded in z around inf 37.0%

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

      1. associate-/l* 84.5%

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

      2. +-commutative 84.5%

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

      3. +-commutative 84.5%

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

      4. +-commutative 84.5%

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

      5. associate-+r+ 84.5%

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

      6. +-commutative 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in y around inf 77.8%

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

   9. Taylor expanded in t around 0 77.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999964e277

   1. Initial program 99.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+278}\right):\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-220} \lor \neg \left(z \leq 3.8 \cdot 10^{-16}\right):\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e-220) (not (<= z 3.8e-16)))
   (+ a (/ z (+ 1.0 (/ t (+ x y)))))
   (/ (+ (* y (- a b)) (* z (+ x y))) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e-220) || !(z <= 3.8e-16)) {
		tmp = a + (z / (1.0 + (t / (x + y))));
	} else {
		tmp = ((y * (a - b)) + (z * (x + y))) / (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) :: tmp
    if ((z <= (-2.6d-220)) .or. (.not. (z <= 3.8d-16))) then
        tmp = a + (z / (1.0d0 + (t / (x + y))))
    else
        tmp = ((y * (a - b)) + (z * (x + y))) / (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 tmp;
	if ((z <= -2.6e-220) || !(z <= 3.8e-16)) {
		tmp = a + (z / (1.0 + (t / (x + y))));
	} else {
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.6e-220) or not (z <= 3.8e-16):
		tmp = a + (z / (1.0 + (t / (x + y))))
	else:
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e-220) || !(z <= 3.8e-16))
		tmp = Float64(a + Float64(z / Float64(1.0 + Float64(t / Float64(x + y)))));
	else
		tmp = Float64(Float64(Float64(y * Float64(a - b)) + Float64(z * Float64(x + y))) / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.6e-220) || ~((z <= 3.8e-16)))
		tmp = a + (z / (1.0 + (t / (x + y))));
	else
		tmp = ((y * (a - b)) + (z * (x + y))) / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e-220], N[Not[LessEqual[z, 3.8e-16]], $MachinePrecision]], N[(a + N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-220 or 3.80000000000000012e-16 < z

   1. Initial program 56.2%

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

   2. Taylor expanded in a around 0 65.3%

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

      1. associate--l+ 65.3%

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

      2. +-commutative 65.3%

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

      3. +-commutative 65.3%

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

      4. +-commutative 65.3%

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

      5. div-sub 65.2%

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

      6. +-commutative 65.2%

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

      7. *-commutative 65.2%

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

      8. +-commutative 65.2%

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

   4. Simplified 65.2%

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

   5. Taylor expanded in z around inf 57.9%

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

      1. associate-/l* 84.8%

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

      2. +-commutative 84.8%

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

      3. +-commutative 84.8%

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

      4. +-commutative 84.8%

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

      5. associate-+r+ 84.8%

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

      6. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in y around inf 77.4%

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

   9. Taylor expanded in t around 0 77.4%

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

   if -2.6e-220 < z < 3.80000000000000012e-16

   1. Initial program 79.8%

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

   2. Taylor expanded in t around 0 65.1%

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

      1. sub-neg 65.1%

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

      2. +-commutative 65.1%

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

      3. associate-+r+ 65.1%

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

      4. +-commutative 65.1%

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

      5. sub-neg 65.1%

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

      6. distribute-rgt-out-- 65.3%

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

      7. +-commutative 65.3%

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

      8. +-commutative 65.3%

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

   4. Simplified 65.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-220} \lor \neg \left(z \leq 3.8 \cdot 10^{-16}\right):\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ \end{array} \]

