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

Percentage Accurate: 60.5% → 86.8%

Time: 24.6s

Alternatives: 17

Speedup: 0.5×

• could not determine a ground truth

  1. x = 30500968.713011652
  2. y = -4.556703472759178e+229
  3. z = 4.851089828593916e+256
  4. t = -9.023261469701812e-53
  5. a = 1.5818085780109264e+255
  6. b = -6.294182690210135e+69

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{t_1}\\ t_3 := \left(y + t\right) \cdot a\\ t_4 := \frac{\left(t_3 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq 10^{+253}\right):\\ \;\;\;\;z + a \cdot \left(t_2 + \frac{t}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t_2 + \frac{x}{t_1}\right) + \frac{t_3 - y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ y t_1))
        (t_3 (* (+ y t) a))
        (t_4 (/ (- (+ t_3 (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 1e+253)))
     (+ z (* a (+ t_2 (/ t t_1))))
     (+ (* z (+ t_2 (/ x t_1))) (/ (- t_3 (* y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 1e+253)) {
		tmp = z + (a * (t_2 + (t / t_1)));
	} else {
		tmp = (z * (t_2 + (x / t_1))) + ((t_3 - (y * b)) / t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 1e+253)) {
		tmp = z + (a * (t_2 + (t / t_1)));
	} else {
		tmp = (z * (t_2 + (x / t_1))) + ((t_3 - (y * b)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = y / t_1
	t_3 = (y + t) * a
	t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 1e+253):
		tmp = z + (a * (t_2 + (t / t_1)))
	else:
		tmp = (z * (t_2 + (x / t_1))) + ((t_3 - (y * b)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(y + t) * a)
	t_4 = Float64(Float64(Float64(t_3 + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 1e+253))
		tmp = Float64(z + Float64(a * Float64(t_2 + Float64(t / t_1))));
	else
		tmp = Float64(Float64(z * Float64(t_2 + Float64(x / t_1))) + Float64(Float64(t_3 - Float64(y * b)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = y / t_1;
	t_3 = (y + t) * a;
	t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 1e+253)))
		tmp = z + (a * (t_2 + (t / t_1)));
	else
		tmp = (z * (t_2 + (x / t_1))) + ((t_3 - (y * b)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 1e+253]], $MachinePrecision]], N[(z + N[(a * N[(t$95$2 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(t$95$2 + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.6%

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

   3. Taylor expanded in a around 0 39.9%

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

      1. associate--l+ 39.9%

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

      2. +-commutative 39.9%

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

      3. associate-+r+ 39.9%

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

      4. associate-+r+ 39.9%

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

      5. div-sub 39.9%

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

      6. +-commutative 39.9%

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

      7. *-commutative 39.9%

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

      8. associate-+r+ 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in x around inf 74.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e252

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 99.1%

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

      1. associate--l+ 99.1%

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

      2. associate-+r+ 99.1%

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

      3. associate-+r+ 99.1%

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

      4. div-sub 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-+r+ 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{x}{y + \left(x + t\right)}\right) + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(\left(y + t\right) \cdot a + t_1\right) - y \cdot b}{t_2}\\ t_4 := a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right)\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+253}\right):\\ \;\;\;\;z + t_4\\ \mathbf{else}:\\ \;\;\;\;t_4 + \frac{t_1 - y \cdot b}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* (+ y t) a) t_1) (* y b)) t_2))
        (t_4 (* a (+ (/ y t_2) (/ t t_2)))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 1e+253)))
     (+ z t_4)
     (+ t_4 (/ (- t_1 (* y b)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = y + (x + t);
	double t_3 = ((((y + t) * a) + t_1) - (y * b)) / t_2;
	double t_4 = a * ((y / t_2) + (t / t_2));
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 1e+253)) {
		tmp = z + t_4;
	} else {
		tmp = t_4 + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = y + (x + t);
	double t_3 = ((((y + t) * a) + t_1) - (y * b)) / t_2;
	double t_4 = a * ((y / t_2) + (t / t_2));
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 1e+253)) {
		tmp = z + t_4;
	} else {
		tmp = t_4 + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x + y)
	t_2 = y + (x + t)
	t_3 = ((((y + t) * a) + t_1) - (y * b)) / t_2
	t_4 = a * ((y / t_2) + (t / t_2))
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 1e+253):
		tmp = z + t_4
	else:
		tmp = t_4 + ((t_1 - (y * b)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2)))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 1e+253))
		tmp = Float64(z + t_4);
	else
		tmp = Float64(t_4 + Float64(Float64(t_1 - Float64(y * b)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x + y);
	t_2 = y + (x + t);
	t_3 = ((((y + t) * a) + t_1) - (y * b)) / t_2;
	t_4 = a * ((y / t_2) + (t / t_2));
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 1e+253)))
		tmp = z + t_4;
	else
		tmp = t_4 + ((t_1 - (y * b)) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * 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] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 1e+253]], $MachinePrecision]], N[(z + t$95$4), $MachinePrecision], N[(t$95$4 + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.6%

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

   3. Taylor expanded in a around 0 39.9%

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

      1. associate--l+ 39.9%

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

      2. +-commutative 39.9%

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

      3. associate-+r+ 39.9%

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

      4. associate-+r+ 39.9%

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

      5. div-sub 39.9%

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

      6. +-commutative 39.9%

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

      7. *-commutative 39.9%

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

      8. associate-+r+ 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in x around inf 74.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e252

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 99.1%

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

      1. associate--l+ 99.1%

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

      2. +-commutative 99.1%

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

      3. associate-+r+ 99.1%

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

      4. associate-+r+ 99.1%

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

      5. div-sub 99.1%

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

      6. +-commutative 99.1%

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

      7. *-commutative 99.1%

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

      8. associate-+r+ 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right) + \frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+253}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+253)))
     (+ z (* a (+ (/ y t_1) (/ t 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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+253)) {
		tmp = z + (a * ((y / t_1) + (t / 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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+253)) {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+253):
		tmp = z + (a * ((y / t_1) + (t / 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(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+253))
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / 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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+253)))
		tmp = z + (a * ((y / t_1) + (t / 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[(N[(y + t), $MachinePrecision] * a), $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, 1e+253]], $MachinePrecision]], N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / 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 9.9999999999999994e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.6%

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

   3. Taylor expanded in a around 0 39.9%

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

      1. associate--l+ 39.9%

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

      2. +-commutative 39.9%

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

      3. associate-+r+ 39.9%

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

      4. associate-+r+ 39.9%

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

      5. div-sub 39.9%

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

      6. +-commutative 39.9%

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

      7. *-commutative 39.9%

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

      8. associate-+r+ 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in x around inf 74.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e252

