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

Percentage Accurate: 59.2% → 99.5%

Time: 16.4s

Alternatives: 14

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.2% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) - b \cdot \frac{y}{t_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 5e+292)))
     (+
      (/ (+ x y) (/ t_1 z))
      (- (* a (+ (/ y t_1) (/ t t_1))) (* b (/ y t_2))))
     t_3)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 5e+292)) {
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (b * (y / t_2)));
	} 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 = x + (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 5e+292)) {
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (b * (y / t_2)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = y + (x + t)
	t_3 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 5e+292):
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (b * (y / t_2)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 5e+292))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) - Float64(b * Float64(y / t_2))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = y + (x + t);
	t_3 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 5e+292)))
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (b * (y / t_2)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $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, 5e+292]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$2), $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 4.9999999999999996e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

   2. Taylor expanded in a around 0 32.3%

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

      1. associate--l+ 32.3%

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

      2. associate-/l* 79.0%

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

      3. associate-+r+ 79.0%

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

      4. associate-+r+ 79.0%

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

      5. associate-+r+ 79.0%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

      1. associate-/r/ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e292

   1. Initial program 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a \cdot \left(\frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}\right) - b \cdot \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - b \cdot \frac{y}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+292)))
     (+ (/ (+ x y) (/ (+ x (+ y t)) z)) (- a (* b (/ y t_1))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+292)) {
		tmp = ((x + y) / ((x + (y + t)) / z)) + (a - (b * (y / t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+292)) {
		tmp = ((x + y) / ((x + (y + t)) / z)) + (a - (b * (y / t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+292):
		tmp = ((x + y) / ((x + (y + t)) / z)) + (a - (b * (y / t_1)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+292))
		tmp = Float64(Float64(Float64(x + y) / Float64(Float64(x + Float64(y + t)) / z)) + Float64(a - Float64(b * Float64(y / t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+292)))
		tmp = ((x + y) / ((x + (y + t)) / z)) + (a - (b * (y / t_1)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+292]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999996e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

   2. Taylor expanded in a around 0 32.3%

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

      1. associate--l+ 32.3%

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

      2. associate-/l* 79.0%

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

      3. associate-+r+ 79.0%

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

      4. associate-+r+ 79.0%

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

      5. associate-+r+ 79.0%

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

      6. associate-/l* 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

      1. associate-/r/ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 91.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e292

   1. Initial program 99.6%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}} + \left(a - b \cdot \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+292))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+292)) {
		tmp = (z + a) - b;
	} 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+292)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+292):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+292))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+292)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $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, 5e+292]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $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 4.9999999999999996e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