Alternative 4: 58.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{t}{x + y}\\ t_3 := \frac{z}{1 + t_2}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-174}:\\ \;\;\;\;a + \frac{z}{t_2}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ t (+ x y))) (t_3 (/ z (+ 1.0 t_2))))
   (if (<= x -8.5e+67)
     t_3
     (if (<= x 5.5e-275)
       t_1
       (if (<= x 3.4e-174) (+ a (/ z t_2)) (if (<= x 1.05e+143) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = t / (x + y);
	double t_3 = z / (1.0 + t_2);
	double tmp;
	if (x <= -8.5e+67) {
		tmp = t_3;
	} else if (x <= 5.5e-275) {
		tmp = t_1;
	} else if (x <= 3.4e-174) {
		tmp = a + (z / t_2);
	} else if (x <= 1.05e+143) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = t / (x + y)
    t_3 = z / (1.0d0 + t_2)
    if (x <= (-8.5d+67)) then
        tmp = t_3
    else if (x <= 5.5d-275) then
        tmp = t_1
    else if (x <= 3.4d-174) then
        tmp = a + (z / t_2)
    else if (x <= 1.05d+143) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = t / (x + y);
	double t_3 = z / (1.0 + t_2);
	double tmp;
	if (x <= -8.5e+67) {
		tmp = t_3;
	} else if (x <= 5.5e-275) {
		tmp = t_1;
	} else if (x <= 3.4e-174) {
		tmp = a + (z / t_2);
	} else if (x <= 1.05e+143) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = t / (x + y)
	t_3 = z / (1.0 + t_2)
	tmp = 0
	if x <= -8.5e+67:
		tmp = t_3
	elif x <= 5.5e-275:
		tmp = t_1
	elif x <= 3.4e-174:
		tmp = a + (z / t_2)
	elif x <= 1.05e+143:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(t / Float64(x + y))
	t_3 = Float64(z / Float64(1.0 + t_2))
	tmp = 0.0
	if (x <= -8.5e+67)
		tmp = t_3;
	elseif (x <= 5.5e-275)
		tmp = t_1;
	elseif (x <= 3.4e-174)
		tmp = Float64(a + Float64(z / t_2));
	elseif (x <= 1.05e+143)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = t / (x + y);
	t_3 = z / (1.0 + t_2);
	tmp = 0.0;
	if (x <= -8.5e+67)
		tmp = t_3;
	elseif (x <= 5.5e-275)
		tmp = t_1;
	elseif (x <= 3.4e-174)
		tmp = a + (z / t_2);
	elseif (x <= 1.05e+143)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+67], t$95$3, If[LessEqual[x, 5.5e-275], t$95$1, If[LessEqual[x, 3.4e-174], N[(a + N[(z / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+143], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.50000000000000038e67 or 1.04999999999999994e143 < x

   1. Initial program 55.6%

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

   2. Taylor expanded in z around inf 37.0%

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

      1. associate-/l* 61.4%

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

      2. +-commutative 61.4%

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

      3. +-commutative 61.4%

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

   4. Simplified 61.4%

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

   5. Taylor expanded in t around 0 61.4%

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

      1. +-commutative 61.4%

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

   7. Simplified 61.4%

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

   if -8.50000000000000038e67 < x < 5.49999999999999988e-275 or 3.4000000000000002e-174 < x < 1.04999999999999994e143

   1. Initial program 66.7%

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

   2. Taylor expanded in y around inf 66.3%

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

   if 5.49999999999999988e-275 < x < 3.4000000000000002e-174

   1. Initial program 73.9%

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

   2. Taylor expanded in a around 0 87.2%

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

      1. associate--l+ 87.2%

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

      2. +-commutative 87.2%

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

      3. +-commutative 87.2%

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

      4. +-commutative 87.2%

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

      5. div-sub 87.2%

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

      6. +-commutative 87.2%

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

      7. *-commutative 87.2%

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

      8. +-commutative 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 86.9%

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

      2. +-commutative 86.9%

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

      3. +-commutative 86.9%

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

      4. +-commutative 86.9%

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

      5. associate-+r+ 86.9%

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

      6. +-commutative 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around inf 82.4%

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

   9. Taylor expanded in t around inf 69.5%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-275}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-174}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+143}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \end{array} \]

Alternative 5: 66.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+185} \lor \neg \left(x \leq 3.4 \cdot 10^{+120}\right):\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.65e+185) (not (<= x 3.4e+120)))
   (- (+ z (/ (* y a) x)) (/ (* y b) x))
   (+ a (/ z (+ 1.0 (/ t (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.65e+185) || !(x <= 3.4e+120)) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else {
		tmp = a + (z / (1.0 + (t / (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) :: tmp
    if ((x <= (-1.65d+185)) .or. (.not. (x <= 3.4d+120))) then
        tmp = (z + ((y * a) / x)) - ((y * b) / x)
    else
        tmp = a + (z / (1.0d0 + (t / (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 tmp;
	if ((x <= -1.65e+185) || !(x <= 3.4e+120)) {
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	} else {
		tmp = a + (z / (1.0 + (t / (x + y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.65e+185) or not (x <= 3.4e+120):
		tmp = (z + ((y * a) / x)) - ((y * b) / x)
	else:
		tmp = a + (z / (1.0 + (t / (x + y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.65e+185) || !(x <= 3.4e+120))
		tmp = Float64(Float64(z + Float64(Float64(y * a) / x)) - Float64(Float64(y * b) / x));
	else
		tmp = Float64(a + Float64(z / Float64(1.0 + Float64(t / Float64(x + y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.65e+185) || ~((x <= 3.4e+120)))
		tmp = (z + ((y * a) / x)) - ((y * b) / x);
	else
		tmp = a + (z / (1.0 + (t / (x + y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.65e+185], N[Not[LessEqual[x, 3.4e+120]], $MachinePrecision]], N[(N[(z + N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(a + N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000006e185 or 3.39999999999999999e120 < x