   1. Initial program 99.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+253}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + \left(a - b\right)\\ t_3 := \frac{\left(y + t\right) \cdot a - y \cdot b}{t_1}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -900000:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ z (- a b)))
        (t_3 (/ (- (* (+ y t) a) (* y b)) t_1)))
   (if (<= y -2.5e+59)
     t_2
     (if (<= y -900000.0)
       (/ z (/ t_1 (+ x y)))
       (if (<= y -2.8e-48)
         (/ a (/ (+ x t) t))
         (if (<= y -4.8e-123)
           (+ z (/ y (/ x (- a b))))
           (if (<= y 5.2e-227)
             (/ a (/ t_1 (+ y t)))
             (if (<= y 3.6e-83)
               t_3
               (if (<= y 2e-71)
                 (* (+ x y) (/ z (+ t (+ x y))))
                 (if (<= y 2.8e-29) 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 = (((y + t) * a) - (y * b)) / t_1;
	double tmp;
	if (y <= -2.5e+59) {
		tmp = t_2;
	} else if (y <= -900000.0) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= -2.8e-48) {
		tmp = a / ((x + t) / t);
	} else if (y <= -4.8e-123) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= 5.2e-227) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 3.6e-83) {
		tmp = t_3;
	} else if (y <= 2e-71) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 2.8e-29) {
		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 = (((y + t) * a) - (y * b)) / t_1
    if (y <= (-2.5d+59)) then
        tmp = t_2
    else if (y <= (-900000.0d0)) then
        tmp = z / (t_1 / (x + y))
    else if (y <= (-2.8d-48)) then
        tmp = a / ((x + t) / t)
    else if (y <= (-4.8d-123)) then
        tmp = z + (y / (x / (a - b)))
    else if (y <= 5.2d-227) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 3.6d-83) then
        tmp = t_3
    else if (y <= 2d-71) then
        tmp = (x + y) * (z / (t + (x + y)))
    else if (y <= 2.8d-29) 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 = (((y + t) * a) - (y * b)) / t_1;
	double tmp;
	if (y <= -2.5e+59) {
		tmp = t_2;
	} else if (y <= -900000.0) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= -2.8e-48) {
		tmp = a / ((x + t) / t);
	} else if (y <= -4.8e-123) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= 5.2e-227) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 3.6e-83) {
		tmp = t_3;
	} else if (y <= 2e-71) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 2.8e-29) {
		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 = (((y + t) * a) - (y * b)) / t_1
	tmp = 0
	if y <= -2.5e+59:
		tmp = t_2
	elif y <= -900000.0:
		tmp = z / (t_1 / (x + y))
	elif y <= -2.8e-48:
		tmp = a / ((x + t) / t)
	elif y <= -4.8e-123:
		tmp = z + (y / (x / (a - b)))
	elif y <= 5.2e-227:
		tmp = a / (t_1 / (y + t))
	elif y <= 3.6e-83:
		tmp = t_3
	elif y <= 2e-71:
		tmp = (x + y) * (z / (t + (x + y)))
	elif y <= 2.8e-29:
		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(z + Float64(a - b))
	t_3 = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (y <= -2.5e+59)
		tmp = t_2;
	elseif (y <= -900000.0)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif (y <= -2.8e-48)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (y <= -4.8e-123)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif (y <= 5.2e-227)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 3.6e-83)
		tmp = t_3;
	elseif (y <= 2e-71)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(t + Float64(x + y))));
	elseif (y <= 2.8e-29)
		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 = (((y + t) * a) - (y * b)) / t_1;
	tmp = 0.0;
	if (y <= -2.5e+59)
		tmp = t_2;
	elseif (y <= -900000.0)
		tmp = z / (t_1 / (x + y));
	elseif (y <= -2.8e-48)
		tmp = a / ((x + t) / t);
	elseif (y <= -4.8e-123)
		tmp = z + (y / (x / (a - b)));
	elseif (y <= 5.2e-227)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 3.6e-83)
		tmp = t_3;
	elseif (y <= 2e-71)
		tmp = (x + y) * (z / (t + (x + y)));
	elseif (y <= 2.8e-29)
		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[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[y, -2.5e+59], t$95$2, If[LessEqual[y, -900000.0], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-48], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-123], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-227], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-83], t$95$3, If[LessEqual[y, 2e-71], N[(N[(x + y), $MachinePrecision] * N[(z / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-29], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.4999999999999999e59 or 2.8000000000000002e-29 < y

   1. Initial program 43.3%

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

   3. Taylor expanded in y around inf 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. neg-mul-1 74.8%

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

      2. associate-+r+ 74.8%

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

      3. +-commutative 74.8%

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

      4. associate-+l+ 74.8%

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

      5. sub-neg 74.8%

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

   6. Simplified 74.8%

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

   if -2.4999999999999999e59 < y < -9e5

   1. Initial program 60.4%

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

   3. Taylor expanded in z around inf 36.1%

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

      1. associate-/l* 67.4%

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

      2. associate-+r+ 67.4%

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

      3. +-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -9e5 < y < -2.80000000000000005e-48

   1. Initial program 73.8%

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

   3. Taylor expanded in t around inf 33.4%

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

      1. div-inv 33.1%

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

      2. +-commutative 33.1%

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

      3. associate-+l+ 33.1%

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

      4. +-commutative 33.1%

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

   5. Applied egg-rr 33.1%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-/l* 59.5%

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

   8. Simplified 59.5%

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

   if -2.80000000000000005e-48 < y < -4.8e-123

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0 82.5%

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

      1. sub-neg 82.5%

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

      2. mul-1-neg 82.5%

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

      3. +-commutative 82.5%

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

      4. associate-+r+ 82.5%

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

      5. +-commutative 82.5%

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

      6. associate-*r* 82.5%

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

      7. distribute-rgt-in 82.5%

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

      8. mul-1-neg 82.5%

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

      9. +-commutative 82.5%

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

      10. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 82.8%

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

      1. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -4.8e-123 < y < 5.20000000000000023e-227

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf 44.7%

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

      1. associate-/l* 63.6%

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

      2. associate-+r+ 63.6%

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

   5. Simplified 63.6%

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

   if 5.20000000000000023e-227 < y < 3.60000000000000012e-83 or 1.9999999999999998e-71 < y < 2.8000000000000002e-29

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if 3.60000000000000012e-83 < y < 1.9999999999999998e-71