   2. Taylor expanded in y around inf 76.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e292

   1. Initial program 99.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 4: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a \cdot \left(y + t\right) + z \cdot \left(x + y\right)}{t_1}\\ \mathbf{if}\;y \leq -48000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (- (+ z a) b))
        (t_3 (/ (+ (* a (+ y t)) (* z (+ x y))) t_1)))
   (if (<= y -48000000000000.0)
     t_2
     (if (<= y -4.1e-76)
       (/ (- (* t a) (* y b)) t_1)
       (if (<= y -8e-144)
         t_3
         (if (<= y -8.8e-167)
           (/ (- (* x z) (* y b)) t_1)
           (if (<= y 1.9e+26) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = ((a * (y + t)) + (z * (x + y))) / t_1;
	double tmp;
	if (y <= -48000000000000.0) {
		tmp = t_2;
	} else if (y <= -4.1e-76) {
		tmp = ((t * a) - (y * b)) / t_1;
	} else if (y <= -8e-144) {
		tmp = t_3;
	} else if (y <= -8.8e-167) {
		tmp = ((x * z) - (y * b)) / t_1;
	} else if (y <= 1.9e+26) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    t_3 = ((a * (y + t)) + (z * (x + y))) / t_1
    if (y <= (-48000000000000.0d0)) then
        tmp = t_2
    else if (y <= (-4.1d-76)) then
        tmp = ((t * a) - (y * b)) / t_1
    else if (y <= (-8d-144)) then
        tmp = t_3
    else if (y <= (-8.8d-167)) then
        tmp = ((x * z) - (y * b)) / t_1
    else if (y <= 1.9d+26) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = ((a * (y + t)) + (z * (x + y))) / t_1;
	double tmp;
	if (y <= -48000000000000.0) {
		tmp = t_2;
	} else if (y <= -4.1e-76) {
		tmp = ((t * a) - (y * b)) / t_1;
	} else if (y <= -8e-144) {
		tmp = t_3;
	} else if (y <= -8.8e-167) {
		tmp = ((x * z) - (y * b)) / t_1;
	} else if (y <= 1.9e+26) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	t_3 = ((a * (y + t)) + (z * (x + y))) / t_1
	tmp = 0
	if y <= -48000000000000.0:
		tmp = t_2
	elif y <= -4.1e-76:
		tmp = ((t * a) - (y * b)) / t_1
	elif y <= -8e-144:
		tmp = t_3
	elif y <= -8.8e-167:
		tmp = ((x * z) - (y * b)) / t_1
	elif y <= 1.9e+26:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) / t_1)
	tmp = 0.0
	if (y <= -48000000000000.0)
		tmp = t_2;
	elseif (y <= -4.1e-76)
		tmp = Float64(Float64(Float64(t * a) - Float64(y * b)) / t_1);
	elseif (y <= -8e-144)
		tmp = t_3;
	elseif (y <= -8.8e-167)
		tmp = Float64(Float64(Float64(x * z) - Float64(y * b)) / t_1);
	elseif (y <= 1.9e+26)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	t_3 = ((a * (y + t)) + (z * (x + y))) / t_1;
	tmp = 0.0;
	if (y <= -48000000000000.0)
		tmp = t_2;
	elseif (y <= -4.1e-76)
		tmp = ((t * a) - (y * b)) / t_1;
	elseif (y <= -8e-144)
		tmp = t_3;
	elseif (y <= -8.8e-167)
		tmp = ((x * z) - (y * b)) / t_1;
	elseif (y <= 1.9e+26)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[y, -48000000000000.0], t$95$2, If[LessEqual[y, -4.1e-76], N[(N[(N[(t * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, -8e-144], t$95$3, If[LessEqual[y, -8.8e-167], N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 1.9e+26], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8e13 or 1.9000000000000001e26 < y

   1. Initial program 34.0%

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

   2. Taylor expanded in y around inf 77.8%

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

   if -4.8e13 < y < -4.0999999999999998e-76

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 69.9%

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

   if -4.0999999999999998e-76 < y < -7.9999999999999996e-144 or -8.7999999999999999e-167 < y < 1.9000000000000001e26