   1. Initial program 57.2%

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

   2. Taylor expanded in x around inf 64.0%

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

   3. Taylor expanded in t around 0 64.3%

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

   if -1.65000000000000006e185 < x < 3.39999999999999999e120

   1. Initial program 65.6%

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

   2. Taylor expanded in a around 0 77.6%

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

      1. associate--l+ 77.6%

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

      2. +-commutative 77.6%

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

      3. +-commutative 77.6%

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

      4. +-commutative 77.6%

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

      5. div-sub 77.6%

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

      6. +-commutative 77.6%

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

      7. *-commutative 77.6%

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

      8. +-commutative 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in z around inf 64.4%

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

      1. associate-/l* 81.7%

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

      2. +-commutative 81.7%

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

      3. +-commutative 81.7%

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

      4. +-commutative 81.7%

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

      5. associate-+r+ 81.7%

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

      6. +-commutative 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in y around inf 74.5%

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

   9. Taylor expanded in t around 0 74.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+185} \lor \neg \left(x \leq 3.4 \cdot 10^{+120}\right):\\ \;\;\;\;\left(z + \frac{y \cdot a}{x}\right) - \frac{y \cdot b}{x}\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \end{array} \]

Alternative 6: 58.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{z}{\frac{x + t}{x}}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-173}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ z (/ (+ x t) x))))
   (if (<= x -9e+138)
     t_2
     (if (<= x 5.5e-275)
       t_1
       (if (<= x 2.9e-173)
         (+ a (/ z (/ t (+ x y))))
         (if (<= x 1.15e+145) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z / ((x + t) / x);
	double tmp;
	if (x <= -9e+138) {
		tmp = t_2;
	} else if (x <= 5.5e-275) {
		tmp = t_1;
	} else if (x <= 2.9e-173) {
		tmp = a + (z / (t / (x + y)));
	} else if (x <= 1.15e+145) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z / ((x + t) / x)
    if (x <= (-9d+138)) then
        tmp = t_2
    else if (x <= 5.5d-275) then
        tmp = t_1
    else if (x <= 2.9d-173) then
        tmp = a + (z / (t / (x + y)))
    else if (x <= 1.15d+145) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z / ((x + t) / x);
	double tmp;
	if (x <= -9e+138) {
		tmp = t_2;
	} else if (x <= 5.5e-275) {
		tmp = t_1;
	} else if (x <= 2.9e-173) {
		tmp = a + (z / (t / (x + y)));
	} else if (x <= 1.15e+145) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z / ((x + t) / x)
	tmp = 0
	if x <= -9e+138:
		tmp = t_2
	elif x <= 5.5e-275:
		tmp = t_1
	elif x <= 2.9e-173:
		tmp = a + (z / (t / (x + y)))
	elif x <= 1.15e+145:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z / Float64(Float64(x + t) / x))
	tmp = 0.0
	if (x <= -9e+138)
		tmp = t_2;
	elseif (x <= 5.5e-275)
		tmp = t_1;
	elseif (x <= 2.9e-173)
		tmp = Float64(a + Float64(z / Float64(t / Float64(x + y))));
	elseif (x <= 1.15e+145)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z / ((x + t) / x);
	tmp = 0.0;
	if (x <= -9e+138)
		tmp = t_2;
	elseif (x <= 5.5e-275)
		tmp = t_1;
	elseif (x <= 2.9e-173)
		tmp = a + (z / (t / (x + y)));
	elseif (x <= 1.15e+145)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+138], t$95$2, If[LessEqual[x, 5.5e-275], t$95$1, If[LessEqual[x, 2.9e-173], N[(a + N[(z / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+145], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999963e138 or 1.15e145 < x