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. +-commutative 91.9%

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

      3. *-commutative 91.9%

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

      4. associate-*r/ 92.5%

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

   8. Simplified 92.5%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \frac{z}{t + \left(y + x\right)}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+59}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq -900000:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + \left(a - b\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -27000000:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-121}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-69}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ z (- a b))))
   (if (<= y -1.25e+59)
     t_2
     (if (<= y -27000000.0)
       (/ z (/ t_1 (+ x y)))
       (if (<= y -4.2e-42)
         (/ a (/ (+ x t) t))
         (if (<= y -2.4e-121)
           (+ z (/ y (/ x (- a b))))
           (if (<= y 5.3e-83)
             (/ a (/ t_1 (+ y t)))
             (if (<= y 1.75e-69)
               (* (+ x y) (/ z (+ t (+ x y))))
               (if (<= y 1.05e-63) (/ y (/ (+ x y) (- a b))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z + (a - b);
	double tmp;
	if (y <= -1.25e+59) {
		tmp = t_2;
	} else if (y <= -27000000.0) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= -4.2e-42) {
		tmp = a / ((x + t) / t);
	} else if (y <= -2.4e-121) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= 5.3e-83) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.75e-69) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 1.05e-63) {
		tmp = y / ((x + y) / (a - b));
	} 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 <= (-1.25d+59)) then
        tmp = t_2
    else if (y <= (-27000000.0d0)) then
        tmp = z / (t_1 / (x + y))
    else if (y <= (-4.2d-42)) then
        tmp = a / ((x + t) / t)
    else if (y <= (-2.4d-121)) then
        tmp = z + (y / (x / (a - b)))
    else if (y <= 5.3d-83) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 1.75d-69) then
        tmp = (x + y) * (z / (t + (x + y)))
    else if (y <= 1.05d-63) then
        tmp = y / ((x + y) / (a - b))
    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 <= -1.25e+59) {
		tmp = t_2;
	} else if (y <= -27000000.0) {
		tmp = z / (t_1 / (x + y));
	} else if (y <= -4.2e-42) {
		tmp = a / ((x + t) / t);
	} else if (y <= -2.4e-121) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= 5.3e-83) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.75e-69) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 1.05e-63) {
		tmp = y / ((x + y) / (a - b));
	} 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 <= -1.25e+59:
		tmp = t_2
	elif y <= -27000000.0:
		tmp = z / (t_1 / (x + y))
	elif y <= -4.2e-42:
		tmp = a / ((x + t) / t)
	elif y <= -2.4e-121:
		tmp = z + (y / (x / (a - b)))
	elif y <= 5.3e-83:
		tmp = a / (t_1 / (y + t))
	elif y <= 1.75e-69:
		tmp = (x + y) * (z / (t + (x + y)))
	elif y <= 1.05e-63:
		tmp = y / ((x + y) / (a - b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z + Float64(a - b))
	tmp = 0.0
	if (y <= -1.25e+59)
		tmp = t_2;
	elseif (y <= -27000000.0)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	elseif (y <= -4.2e-42)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (y <= -2.4e-121)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif (y <= 5.3e-83)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 1.75e-69)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(t + Float64(x + y))));
	elseif (y <= 1.05e-63)
		tmp = Float64(y / Float64(Float64(x + y) / Float64(a - b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z + (a - b);
	tmp = 0.0;
	if (y <= -1.25e+59)
		tmp = t_2;
	elseif (y <= -27000000.0)
		tmp = z / (t_1 / (x + y));
	elseif (y <= -4.2e-42)
		tmp = a / ((x + t) / t);
	elseif (y <= -2.4e-121)
		tmp = z + (y / (x / (a - b)));
	elseif (y <= 5.3e-83)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 1.75e-69)
		tmp = (x + y) * (z / (t + (x + y)));
	elseif (y <= 1.05e-63)
		tmp = y / ((x + y) / (a - b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+59], t$95$2, If[LessEqual[y, -27000000.0], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-42], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-121], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-83], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-69], N[(N[(x + y), $MachinePrecision] * N[(z / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-63], N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.2499999999999999e59 or 1.05e-63 < y

   1. Initial program 44.6%

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

   3. Taylor expanded in y around inf 73.5%

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

   4. Taylor expanded in b around 0 73.5%

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

      1. neg-mul-1 73.5%

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

      2. associate-+r+ 73.5%

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

      3. +-commutative 73.5%

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

      4. associate-+l+ 73.6%

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

      5. sub-neg 73.6%

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

   6. Simplified 73.6%

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

   if -1.2499999999999999e59 < y < -2.7e7

   1. Initial program 60.4%

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

   3. Taylor expanded in z around inf 36.1%

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

      1. associate-/l* 67.4%

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

      2. associate-+r+ 67.4%

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

      3. +-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -2.7e7 < y < -4.20000000000000013e-42

   1. Initial program 73.8%

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

   3. Taylor expanded in t around inf 33.4%

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

      1. div-inv 33.1%

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

      2. +-commutative 33.1%

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

      3. associate-+l+ 33.1%

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

      4. +-commutative 33.1%

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

   5. Applied egg-rr 33.1%

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

   6. Taylor expanded in y around 0 33.5%

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

      1. associate-/l* 59.5%

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

   8. Simplified 59.5%

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

   if -4.20000000000000013e-42 < y < -2.40000000000000003e-121

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0 82.5%

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

      1. sub-neg 82.5%

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

      2. mul-1-neg 82.5%

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

      3. +-commutative 82.5%

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

      4. associate-+r+ 82.5%

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

      5. +-commutative 82.5%

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

      6. associate-*r* 82.5%

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

      7. distribute-rgt-in 82.5%

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

      8. mul-1-neg 82.5%

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

      9. +-commutative 82.5%

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

      10. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 82.8%

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

      1. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -2.40000000000000003e-121 < y < 5.3e-83

   1. Initial program 82.3%

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

   3. Taylor expanded in a around inf 46.7%

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

      1. associate-/l* 60.7%

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

      2. associate-+r+ 60.7%

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

   5. Simplified 60.7%

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

   if 5.3e-83 < y < 1.7500000000000001e-69

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. +-commutative 91.9%

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

      3. *-commutative 91.9%

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

      4. associate-*r/ 92.5%

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

   8. Simplified 92.5%

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

   if 1.7500000000000001e-69 < y < 1.05e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. +-commutative 68.3%