   1. Initial program 76.0%

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

   2. Taylor expanded in b around 0 69.1%

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

   if -7.9999999999999996e-144 < y < -8.7999999999999999e-167

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 80.9%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -48000000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-144}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-167}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2700000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-75}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -2700000000000.0)
     t_2
     (if (<= y -1e-75)
       (/ (- (* t a) (* y b)) t_1)
       (if (<= y -2.4e-117)
         (/ (+ x y) (/ (+ x (+ y t)) z))
         (if (<= y 1.6e-51)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 3e+64) (* z (/ (+ x y) t_1)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2700000000000.0) {
		tmp = t_2;
	} else if (y <= -1e-75) {
		tmp = ((t * a) - (y * b)) / t_1;
	} else if (y <= -2.4e-117) {
		tmp = (x + y) / ((x + (y + t)) / z);
	} else if (y <= 1.6e-51) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3e+64) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (y <= (-2700000000000.0d0)) then
        tmp = t_2
    else if (y <= (-1d-75)) then
        tmp = ((t * a) - (y * b)) / t_1
    else if (y <= (-2.4d-117)) then
        tmp = (x + y) / ((x + (y + t)) / z)
    else if (y <= 1.6d-51) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 3d+64) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2700000000000.0) {
		tmp = t_2;
	} else if (y <= -1e-75) {
		tmp = ((t * a) - (y * b)) / t_1;
	} else if (y <= -2.4e-117) {
		tmp = (x + y) / ((x + (y + t)) / z);
	} else if (y <= 1.6e-51) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3e+64) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -2700000000000.0:
		tmp = t_2
	elif y <= -1e-75:
		tmp = ((t * a) - (y * b)) / t_1
	elif y <= -2.4e-117:
		tmp = (x + y) / ((x + (y + t)) / z)
	elif y <= 1.6e-51:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 3e+64:
		tmp = z * ((x + y) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2700000000000.0)
		tmp = t_2;
	elseif (y <= -1e-75)
		tmp = Float64(Float64(Float64(t * a) - Float64(y * b)) / t_1);
	elseif (y <= -2.4e-117)
		tmp = Float64(Float64(x + y) / Float64(Float64(x + Float64(y + t)) / z));
	elseif (y <= 1.6e-51)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 3e+64)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2700000000000.0)
		tmp = t_2;
	elseif (y <= -1e-75)
		tmp = ((t * a) - (y * b)) / t_1;
	elseif (y <= -2.4e-117)
		tmp = (x + y) / ((x + (y + t)) / z);
	elseif (y <= 1.6e-51)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 3e+64)
		tmp = z * ((x + y) / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2700000000000.0], t$95$2, If[LessEqual[y, -1e-75], N[(N[(N[(t * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, -2.4e-117], N[(N[(x + y), $MachinePrecision] / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-51], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+64], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7e12 or 3.0000000000000002e64 < y

   1. Initial program 33.9%

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

   2. Taylor expanded in y around inf 80.2%

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

   if -2.7e12 < y < -9.9999999999999996e-76

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 69.9%

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

   if -9.9999999999999996e-76 < y < -2.40000000000000014e-117

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 59.4%

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

      1. associate-/l* 86.3%

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

      2. associate-+r+ 86.3%

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

   4. Simplified 86.3%

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

   if -2.40000000000000014e-117 < y < 1.6e-51

   1. Initial program 77.3%

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

   2. Taylor expanded in y around 0 62.8%

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

   if 1.6e-51 < y < 3.0000000000000002e64

   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 z around inf 47.2%

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

      1. associate-/l* 73.0%

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

      2. associate-+r+ 73.0%

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

   4. Simplified 73.0%

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

      1. associate-/r/ 78.7%

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

      2. associate-+l+ 78.7%

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

      3. +-commutative 78.7%

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

   6. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\frac{y + x}{y + \left(x + t\right)} \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2700000000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-75}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x + y}{\frac{x + \left(y + t\right)}{z}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 63.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.6e-113)
     t_1
     (if (<= y 7.5e-52)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 4.2e+65) (* z (/ (+ x y) (+ y (+ x t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.6e-113) {
		tmp = t_1;
	} else if (y <= 7.5e-52) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.2e+65) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.6d-113)) then
        tmp = t_1
    else if (y <= 7.5d-52) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4.2d+65) then
        tmp = z * ((x + y) / (y + (x + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.6e-113) {
		tmp = t_1;
	} else if (y <= 7.5e-52) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.2e+65) {
		tmp = z * ((x + y) / (y + (x + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.6e-113:
		tmp = t_1
	elif y <= 7.5e-52:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4.2e+65:
		tmp = z * ((x + y) / (y + (x + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.6e-113)
		tmp = t_1;
	elseif (y <= 7.5e-52)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4.2e+65)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.6e-113)
		tmp = t_1;
	elseif (y <= 7.5e-52)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4.2e+65)
		tmp = z * ((x + y) / (y + (x + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.6e-113], t$95$1, If[LessEqual[y, 7.5e-52], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+65], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000016e-113 or 4.19999999999999983e65 < y