   1. Initial program 59.0%

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

   2. Taylor expanded in z around inf 39.6%

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

      1. associate-/l* 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 60.3%

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

   if -8.99999999999999963e138 < x < 5.49999999999999988e-275 or 2.8999999999999998e-173 < x < 1.15e145

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 65.9%

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

   if 5.49999999999999988e-275 < x < 2.8999999999999998e-173

   1. Initial program 73.9%

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

   2. Taylor expanded in a around 0 87.2%

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

      1. associate--l+ 87.2%

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

      2. +-commutative 87.2%

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

      3. +-commutative 87.2%

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

      4. +-commutative 87.2%

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

      5. div-sub 87.2%

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

      6. +-commutative 87.2%

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

      7. *-commutative 87.2%

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

      8. +-commutative 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 86.9%

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

      2. +-commutative 86.9%

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

      3. +-commutative 86.9%

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

      4. +-commutative 86.9%

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

      5. associate-+r+ 86.9%

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

      6. +-commutative 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around inf 82.4%

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

   9. Taylor expanded in t around inf 69.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+138}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-275}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-173}:\\ \;\;\;\;a + \frac{z}{\frac{t}{x + y}}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \end{array} \]

Alternative 7: 52.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+178}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-77}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.1e+178)
   (/ (- b) (/ (+ t (+ x y)) y))
   (if (<= b -5.1e-77)
     (- (+ z a) b)
     (if (<= b -2.7e-243) (/ z (+ 1.0 (/ t (+ x y)))) (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.1e+178) {
		tmp = -b / ((t + (x + y)) / y);
	} else if (b <= -5.1e-77) {
		tmp = (z + a) - b;
	} else if (b <= -2.7e-243) {
		tmp = z / (1.0 + (t / (x + y)));
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.1d+178)) then
        tmp = -b / ((t + (x + y)) / y)
    else if (b <= (-5.1d-77)) then
        tmp = (z + a) - b
    else if (b <= (-2.7d-243)) then
        tmp = z / (1.0d0 + (t / (x + y)))
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.1e+178) {
		tmp = -b / ((t + (x + y)) / y);
	} else if (b <= -5.1e-77) {
		tmp = (z + a) - b;
	} else if (b <= -2.7e-243) {
		tmp = z / (1.0 + (t / (x + y)));
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.1e+178:
		tmp = -b / ((t + (x + y)) / y)
	elif b <= -5.1e-77:
		tmp = (z + a) - b
	elif b <= -2.7e-243:
		tmp = z / (1.0 + (t / (x + y)))
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.1e+178)
		tmp = Float64(Float64(-b) / Float64(Float64(t + Float64(x + y)) / y));
	elseif (b <= -5.1e-77)
		tmp = Float64(Float64(z + a) - b);
	elseif (b <= -2.7e-243)
		tmp = Float64(z / Float64(1.0 + Float64(t / Float64(x + y))));
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.1e+178)
		tmp = -b / ((t + (x + y)) / y);
	elseif (b <= -5.1e-77)
		tmp = (z + a) - b;
	elseif (b <= -2.7e-243)
		tmp = z / (1.0 + (t / (x + y)));
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.1e+178], N[((-b) / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.1e-77], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, -2.7e-243], N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.09999999999999996e178

   1. Initial program 57.2%

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

   2. Taylor expanded in b around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. associate-/l* 54.3%

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

      3. distribute-neg-frac 54.3%

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

      4. +-commutative 54.3%

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

   4. Simplified 54.3%

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

   if -4.09999999999999996e178 < b < -5.10000000000000032e-77

   1. Initial program 61.2%

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

   2. Taylor expanded in y around inf 67.3%

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

   if -5.10000000000000032e-77 < b < -2.7000000000000001e-243

   1. Initial program 71.1%

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

   2. Taylor expanded in z around inf 52.3%

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

      1. associate-/l* 71.0%

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

      2. +-commutative 71.0%

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

      3. +-commutative 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around 0 71.0%