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

      4. associate-+r+ 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-*r* 68.3%

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

      7. distribute-rgt-in 68.3%

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

      8. mul-1-neg 68.3%

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

      9. +-commutative 68.3%

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

      10. +-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around 0 68.3%

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

      1. associate-/l* 68.3%

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

      2. +-commutative 68.3%

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

   8. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{y + x}{a - b}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq -27000000:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-121}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-69}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(a - b\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-112}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-70}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (- a b))))
   (if (<= y -7.6e+21)
     t_1
     (if (<= y -1.45e-112)
       (+ z (/ y (/ x (- a b))))
       (if (<= y -2.4e-145)
         t_1
         (if (<= y 8.5e-84)
           (/ a (/ (+ x t) t))
           (if (<= y 1.15e-70)
             (* (+ x y) (/ z (+ t (+ x y))))
             (if (<= y 1e-63) (/ y (/ (+ x y) (- a b))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a - b);
	double tmp;
	if (y <= -7.6e+21) {
		tmp = t_1;
	} else if (y <= -1.45e-112) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= -2.4e-145) {
		tmp = t_1;
	} else if (y <= 8.5e-84) {
		tmp = a / ((x + t) / t);
	} else if (y <= 1.15e-70) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 1e-63) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a - b)
    if (y <= (-7.6d+21)) then
        tmp = t_1
    else if (y <= (-1.45d-112)) then
        tmp = z + (y / (x / (a - b)))
    else if (y <= (-2.4d-145)) then
        tmp = t_1
    else if (y <= 8.5d-84) then
        tmp = a / ((x + t) / t)
    else if (y <= 1.15d-70) then
        tmp = (x + y) * (z / (t + (x + y)))
    else if (y <= 1d-63) then
        tmp = y / ((x + y) / (a - b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a - b);
	double tmp;
	if (y <= -7.6e+21) {
		tmp = t_1;
	} else if (y <= -1.45e-112) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= -2.4e-145) {
		tmp = t_1;
	} else if (y <= 8.5e-84) {
		tmp = a / ((x + t) / t);
	} else if (y <= 1.15e-70) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 1e-63) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a - b)
	tmp = 0
	if y <= -7.6e+21:
		tmp = t_1
	elif y <= -1.45e-112:
		tmp = z + (y / (x / (a - b)))
	elif y <= -2.4e-145:
		tmp = t_1
	elif y <= 8.5e-84:
		tmp = a / ((x + t) / t)
	elif y <= 1.15e-70:
		tmp = (x + y) * (z / (t + (x + y)))
	elif y <= 1e-63:
		tmp = y / ((x + y) / (a - b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a - b))
	tmp = 0.0
	if (y <= -7.6e+21)
		tmp = t_1;
	elseif (y <= -1.45e-112)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif (y <= -2.4e-145)
		tmp = t_1;
	elseif (y <= 8.5e-84)
		tmp = Float64(a / Float64(Float64(x + t) / t));
	elseif (y <= 1.15e-70)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(t + Float64(x + y))));
	elseif (y <= 1e-63)
		tmp = Float64(y / Float64(Float64(x + y) / Float64(a - b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a - b);
	tmp = 0.0;
	if (y <= -7.6e+21)
		tmp = t_1;
	elseif (y <= -1.45e-112)
		tmp = z + (y / (x / (a - b)));
	elseif (y <= -2.4e-145)
		tmp = t_1;
	elseif (y <= 8.5e-84)
		tmp = a / ((x + t) / t);
	elseif (y <= 1.15e-70)
		tmp = (x + y) * (z / (t + (x + y)));
	elseif (y <= 1e-63)
		tmp = y / ((x + y) / (a - b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+21], t$95$1, If[LessEqual[y, -1.45e-112], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-145], t$95$1, If[LessEqual[y, 8.5e-84], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-70], N[(N[(x + y), $MachinePrecision] * N[(z / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-63], N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.6e21 or -1.44999999999999996e-112 < y < -2.40000000000000015e-145 or 1.00000000000000007e-63 < y

   1. Initial program 47.7%

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

   3. Taylor expanded in y around inf 70.8%

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

   4. Taylor expanded in b around 0 70.8%

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

      1. neg-mul-1 70.8%

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

      2. associate-+r+ 70.8%

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

      3. +-commutative 70.8%

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

      4. associate-+l+ 70.8%

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

      5. sub-neg 70.8%

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

   6. Simplified 70.8%

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

   if -7.6e21 < y < -1.44999999999999996e-112

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0 67.6%

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

      1. sub-neg 67.6%

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

      2. mul-1-neg 67.6%

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

      3. +-commutative 67.6%

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

      4. associate-+r+ 67.6%

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

      5. +-commutative 67.6%

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

      6. associate-*r* 67.6%

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

      7. distribute-rgt-in 67.6%

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

      8. mul-1-neg 67.6%

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

      9. +-commutative 67.6%

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

      10. +-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around inf 60.9%

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

      1. associate-/l* 60.9%

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

   8. Simplified 60.9%

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

   if -2.40000000000000015e-145 < y < 8.4999999999999994e-84

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 46.0%

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

      1. div-inv 45.9%

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

      2. +-commutative 45.9%

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

      3. associate-+l+ 45.9%

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

      4. +-commutative 45.9%

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

   5. Applied egg-rr 45.9%

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

   6. Taylor expanded in y around 0 45.9%

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

      1. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if 8.4999999999999994e-84 < y < 1.15e-70

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. +-commutative 91.9%

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

      3. *-commutative 91.9%

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

      4. associate-*r/ 92.5%

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

   8. Simplified 92.5%

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

   if 1.15e-70 < y < 1.00000000000000007e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. +-commutative 68.3%

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

      4. associate-+r+ 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-*r* 68.3%

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

      7. distribute-rgt-in 68.3%

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

      8. mul-1-neg 68.3%

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

      9. +-commutative 68.3%

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

      10. +-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around 0 68.3%

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

      1. associate-/l* 68.3%

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

      2. +-commutative 68.3%

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

   8. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{y + x}{a - b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+21}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-112}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-70}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(a - b\right)\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-116}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \frac{t}{t_2}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t_2}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (- a b))) (t_2 (+ t (+ x y))))
   (if (<= y -9e+23)
     t_1
     (if (<= y -1.95e-116)
       (+ z (/ y (/ x (- a b))))
       (if (<= y -2.4e-145)
         t_1
         (if (<= y 3.5e-83)
           (* a (/ t t_2))
           (if (<= y 1.1e-69)
             (* (+ x y) (/ z t_2))
             (if (<= y 1e-63) (/ y (/ (+ x y) (- a b))) t_1))))))))

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 tmp;
	if (y <= -9e+23) {
		tmp = t_1;
	} else if (y <= -1.95e-116) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= -2.4e-145) {
		tmp = t_1;
	} else if (y <= 3.5e-83) {
		tmp = a * (t / t_2);
	} else if (y <= 1.1e-69) {
		tmp = (x + y) * (z / t_2);
	} else if (y <= 1e-63) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (a - b)
    t_2 = t + (x + y)
    if (y <= (-9d+23)) then
        tmp = t_1
    else if (y <= (-1.95d-116)) then
        tmp = z + (y / (x / (a - b)))
    else if (y <= (-2.4d-145)) then
        tmp = t_1
    else if (y <= 3.5d-83) then
        tmp = a * (t / t_2)
    else if (y <= 1.1d-69) then
        tmp = (x + y) * (z / t_2)
    else if (y <= 1d-63) then
        tmp = y / ((x + y) / (a - b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a - b);
	double t_2 = t + (x + y);
	double tmp;
	if (y <= -9e+23) {
		tmp = t_1;
	} else if (y <= -1.95e-116) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= -2.4e-145) {
		tmp = t_1;
	} else if (y <= 3.5e-83) {
		tmp = a * (t / t_2);
	} else if (y <= 1.1e-69) {
		tmp = (x + y) * (z / t_2);
	} else if (y <= 1e-63) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a - b)
	t_2 = t + (x + y)
	tmp = 0
	if y <= -9e+23:
		tmp = t_1
	elif y <= -1.95e-116:
		tmp = z + (y / (x / (a - b)))
	elif y <= -2.4e-145:
		tmp = t_1
	elif y <= 3.5e-83:
		tmp = a * (t / t_2)
	elif y <= 1.1e-69:
		tmp = (x + y) * (z / t_2)
	elif y <= 1e-63:
		tmp = y / ((x + y) / (a - b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a - b))
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (y <= -9e+23)
		tmp = t_1;
	elseif (y <= -1.95e-116)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif (y <= -2.4e-145)
		tmp = t_1;
	elseif (y <= 3.5e-83)
		tmp = Float64(a * Float64(t / t_2));
	elseif (y <= 1.1e-69)
		tmp = Float64(Float64(x + y) * Float64(z / t_2));
	elseif (y <= 1e-63)
		tmp = Float64(y / Float64(Float64(x + y) / Float64(a - b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a - b);
	t_2 = t + (x + y);
	tmp = 0.0;
	if (y <= -9e+23)
		tmp = t_1;
	elseif (y <= -1.95e-116)
		tmp = z + (y / (x / (a - b)));
	elseif (y <= -2.4e-145)
		tmp = t_1;
	elseif (y <= 3.5e-83)
		tmp = a * (t / t_2);
	elseif (y <= 1.1e-69)
		tmp = (x + y) * (z / t_2);
	elseif (y <= 1e-63)
		tmp = y / ((x + y) / (a - b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+23], t$95$1, If[LessEqual[y, -1.95e-116], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-145], t$95$1, If[LessEqual[y, 3.5e-83], N[(a * N[(t / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-69], N[(N[(x + y), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-63], N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.99999999999999958e23 or -1.95e-116 < y < -2.40000000000000015e-145 or 1.00000000000000007e-63 < y