   1. Initial program 43.0%

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

   2. Taylor expanded in y around inf 75.3%

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

   if -4.60000000000000016e-113 < y < 7.50000000000000006e-52

   1. Initial program 76.8%

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

   2. Taylor expanded in y around 0 62.6%

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

   if 7.50000000000000006e-52 < y < 4.19999999999999983e65

   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 z around inf 47.2%

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

      1. associate-/l* 73.0%

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

      2. associate-+r+ 73.0%

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

   4. Simplified 73.0%

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

      1. associate-/r/ 78.7%

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

      2. associate-+l+ 78.7%

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

      3. +-commutative 78.7%

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

   6. Applied egg-rr 78.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-113}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 7: 58.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-73} \lor \neg \left(y \leq 3 \cdot 10^{+64}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.9e-73) (not (<= y 3e+64)))
   (- (+ z a) b)
   (* z (/ (+ x y) (+ y (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.9e-73) || !(y <= 3e+64)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.9d-73)) .or. (.not. (y <= 3d+64))) then
        tmp = (z + a) - b
    else
        tmp = z * ((x + y) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.9e-73) || !(y <= 3e+64)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.9e-73) or not (y <= 3e+64):
		tmp = (z + a) - b
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.9e-73) || !(y <= 3e+64))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.9e-73) || ~((y <= 3e+64)))
		tmp = (z + a) - b;
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.9e-73], N[Not[LessEqual[y, 3e+64]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.90000000000000028e-73 or 3.0000000000000002e64 < y

   1. Initial program 41.1%

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

   2. Taylor expanded in y around inf 76.2%

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

   if -4.90000000000000028e-73 < y < 3.0000000000000002e64

   1. Initial program 75.2%

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

   2. Taylor expanded in z around inf 35.7%

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

      1. associate-/l* 43.9%

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

      2. associate-+r+ 43.9%

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

   4. Simplified 43.9%

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

      1. associate-/r/ 49.8%

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

      2. associate-+l+ 49.8%

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

      3. +-commutative 49.8%

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

   6. Applied egg-rr 49.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-73} \lor \neg \left(y \leq 3 \cdot 10^{+64}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 8: 47.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+93}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.9e+93)
   a
   (if (<= t -6.5e+64)
     (- z b)
     (if (<= t -3.1e-41) a (if (<= t 2.1e+18) (- z b) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e+93) {
		tmp = a;
	} else if (t <= -6.5e+64) {
		tmp = z - b;
	} else if (t <= -3.1e-41) {
		tmp = a;
	} else if (t <= 2.1e+18) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.9d+93)) then
        tmp = a
    else if (t <= (-6.5d+64)) then
        tmp = z - b
    else if (t <= (-3.1d-41)) then
        tmp = a
    else if (t <= 2.1d+18) then
        tmp = z - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e+93) {
		tmp = a;
	} else if (t <= -6.5e+64) {
		tmp = z - b;
	} else if (t <= -3.1e-41) {
		tmp = a;
	} else if (t <= 2.1e+18) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.9e+93:
		tmp = a
	elif t <= -6.5e+64:
		tmp = z - b
	elif t <= -3.1e-41:
		tmp = a
	elif t <= 2.1e+18:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.9e+93)
		tmp = a;
	elseif (t <= -6.5e+64)
		tmp = Float64(z - b);
	elseif (t <= -3.1e-41)
		tmp = a;
	elseif (t <= 2.1e+18)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.9e+93)
		tmp = a;
	elseif (t <= -6.5e+64)
		tmp = z - b;
	elseif (t <= -3.1e-41)
		tmp = a;
	elseif (t <= 2.1e+18)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.9e+93], a, If[LessEqual[t, -6.5e+64], N[(z - b), $MachinePrecision], If[LessEqual[t, -3.1e-41], a, If[LessEqual[t, 2.1e+18], N[(z - b), $MachinePrecision], a]]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.89999999999999969e93 or -6.50000000000000007e64 < t < -3.10000000000000001e-41 or 2.1e18 < t

   1. Initial program 52.2%

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

   2. Taylor expanded in t around inf 50.9%

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

   if -4.89999999999999969e93 < t < -6.50000000000000007e64 or -3.10000000000000001e-41 < t < 2.1e18