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

      1. +-commutative 71.0%

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

   7. Simplified 71.0%

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

   if -2.7000000000000001e-243 < b

   1. Initial program 62.7%

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

   2. Taylor expanded in y around inf 58.3%

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

   3. Taylor expanded in b around 0 62.1%

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

      1. +-commutative 62.1%

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

   5. Simplified 62.1%

      \[\leadsto \color{blue}{z + a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+178}:\\ \;\;\;\;\frac{-b}{\frac{t + \left(x + y\right)}{y}}\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-77}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 8: 68.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-126} \lor \neg \left(z \leq 4.4 \cdot 10^{-148}\right):\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t + \left(x + y\right)}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.8e-126) (not (<= z 4.4e-148)))
   (+ a (/ z (+ 1.0 (/ t (+ x y)))))
   (/ a (/ (+ t (+ x y)) (+ y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e-126) || !(z <= 4.4e-148)) {
		tmp = a + (z / (1.0 + (t / (x + y))));
	} else {
		tmp = a / ((t + (x + y)) / (y + 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 ((z <= (-6.8d-126)) .or. (.not. (z <= 4.4d-148))) then
        tmp = a + (z / (1.0d0 + (t / (x + y))))
    else
        tmp = a / ((t + (x + y)) / (y + 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 ((z <= -6.8e-126) || !(z <= 4.4e-148)) {
		tmp = a + (z / (1.0 + (t / (x + y))));
	} else {
		tmp = a / ((t + (x + y)) / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.8e-126) or not (z <= 4.4e-148):
		tmp = a + (z / (1.0 + (t / (x + y))))
	else:
		tmp = a / ((t + (x + y)) / (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.8e-126) || !(z <= 4.4e-148))
		tmp = Float64(a + Float64(z / Float64(1.0 + Float64(t / Float64(x + y)))));
	else
		tmp = Float64(a / Float64(Float64(t + Float64(x + y)) / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.8e-126) || ~((z <= 4.4e-148)))
		tmp = a + (z / (1.0 + (t / (x + y))));
	else
		tmp = a / ((t + (x + y)) / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.8e-126], N[Not[LessEqual[z, 4.4e-148]], $MachinePrecision]], N[(a + N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e-126 or 4.40000000000000034e-148 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in a around 0 68.7%

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

      1. associate--l+ 68.7%

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

      2. +-commutative 68.7%

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

      3. +-commutative 68.7%

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

      4. +-commutative 68.7%

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

      5. div-sub 68.6%

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

      6. +-commutative 68.6%

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

      7. *-commutative 68.6%

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

      8. +-commutative 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in z around inf 61.0%

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

      1. associate-/l* 85.9%

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

      2. +-commutative 85.9%

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

      3. +-commutative 85.9%

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

      4. +-commutative 85.9%

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

      5. associate-+r+ 85.9%

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

      6. +-commutative 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in y around inf 76.1%

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

   9. Taylor expanded in t around 0 76.1%

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

   if -6.8e-126 < z < 4.40000000000000034e-148

   1. Initial program 75.6%

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

   2. Taylor expanded in a around inf 39.2%

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

      1. associate-/l* 53.9%

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

      2. +-commutative 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-126} \lor \neg \left(z \leq 4.4 \cdot 10^{-148}\right):\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t + \left(x + y\right)}{y + t}}\\ \end{array} \]

Alternative 9: 65.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{if}\;x \leq 1.55 \cdot 10^{+196}:\\ \;\;\;\;a + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (+ 1.0 (/ t (+ x y))))))
   (if (<= x 1.55e+196) (+ a t_1) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (1.0 + (t / (x + y)));
	double tmp;
	if (x <= 1.55e+196) {
		tmp = a + t_1;
	} 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 / (1.0d0 + (t / (x + y)))
    if (x <= 1.55d+196) then
        tmp = a + t_1
    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 / (1.0 + (t / (x + y)));
	double tmp;
	if (x <= 1.55e+196) {
		tmp = a + t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / (1.0 + (t / (x + y)))
	tmp = 0
	if x <= 1.55e+196:
		tmp = a + t_1
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(1.0 + Float64(t / Float64(x + y))))
	tmp = 0.0
	if (x <= 1.55e+196)
		tmp = Float64(a + t_1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z / (1.0 + (t / (x + y)));
	tmp = 0.0;
	if (x <= 1.55e+196)
		tmp = a + t_1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(1.0 + N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.55e+196], N[(a + t$95$1), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if x < 1.55000000000000005e196