   1. Initial program 47.7%

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

   3. Taylor expanded in y around inf 70.8%

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

   4. Taylor expanded in b around 0 70.8%

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

      1. neg-mul-1 70.8%

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

      2. associate-+r+ 70.8%

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

      3. +-commutative 70.8%

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

      4. associate-+l+ 70.8%

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

      5. sub-neg 70.8%

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

   6. Simplified 70.8%

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

   if -8.99999999999999958e23 < y < -1.95e-116

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0 67.6%

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

      1. sub-neg 67.6%

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

      2. mul-1-neg 67.6%

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

      3. +-commutative 67.6%

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

      4. associate-+r+ 67.6%

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

      5. +-commutative 67.6%

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

      6. associate-*r* 67.6%

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

      7. distribute-rgt-in 67.6%

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

      8. mul-1-neg 67.6%

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

      9. +-commutative 67.6%

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

      10. +-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around inf 60.9%

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

      1. associate-/l* 60.9%

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

   8. Simplified 60.9%

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

   if -2.40000000000000015e-145 < y < 3.5000000000000003e-83

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 46.0%

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

      1. +-commutative 46.0%

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

      2. *-un-lft-identity 46.0%

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

      3. times-frac 60.3%

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

      4. associate-+l+ 60.3%

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

      5. +-commutative 60.3%

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

   5. Applied egg-rr 60.3%

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

   if 3.5000000000000003e-83 < y < 1.1e-69

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. +-commutative 91.9%

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

      3. *-commutative 91.9%

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

      4. associate-*r/ 92.5%

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

   8. Simplified 92.5%

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

   if 1.1e-69 < y < 1.00000000000000007e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. +-commutative 68.3%

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

      4. associate-+r+ 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-*r* 68.3%

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

      7. distribute-rgt-in 68.3%

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

      8. mul-1-neg 68.3%

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

      9. +-commutative 68.3%

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

      10. +-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around 0 68.3%

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

      1. associate-/l* 68.3%

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

      2. +-commutative 68.3%

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

   8. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{y + x}{a - b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+23}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-116}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \frac{t}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{-7} \lor \neg \left(a \leq -4.2 \cdot 10^{-40} \lor \neg \left(a \leq -9.5 \cdot 10^{-89}\right) \land a \leq 1.25 \cdot 10^{-138}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= a -3e-7)
           (not
            (or (<= a -4.2e-40) (and (not (<= a -9.5e-89)) (<= a 1.25e-138)))))
     (+ z (* a (+ (/ y t_1) (/ t t_1))))
     (/ (- (* z (+ x y)) (* y b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((a <= -3e-7) || !((a <= -4.2e-40) || (!(a <= -9.5e-89) && (a <= 1.25e-138)))) {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	} else {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((a <= (-3d-7)) .or. (.not. (a <= (-4.2d-40)) .or. (.not. (a <= (-9.5d-89))) .and. (a <= 1.25d-138))) then
        tmp = z + (a * ((y / t_1) + (t / t_1)))
    else
        tmp = ((z * (x + y)) - (y * b)) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((a <= -3e-7) || !((a <= -4.2e-40) || (!(a <= -9.5e-89) && (a <= 1.25e-138)))) {
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	} else {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (a <= -3e-7) or not ((a <= -4.2e-40) or (not (a <= -9.5e-89) and (a <= 1.25e-138))):
		tmp = z + (a * ((y / t_1) + (t / t_1)))
	else:
		tmp = ((z * (x + y)) - (y * b)) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((a <= -3e-7) || !((a <= -4.2e-40) || (!(a <= -9.5e-89) && (a <= 1.25e-138))))
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))));
	else
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((a <= -3e-7) || ~(((a <= -4.2e-40) || (~((a <= -9.5e-89)) && (a <= 1.25e-138)))))
		tmp = z + (a * ((y / t_1) + (t / t_1)));
	else
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -3e-7], N[Not[Or[LessEqual[a, -4.2e-40], And[N[Not[LessEqual[a, -9.5e-89]], $MachinePrecision], LessEqual[a, 1.25e-138]]]], $MachinePrecision]], N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9999999999999999e-7 or -4.20000000000000036e-40 < a < -9.50000000000000028e-89 or 1.24999999999999997e-138 < a

   1. Initial program 53.9%

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

   3. Taylor expanded in a around 0 73.3%

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

      1. associate--l+ 73.3%

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

      2. +-commutative 73.3%

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

      3. associate-+r+ 73.3%

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

      4. associate-+r+ 73.3%

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

      5. div-sub 73.3%

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

      6. +-commutative 73.3%

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

      7. *-commutative 73.3%

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

      8. associate-+r+ 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in x around inf 77.1%

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

   if -2.9999999999999999e-7 < a < -4.20000000000000036e-40 or -9.50000000000000028e-89 < a < 1.24999999999999997e-138