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf 45.7%

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

   3. Taylor expanded in y around inf 55.9%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+93}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 9: 61.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+203} \lor \neg \left(x \leq 1.6 \cdot 10^{+124}\right):\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.45e+203) (not (<= x 1.6e+124)))
   (- z (/ b (/ x y)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.45e+203) || !(x <= 1.6e+124)) {
		tmp = z - (b / (x / y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.45d+203)) .or. (.not. (x <= 1.6d+124))) then
        tmp = z - (b / (x / y))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.45e+203) || !(x <= 1.6e+124)) {
		tmp = z - (b / (x / y));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.45e+203) or not (x <= 1.6e+124):
		tmp = z - (b / (x / y))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.45e+203) || !(x <= 1.6e+124))
		tmp = Float64(z - Float64(b / Float64(x / y)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.45e+203) || ~((x <= 1.6e+124)))
		tmp = z - (b / (x / y));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.45e+203], N[Not[LessEqual[x, 1.6e+124]], $MachinePrecision]], N[(z - N[(b / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000005e203 or 1.59999999999999996e124 < x

   1. Initial program 40.2%

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

   2. Taylor expanded in z around inf 28.6%

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

   3. Taylor expanded in t around 0 28.5%

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

   4. Taylor expanded in y around 0 62.3%

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

      1. +-commutative 62.3%

         \[\leadsto \color{blue}{z + -1 \cdot \frac{y \cdot b}{x}} \]

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

         \[\leadsto \color{blue}{z - \frac{y \cdot b}{x}} \]

      4. *-commutative 62.3%

         \[\leadsto z - \frac{\color{blue}{b \cdot y}}{x} \]

      5. associate-/l* 63.6%

         \[\leadsto z - \color{blue}{\frac{b}{\frac{x}{y}}} \]

   6. Simplified 63.6%

      \[\leadsto \color{blue}{z - \frac{b}{\frac{x}{y}}} \]

   if -1.45000000000000005e203 < x < 1.59999999999999996e124

   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 60.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+203} \lor \neg \left(x \leq 1.6 \cdot 10^{+124}\right):\\ \;\;\;\;z - \frac{b}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 58.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-137} \lor \neg \left(y \leq 6 \cdot 10^{-113}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.9e-137) (not (<= y 6e-113)))
   (- (+ z a) b)
   (/ z (/ (+ x t) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e-137) || !(y <= 6e-113)) {
		tmp = (z + a) - b;
	} else {
		tmp = z / ((x + t) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.9d-137)) .or. (.not. (y <= 6d-113))) then
        tmp = (z + a) - b
    else
        tmp = z / ((x + t) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e-137) || !(y <= 6e-113)) {
		tmp = (z + a) - b;
	} else {
		tmp = z / ((x + t) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.9e-137) or not (y <= 6e-113):
		tmp = (z + a) - b
	else:
		tmp = z / ((x + t) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.9e-137) || !(y <= 6e-113))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z / Float64(Float64(x + t) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.9e-137) || ~((y <= 6e-113)))
		tmp = (z + a) - b;
	else
		tmp = z / ((x + t) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.9e-137], N[Not[LessEqual[y, 6e-113]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999985e-137 or 6.0000000000000002e-113 < y

   1. Initial program 48.3%

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

   2. Taylor expanded in y around inf 70.3%

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

   if -2.89999999999999985e-137 < y < 6.0000000000000002e-113

   1. Initial program 77.0%

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

   2. Taylor expanded in z around inf 34.6%

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

      1. associate-/l* 39.2%

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

      2. associate-+r+ 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in y around 0 33.5%

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

      1. associate-/l* 45.5%

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

      2. +-commutative 45.5%

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

   7. Simplified 45.5%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-137} \lor \neg \left(y \leq 6 \cdot 10^{-113}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \end{array} \]