   1. Initial program 63.4%

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

   2. Taylor expanded in a around 0 74.6%

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

      1. associate--l+ 74.6%

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

      2. +-commutative 74.6%

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

      3. +-commutative 74.6%

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

      4. +-commutative 74.6%

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

      5. div-sub 74.6%

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

      6. +-commutative 74.6%

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

      7. *-commutative 74.6%

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

      8. +-commutative 74.6%

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

   4. Simplified 74.6%

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

   5. Taylor expanded in z around inf 63.0%

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

      1. associate-/l* 81.1%

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

      2. +-commutative 81.1%

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

      3. +-commutative 81.1%

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

      4. +-commutative 81.1%

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

      5. associate-+r+ 81.1%

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

      6. +-commutative 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around inf 68.2%

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

   9. Taylor expanded in t around 0 68.2%

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

   if 1.55000000000000005e196 < x

   1. Initial program 61.6%

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

   2. Taylor expanded in z around inf 48.1%

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

      1. associate-/l* 71.3%

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

      2. +-commutative 71.3%

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

      3. +-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in t around 0 71.3%

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

      1. +-commutative 71.3%

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

   7. Simplified 71.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+196}:\\ \;\;\;\;a + \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \end{array} \]

Alternative 10: 59.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+139} \lor \neg \left(x \leq 6 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -6.8e+139) (not (<= x 6e+143)))
   (/ z (/ (+ x t) x))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6.8e+139) || !(x <= 6e+143)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-6.8d+139)) .or. (.not. (x <= 6d+143))) then
        tmp = z / ((x + t) / x)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6.8e+139) || !(x <= 6e+143)) {
		tmp = z / ((x + t) / x);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -6.8e+139) or not (x <= 6e+143):
		tmp = z / ((x + t) / x)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -6.8e+139) || !(x <= 6e+143))
		tmp = Float64(z / Float64(Float64(x + t) / x));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -6.8e+139) || ~((x <= 6e+143)))
		tmp = z / ((x + t) / x);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -6.8e+139], N[Not[LessEqual[x, 6e+143]], $MachinePrecision]], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000005e139 or 6.0000000000000001e143 < x

   1. Initial program 59.0%

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

   2. Taylor expanded in z around inf 39.6%

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

      1. associate-/l* 60.3%

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

      2. +-commutative 60.3%

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

      3. +-commutative 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around 0 60.3%

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

   if -6.8000000000000005e139 < x < 6.0000000000000001e143

   1. Initial program 65.1%

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

   2. Taylor expanded in y around inf 63.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+139} \lor \neg \left(x \leq 6 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 58.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+146}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.6e+159)
   z
   (if (<= x 3.1e+146) (- (+ z a) b) (* z (- 1.0 (/ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+159) {
		tmp = z;
	} else if (x <= 3.1e+146) {
		tmp = (z + a) - b;
	} else {
		tmp = z * (1.0 - (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.6d+159)) then
        tmp = z
    else if (x <= 3.1d+146) then
        tmp = (z + a) - b
    else
        tmp = z * (1.0d0 - (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+159) {
		tmp = z;
	} else if (x <= 3.1e+146) {
		tmp = (z + a) - b;
	} else {
		tmp = z * (1.0 - (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.6e+159:
		tmp = z
	elif x <= 3.1e+146:
		tmp = (z + a) - b
	else:
		tmp = z * (1.0 - (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.6e+159)
		tmp = z;
	elseif (x <= 3.1e+146)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(1.0 - Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.6e+159)
		tmp = z;
	elseif (x <= 3.1e+146)
		tmp = (z + a) - b;
	else
		tmp = z * (1.0 - (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.6e+159], z, If[LessEqual[x, 3.1e+146], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(1.0 - N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5999999999999999e159

   1. Initial program 58.7%

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

   2. Taylor expanded in x around inf 56.7%

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

   if -9.5999999999999999e159 < x < 3.1000000000000002e146

   1. Initial program 65.3%

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

   2. Taylor expanded in y around inf 62.1%

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

   if 3.1000000000000002e146 < x

   1. Initial program 57.2%

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

   2. Taylor expanded in x around inf 66.7%

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

   3. Taylor expanded in z around inf 61.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+146}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \end{array} \]