   1. Initial program 80.8%

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

   3. Taylor expanded in a around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. *-commutative 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-7} \lor \neg \left(a \leq -4.2 \cdot 10^{-40} \lor \neg \left(a \leq -9.5 \cdot 10^{-89}\right) \land a \leq 1.25 \cdot 10^{-138}\right):\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(a - b\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-122}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-71}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (- a b))))
   (if (<= y -2e+22)
     t_1
     (if (<= y -1.95e-122)
       (+ z (/ y (/ x (- a b))))
       (if (<= y 5.3e-83)
         (/ a (/ (+ y (+ x t)) (+ y t)))
         (if (<= y 4.6e-71)
           (* (+ x y) (/ z (+ t (+ x y))))
           (if (<= y 1e-63) (/ y (/ (+ x y) (- a b))) 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 <= -2e+22) {
		tmp = t_1;
	} else if (y <= -1.95e-122) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= 5.3e-83) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else if (y <= 4.6e-71) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 1e-63) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a - b)
    if (y <= (-2d+22)) then
        tmp = t_1
    else if (y <= (-1.95d-122)) then
        tmp = z + (y / (x / (a - b)))
    else if (y <= 5.3d-83) then
        tmp = a / ((y + (x + t)) / (y + t))
    else if (y <= 4.6d-71) then
        tmp = (x + y) * (z / (t + (x + y)))
    else if (y <= 1d-63) then
        tmp = y / ((x + y) / (a - b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a - b);
	double tmp;
	if (y <= -2e+22) {
		tmp = t_1;
	} else if (y <= -1.95e-122) {
		tmp = z + (y / (x / (a - b)));
	} else if (y <= 5.3e-83) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else if (y <= 4.6e-71) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (y <= 1e-63) {
		tmp = y / ((x + y) / (a - b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a - b)
	tmp = 0
	if y <= -2e+22:
		tmp = t_1
	elif y <= -1.95e-122:
		tmp = z + (y / (x / (a - b)))
	elif y <= 5.3e-83:
		tmp = a / ((y + (x + t)) / (y + t))
	elif y <= 4.6e-71:
		tmp = (x + y) * (z / (t + (x + y)))
	elif y <= 1e-63:
		tmp = y / ((x + y) / (a - b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a - b))
	tmp = 0.0
	if (y <= -2e+22)
		tmp = t_1;
	elseif (y <= -1.95e-122)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif (y <= 5.3e-83)
		tmp = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t)));
	elseif (y <= 4.6e-71)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(t + Float64(x + y))));
	elseif (y <= 1e-63)
		tmp = Float64(y / Float64(Float64(x + y) / Float64(a - b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a - b);
	tmp = 0.0;
	if (y <= -2e+22)
		tmp = t_1;
	elseif (y <= -1.95e-122)
		tmp = z + (y / (x / (a - b)));
	elseif (y <= 5.3e-83)
		tmp = a / ((y + (x + t)) / (y + t));
	elseif (y <= 4.6e-71)
		tmp = (x + y) * (z / (t + (x + y)));
	elseif (y <= 1e-63)
		tmp = y / ((x + y) / (a - b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+22], t$95$1, If[LessEqual[y, -1.95e-122], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-83], N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-71], N[(N[(x + y), $MachinePrecision] * N[(z / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-63], N[(y / N[(N[(x + y), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2e22 or 1.00000000000000007e-63 < y

   1. Initial program 44.7%

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

   3. Taylor expanded in y around inf 72.1%

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

   4. Taylor expanded in b around 0 72.1%

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

      1. neg-mul-1 72.1%

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

      2. associate-+r+ 72.1%

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

      3. +-commutative 72.1%

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

      4. associate-+l+ 72.1%

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

      5. sub-neg 72.1%

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

   6. Simplified 72.1%

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

   if -2e22 < y < -1.94999999999999995e-122

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. mul-1-neg 66.3%

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

      3. +-commutative 66.3%

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

      4. associate-+r+ 66.3%

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

      5. +-commutative 66.3%

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

      6. associate-*r* 66.3%

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

      7. distribute-rgt-in 66.3%

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

      8. mul-1-neg 66.3%

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

      9. +-commutative 66.3%

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

      10. +-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in x around inf 60.2%

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

      1. associate-/l* 60.1%

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

   8. Simplified 60.1%

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

   if -1.94999999999999995e-122 < y < 5.3e-83

   1. Initial program 82.3%

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

   3. Taylor expanded in a around inf 46.7%

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

      1. associate-/l* 60.7%

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

      2. associate-+r+ 60.7%

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

   5. Simplified 60.7%

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

   if 5.3e-83 < y < 4.5999999999999997e-71

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. +-commutative 91.9%

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

      3. *-commutative 91.9%

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

      4. associate-*r/ 92.5%

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

   8. Simplified 92.5%

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

   if 4.5999999999999997e-71 < y < 1.00000000000000007e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. +-commutative 68.3%

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

      4. associate-+r+ 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-*r* 68.3%

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

      7. distribute-rgt-in 68.3%

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

      8. mul-1-neg 68.3%

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

      9. +-commutative 68.3%

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

      10. +-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around 0 68.3%

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

      1. associate-/l* 68.3%

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

      2. +-commutative 68.3%

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

   8. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{y + x}{a - b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+22}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-122}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-71}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;y \leq 10^{-63}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(a - b\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-96}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-145} \lor \neg \left(y \leq 3.7 \cdot 10^{-72}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (- a b))))
   (if (<= y -1e+22)
     t_1
     (if (<= y -5.5e-96)
       (+ z (/ y (/ x (- a b))))
       (if (or (<= y -3e-145) (not (<= y 3.7e-72)))
         t_1
         (/ a (/ (+ x t) t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a - b);
	double tmp;
	if (y <= -1e+22) {
		tmp = t_1;
	} else if (y <= -5.5e-96) {
		tmp = z + (y / (x / (a - b)));
	} else if ((y <= -3e-145) || !(y <= 3.7e-72)) {
		tmp = t_1;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a - b)
    if (y <= (-1d+22)) then
        tmp = t_1
    else if (y <= (-5.5d-96)) then
        tmp = z + (y / (x / (a - b)))
    else if ((y <= (-3d-145)) .or. (.not. (y <= 3.7d-72))) then
        tmp = t_1
    else
        tmp = a / ((x + t) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a - b);
	double tmp;
	if (y <= -1e+22) {
		tmp = t_1;
	} else if (y <= -5.5e-96) {
		tmp = z + (y / (x / (a - b)));
	} else if ((y <= -3e-145) || !(y <= 3.7e-72)) {
		tmp = t_1;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a - b)
	tmp = 0
	if y <= -1e+22:
		tmp = t_1
	elif y <= -5.5e-96:
		tmp = z + (y / (x / (a - b)))
	elif (y <= -3e-145) or not (y <= 3.7e-72):
		tmp = t_1
	else:
		tmp = a / ((x + t) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a - b))
	tmp = 0.0
	if (y <= -1e+22)
		tmp = t_1;
	elseif (y <= -5.5e-96)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif ((y <= -3e-145) || !(y <= 3.7e-72))
		tmp = t_1;
	else
		tmp = Float64(a / Float64(Float64(x + t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a - b);
	tmp = 0.0;
	if (y <= -1e+22)
		tmp = t_1;
	elseif (y <= -5.5e-96)
		tmp = z + (y / (x / (a - b)));
	elseif ((y <= -3e-145) || ~((y <= 3.7e-72)))
		tmp = t_1;
	else
		tmp = a / ((x + t) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+22], t$95$1, If[LessEqual[y, -5.5e-96], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3e-145], N[Not[LessEqual[y, 3.7e-72]], $MachinePrecision]], t$95$1, N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e22 or -5.4999999999999997e-96 < y < -2.99999999999999992e-145 or 3.6999999999999998e-72 < y