Alternative 11: 43.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-70}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-303}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-296}:\\ \;\;\;\;-b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.12e-70)
   a
   (if (<= t -1.4e-303) z (if (<= t 7e-296) (- b) (if (<= t 8.5e+80) z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.12e-70) {
		tmp = a;
	} else if (t <= -1.4e-303) {
		tmp = z;
	} else if (t <= 7e-296) {
		tmp = -b;
	} else if (t <= 8.5e+80) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.12d-70)) then
        tmp = a
    else if (t <= (-1.4d-303)) then
        tmp = z
    else if (t <= 7d-296) then
        tmp = -b
    else if (t <= 8.5d+80) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.12e-70) {
		tmp = a;
	} else if (t <= -1.4e-303) {
		tmp = z;
	} else if (t <= 7e-296) {
		tmp = -b;
	} else if (t <= 8.5e+80) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.12e-70:
		tmp = a
	elif t <= -1.4e-303:
		tmp = z
	elif t <= 7e-296:
		tmp = -b
	elif t <= 8.5e+80:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.12e-70)
		tmp = a;
	elseif (t <= -1.4e-303)
		tmp = z;
	elseif (t <= 7e-296)
		tmp = Float64(-b);
	elseif (t <= 8.5e+80)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.12e-70)
		tmp = a;
	elseif (t <= -1.4e-303)
		tmp = z;
	elseif (t <= 7e-296)
		tmp = -b;
	elseif (t <= 8.5e+80)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.12e-70], a, If[LessEqual[t, -1.4e-303], z, If[LessEqual[t, 7e-296], (-b), If[LessEqual[t, 8.5e+80], z, a]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12e-70 or 8.50000000000000007e80 < t

   1. Initial program 51.3%

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

   2. Taylor expanded in t around inf 50.4%

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

   if -1.12e-70 < t < -1.4e-303 or 6.9999999999999998e-296 < t < 8.50000000000000007e80

   1. Initial program 63.5%

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

   2. Taylor expanded in x around inf 52.7%

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

   if -1.4e-303 < t < 6.9999999999999998e-296

   1. Initial program 67.3%

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

   2. Taylor expanded in b around inf 54.6%

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

      1. associate-*r/ 54.6%

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

      2. neg-mul-1 54.6%

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

      3. distribute-rgt-neg-in 54.6%

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

      4. associate-+r+ 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in y around inf 69.9%

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

      1. mul-1-neg 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-70}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-303}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-296}:\\ \;\;\;\;-b\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12: 58.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+175}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t 5.2e+175) (- (+ z a) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.2e+175) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 5.2d+175) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.2e+175) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 5.2e+175:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 5.2e+175)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 5.2e+175)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 5.2e+175], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < 5.2000000000000001e175

   1. Initial program 60.2%

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

   2. Taylor expanded in y around inf 57.7%

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

   if 5.2000000000000001e175 < t

   1. Initial program 40.9%

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

   2. Taylor expanded in t around inf 64.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+175}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 44.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-70}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.12e-70) a (if (<= t 5.8e+80) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.12e-70) {
		tmp = a;
	} else if (t <= 5.8e+80) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.12d-70)) then
        tmp = a
    else if (t <= 5.8d+80) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.12e-70) {
		tmp = a;
	} else if (t <= 5.8e+80) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.12e-70:
		tmp = a
	elif t <= 5.8e+80:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.12e-70)
		tmp = a;
	elseif (t <= 5.8e+80)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.12e-70)
		tmp = a;
	elseif (t <= 5.8e+80)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.12e-70], a, If[LessEqual[t, 5.8e+80], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e-70 or 5.79999999999999971e80 < t

   1. Initial program 51.3%

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

   2. Taylor expanded in t around inf 50.4%

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

   if -1.12e-70 < t < 5.79999999999999971e80

   1. Initial program 63.7%

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

   2. Taylor expanded in x around inf 50.6%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-70}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 33.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.0%

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

2. Taylor expanded in t around inf 30.9%

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

3. Final simplification 30.9%

   \[\leadsto a \]

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 2023274 
(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)))