Alternative 12: 52.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-274}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+194}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.55e-257)
   (+ z a)
   (if (<= x 5.6e-274) (- a b) (if (<= x 8.5e+194) (+ z a) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e-257) {
		tmp = z + a;
	} else if (x <= 5.6e-274) {
		tmp = a - b;
	} else if (x <= 8.5e+194) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.55d-257)) then
        tmp = z + a
    else if (x <= 5.6d-274) then
        tmp = a - b
    else if (x <= 8.5d+194) then
        tmp = z + a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e-257) {
		tmp = z + a;
	} else if (x <= 5.6e-274) {
		tmp = a - b;
	} else if (x <= 8.5e+194) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.55e-257:
		tmp = z + a
	elif x <= 5.6e-274:
		tmp = a - b
	elif x <= 8.5e+194:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.55e-257)
		tmp = Float64(z + a);
	elseif (x <= 5.6e-274)
		tmp = Float64(a - b);
	elseif (x <= 8.5e+194)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.55e-257)
		tmp = z + a;
	elseif (x <= 5.6e-274)
		tmp = a - b;
	elseif (x <= 8.5e+194)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.55e-257], N[(z + a), $MachinePrecision], If[LessEqual[x, 5.6e-274], N[(a - b), $MachinePrecision], If[LessEqual[x, 8.5e+194], N[(z + a), $MachinePrecision], z]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000004e-257 or 5.5999999999999995e-274 < x < 8.50000000000000026e194

   1. Initial program 62.0%

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

   2. Taylor expanded in y around inf 55.5%

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

   3. Taylor expanded in b around 0 54.4%

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

      1. +-commutative 54.4%

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

   5. Simplified 54.4%

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

   if -1.55000000000000004e-257 < x < 5.5999999999999995e-274

   1. Initial program 82.2%

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

   2. Taylor expanded in y around inf 73.6%

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

   3. Taylor expanded in z around 0 76.0%

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

   if 8.50000000000000026e194 < x

   1. Initial program 61.6%

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

   2. Taylor expanded in x around inf 68.6%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-274}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+194}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13: 58.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+144}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.2e+159) z (if (<= x 8.2e+144) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.2e+159) {
		tmp = z;
	} else if (x <= 8.2e+144) {
		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 <= (-7.2d+159)) then
        tmp = z
    else if (x <= 8.2d+144) 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 <= -7.2e+159) {
		tmp = z;
	} else if (x <= 8.2e+144) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.2e+159:
		tmp = z
	elif x <= 8.2e+144:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.2e+159)
		tmp = z;
	elseif (x <= 8.2e+144)
		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 <= -7.2e+159)
		tmp = z;
	elseif (x <= 8.2e+144)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.2e+159], z, If[LessEqual[x, 8.2e+144], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000073e159 or 8.20000000000000002e144 < x

   1. Initial program 57.8%

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

   2. Taylor expanded in x around inf 59.1%

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

   if -7.20000000000000073e159 < x < 8.20000000000000002e144

   1. Initial program 65.3%

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

   2. Taylor expanded in y around inf 62.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+144}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 14: 44.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+54}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+117}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.1e+54) a (if (<= a 1.7e+117) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.1e+54) {
		tmp = a;
	} else if (a <= 1.7e+117) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.1d+54)) then
        tmp = a
    else if (a <= 1.7d+117) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.1e+54) {
		tmp = a;
	} else if (a <= 1.7e+117) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.1e+54:
		tmp = a
	elif a <= 1.7e+117:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.1e+54)
		tmp = a;
	elseif (a <= 1.7e+117)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.1e+54)
		tmp = a;
	elseif (a <= 1.7e+117)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.1e+54], a, If[LessEqual[a, 1.7e+117], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -4.09999999999999967e54 or 1.7e117 < a

   1. Initial program 42.4%

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

   2. Taylor expanded in t around inf 51.2%

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

   if -4.09999999999999967e54 < a < 1.7e117

   1. Initial program 75.3%

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

   2. Taylor expanded in x around inf 52.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+54}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+117}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 52.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+194}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 2.2e+194) (+ z a) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.2e+194) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 2.2d+194) then
        tmp = z + a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.2e+194) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.2e+194:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.2e+194)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 2.2e+194)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.2e+194], N[(z + a), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 2.2000000000000001e194

   1. Initial program 63.4%

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

   2. Taylor expanded in y around inf 56.8%

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

   3. Taylor expanded in b around 0 53.3%

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

      1. +-commutative 53.3%

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

   5. Simplified 53.3%

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

   if 2.2000000000000001e194 < x

   1. Initial program 61.6%

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

   2. Taylor expanded in x around inf 68.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+194}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16: 33.2% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.2%

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

2. Taylor expanded in t around inf 29.8%

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

3. Final simplification 29.8%

   \[\leadsto a \]

Developer target: 82.9% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023306 
(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)))