   1. Initial program 49.0%

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

   3. Taylor expanded in y around inf 70.3%

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

   4. Taylor expanded in b around 0 70.3%

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

      1. neg-mul-1 70.3%

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

      2. associate-+r+ 70.3%

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

      3. +-commutative 70.3%

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

      4. associate-+l+ 70.3%

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

      5. sub-neg 70.3%

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

   6. Simplified 70.3%

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

   if -1e22 < y < -5.4999999999999997e-96

   1. Initial program 82.0%

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

   3. Taylor expanded in t around 0 67.6%

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

      1. sub-neg 67.6%

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

      2. mul-1-neg 67.6%

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

      3. +-commutative 67.6%

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

      4. associate-+r+ 67.6%

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

      5. +-commutative 67.6%

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

      6. associate-*r* 67.6%

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

      7. distribute-rgt-in 67.6%

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

      8. mul-1-neg 67.6%

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

      9. +-commutative 67.6%

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

      10. +-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around inf 60.9%

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

      1. associate-/l* 60.9%

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

   8. Simplified 60.9%

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

   if -2.99999999999999992e-145 < y < 3.6999999999999998e-72

   1. Initial program 82.6%

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

   3. Taylor expanded in t around inf 43.8%

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

      1. div-inv 43.7%

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

      2. +-commutative 43.7%

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

      3. associate-+l+ 43.7%

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

      4. +-commutative 43.7%

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

   5. Applied egg-rr 43.7%

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

   6. Taylor expanded in y around 0 43.8%

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

      1. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+22}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-96}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-145} \lor \neg \left(y \leq 3.7 \cdot 10^{-72}\right):\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-250}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) (/ a (+ y (+ x t))))))
   (if (<= a -1.7e+33)
     t_1
     (if (<= a -3.6e-250)
       (* (+ x y) (/ z (+ t (+ x y))))
       (if (<= a 9.5e+19) (+ z (- a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * (a / (y + (x + t)));
	double tmp;
	if (a <= -1.7e+33) {
		tmp = t_1;
	} else if (a <= -3.6e-250) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (a <= 9.5e+19) {
		tmp = z + (a - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y + t) * (a / (y + (x + t)))
    if (a <= (-1.7d+33)) then
        tmp = t_1
    else if (a <= (-3.6d-250)) then
        tmp = (x + y) * (z / (t + (x + y)))
    else if (a <= 9.5d+19) then
        tmp = z + (a - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * (a / (y + (x + t)));
	double tmp;
	if (a <= -1.7e+33) {
		tmp = t_1;
	} else if (a <= -3.6e-250) {
		tmp = (x + y) * (z / (t + (x + y)));
	} else if (a <= 9.5e+19) {
		tmp = z + (a - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) * (a / (y + (x + t)))
	tmp = 0
	if a <= -1.7e+33:
		tmp = t_1
	elif a <= -3.6e-250:
		tmp = (x + y) * (z / (t + (x + y)))
	elif a <= 9.5e+19:
		tmp = z + (a - b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * Float64(a / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (a <= -1.7e+33)
		tmp = t_1;
	elseif (a <= -3.6e-250)
		tmp = Float64(Float64(x + y) * Float64(z / Float64(t + Float64(x + y))));
	elseif (a <= 9.5e+19)
		tmp = Float64(z + Float64(a - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) * (a / (y + (x + t)));
	tmp = 0.0;
	if (a <= -1.7e+33)
		tmp = t_1;
	elseif (a <= -3.6e-250)
		tmp = (x + y) * (z / (t + (x + y)));
	elseif (a <= 9.5e+19)
		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[(y + t), $MachinePrecision] * N[(a / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+33], t$95$1, If[LessEqual[a, -3.6e-250], N[(N[(x + y), $MachinePrecision] * N[(z / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+19], N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7e33 or 9.5e19 < a

   1. Initial program 48.2%

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

   3. Taylor expanded in a around inf 37.5%

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

      1. expm1-log1p-u 19.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right)\right)} \]

      2. expm1-udef 15.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)}\right)} - 1} \]

      3. associate-+r+ 15.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{a \cdot \left(t + y\right)}{\color{blue}{\left(t + x\right) + y}}\right)} - 1 \]

      4. associate-/l* 33.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{\left(t + x\right) + y}{t + y}}}\right)} - 1 \]

      5. +-commutative 33.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{a}{\frac{\color{blue}{y + \left(t + x\right)}}{t + y}}\right)} - 1 \]

      6. +-commutative 33.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{a}{\frac{y + \color{blue}{\left(x + t\right)}}{t + y}}\right)} - 1 \]

      7. +-commutative 33.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{a}{\frac{y + \left(x + t\right)}{\color{blue}{y + t}}}\right)} - 1 \]

   5. Applied egg-rr 33.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 36.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\right)\right)} \]

      2. expm1-log1p 72.3%

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

      3. associate-/r/ 70.5%

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

      4. +-commutative 70.5%

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

   7. Simplified 70.5%

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

   if -1.7e33 < a < -3.59999999999999982e-250

   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. Add Preprocessing

   3. Taylor expanded in z around inf 46.5%

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

      1. +-commutative 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in z around 0 46.5%

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

      1. +-commutative 46.5%

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

      2. +-commutative 46.5%

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

      3. *-commutative 46.5%

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

      4. associate-*r/ 57.5%

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

   8. Simplified 57.5%

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

   if -3.59999999999999982e-250 < a < 9.5e19

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf 56.6%

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

   4. Taylor expanded in b around 0 56.6%

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

      1. neg-mul-1 56.6%

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

      2. associate-+r+ 56.6%

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

      3. +-commutative 56.6%

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

      4. associate-+l+ 56.6%

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

      5. sub-neg 56.6%

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

   6. Simplified 56.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-250}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-170}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ a (/ t_1 (+ y t)))))
   (if (<= a -1e+15)
     t_2
     (if (<= a 1.7e-170)
       (/ (- (* z (+ x y)) (* y b)) t_1)
       (if (<= a 1.05e-12) (/ z (/ t_1 (+ x y))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double tmp;
	if (a <= -1e+15) {
		tmp = t_2;
	} else if (a <= 1.7e-170) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (a <= 1.05e-12) {
		tmp = z / (t_1 / (x + y));
	} 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 = a / (t_1 / (y + t))
    if (a <= (-1d+15)) then
        tmp = t_2
    else if (a <= 1.7d-170) then
        tmp = ((z * (x + y)) - (y * b)) / t_1
    else if (a <= 1.05d-12) then
        tmp = z / (t_1 / (x + y))
    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 = a / (t_1 / (y + t));
	double tmp;
	if (a <= -1e+15) {
		tmp = t_2;
	} else if (a <= 1.7e-170) {
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	} else if (a <= 1.05e-12) {
		tmp = z / (t_1 / (x + y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a / (t_1 / (y + t))
	tmp = 0
	if a <= -1e+15:
		tmp = t_2
	elif a <= 1.7e-170:
		tmp = ((z * (x + y)) - (y * b)) / t_1
	elif a <= 1.05e-12:
		tmp = z / (t_1 / (x + y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	tmp = 0.0
	if (a <= -1e+15)
		tmp = t_2;
	elseif (a <= 1.7e-170)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_1);
	elseif (a <= 1.05e-12)
		tmp = Float64(z / Float64(t_1 / Float64(x + y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a / (t_1 / (y + t));
	tmp = 0.0;
	if (a <= -1e+15)
		tmp = t_2;
	elseif (a <= 1.7e-170)
		tmp = ((z * (x + y)) - (y * b)) / t_1;
	elseif (a <= 1.05e-12)
		tmp = z / (t_1 / (x + y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+15], t$95$2, If[LessEqual[a, 1.7e-170], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[a, 1.05e-12], N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e15 or 1.04999999999999997e-12 < a

   1. Initial program 49.2%

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

   3. Taylor expanded in a around inf 37.7%

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

      1. associate-/l* 70.7%

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

      2. associate-+r+ 70.7%

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

   5. Simplified 70.7%

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

   if -1e15 < a < 1.70000000000000006e-170

   1. Initial program 79.9%

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

   3. Taylor expanded in a around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if 1.70000000000000006e-170 < a < 1.04999999999999997e-12

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 30.3%

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

      1. associate-/l* 61.8%

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

      2. associate-+r+ 61.8%

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

      3. +-commutative 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-170}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-145} \lor \neg \left(y \leq 3.5 \cdot 10^{-72}\right):\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e-145) (not (<= y 3.5e-72)))
   (+ z (- a b))
   (/ a (/ (+ x t) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e-145) || !(y <= 3.5e-72)) {
		tmp = z + (a - b);
	} else {
		tmp = a / ((x + t) / 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 <= (-2.6d-145)) .or. (.not. (y <= 3.5d-72))) then
        tmp = z + (a - b)
    else
        tmp = a / ((x + t) / 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 <= -2.6e-145) || !(y <= 3.5e-72)) {
		tmp = z + (a - b);
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e-145) or not (y <= 3.5e-72):
		tmp = z + (a - b)
	else:
		tmp = a / ((x + t) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e-145) || !(y <= 3.5e-72))
		tmp = Float64(z + Float64(a - b));
	else
		tmp = Float64(a / Float64(Float64(x + t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.6e-145) || ~((y <= 3.5e-72)))
		tmp = z + (a - b);
	else
		tmp = a / ((x + t) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e-145], N[Not[LessEqual[y, 3.5e-72]], $MachinePrecision]], N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-145 or 3.5e-72 < y

   1. Initial program 52.9%

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

   3. Taylor expanded in y around inf 66.7%

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

   4. Taylor expanded in b around 0 66.7%

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

      1. neg-mul-1 66.7%

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

      2. associate-+r+ 66.7%

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

      3. +-commutative 66.7%

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

      4. associate-+l+ 66.7%

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

      5. sub-neg 66.7%

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

   6. Simplified 66.7%

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

   if -2.6e-145 < y < 3.5e-72

   1. Initial program 82.6%

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

   3. Taylor expanded in t around inf 43.8%

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

      1. div-inv 43.7%

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

      2. +-commutative 43.7%

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

      3. associate-+l+ 43.7%

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

      4. +-commutative 43.7%

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

   5. Applied egg-rr 43.7%

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

   6. Taylor expanded in y around 0 43.8%

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

      1. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-145} \lor \neg \left(y \leq 3.5 \cdot 10^{-72}\right):\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+246}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 10^{+218}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.3e+246) z (if (<= x 1e+218) (+ z (- a b)) (* t (/ a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.3e+246) {
		tmp = z;
	} else if (x <= 1e+218) {
		tmp = z + (a - b);
	} else {
		tmp = t * (a / 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 <= (-4.3d+246)) then
        tmp = z
    else if (x <= 1d+218) then
        tmp = z + (a - b)
    else
        tmp = t * (a / 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 <= -4.3e+246) {
		tmp = z;
	} else if (x <= 1e+218) {
		tmp = z + (a - b);
	} else {
		tmp = t * (a / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.3e+246:
		tmp = z
	elif x <= 1e+218:
		tmp = z + (a - b)
	else:
		tmp = t * (a / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.3e+246)
		tmp = z;
	elseif (x <= 1e+218)
		tmp = Float64(z + Float64(a - b));
	else
		tmp = Float64(t * Float64(a / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.3e+246)
		tmp = z;
	elseif (x <= 1e+218)
		tmp = z + (a - b);
	else
		tmp = t * (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.3e+246], z, If[LessEqual[x, 1e+218], N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision], N[(t * N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.30000000000000028e246

   1. Initial program 59.1%

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

   3. Taylor expanded in x around inf 58.3%

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

   if -4.30000000000000028e246 < x < 1.00000000000000008e218

   1. Initial program 62.9%

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

   3. Taylor expanded in y around inf 59.5%

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

   4. Taylor expanded in b around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. associate-+r+ 59.5%

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

      3. +-commutative 59.5%

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

      4. associate-+l+ 59.5%

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

      5. sub-neg 59.5%

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

   6. Simplified 59.5%

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

   if 1.00000000000000008e218 < x

   1. Initial program 37.0%

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

   3. Taylor expanded in t around inf 25.6%

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

      1. div-inv 25.4%

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

      2. +-commutative 25.4%

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

      3. associate-+l+ 25.4%

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

      4. +-commutative 25.4%

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

   5. Applied egg-rr 25.4%

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

   6. Taylor expanded in x around inf 25.6%

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

      1. associate-/l* 52.6%

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

      2. associate-/r/ 63.0%

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

   8. Simplified 63.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+246}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 10^{+218}:\\ \;\;\;\;z + \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.5e+14) a (if (<= a 3.2e-13) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.5e+14) {
		tmp = a;
	} else if (a <= 3.2e-13) {
		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 <= (-7.5d+14)) then
        tmp = a
    else if (a <= 3.2d-13) 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 <= -7.5e+14) {
		tmp = a;
	} else if (a <= 3.2e-13) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.5e+14:
		tmp = a
	elif a <= 3.2e-13:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.5e+14)
		tmp = a;
	elseif (a <= 3.2e-13)
		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 <= -7.5e+14)
		tmp = a;
	elseif (a <= 3.2e-13)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.5e+14], a, If[LessEqual[a, 3.2e-13], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e14 or 3.2e-13 < a

   1. Initial program 49.2%

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

   3. Taylor expanded in t around inf 51.9%

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

   if -7.5e14 < a < 3.2e-13

   1. Initial program 76.1%

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

   3. Taylor expanded in x around inf 41.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-13}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.2% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + 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 = z + a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 61.8%

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

3. Taylor expanded in y around inf 56.1%

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

4. Taylor expanded in b around 0 50.7%

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

   1. +-commutative 50.7%

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

6. Simplified 50.7%

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

7. Final simplification 50.7%

   \[\leadsto z + a \]
8. Add Preprocessing

Alternative 17: 32.3% 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 61.8%

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

3. Taylor expanded in t around inf 34.9%

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

4. Final simplification 34.9%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.3% 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 2024024 
(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)))