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

Percentage Accurate: 60.4% → 93.3%

Time: 13.9s

Alternatives: 19

Speedup: 1.2×

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: 60.4% 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: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{z - b}{\frac{t_1}{y}}\\ \mathbf{if}\;x \leq -3.65 \cdot 10^{+127} \lor \neg \left(x \leq 3.8 \cdot 10^{+167}\right):\\ \;\;\;\;t_2 + \left(z + \frac{a}{t_1} \cdot \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{x \cdot z}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ (- z b) (/ t_1 y))))
   (if (or (<= x -3.65e+127) (not (<= x 3.8e+167)))
     (+ t_2 (+ z (* (/ a t_1) (+ y t))))
     (+ t_2 (+ (/ a (/ t_1 (+ y t))) (/ (* x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z - b) / (t_1 / y);
	double tmp;
	if ((x <= -3.65e+127) || !(x <= 3.8e+167)) {
		tmp = t_2 + (z + ((a / t_1) * (y + t)));
	} else {
		tmp = t_2 + ((a / (t_1 / (y + t))) + ((x * z) / 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 = y + (x + t)
    t_2 = (z - b) / (t_1 / y)
    if ((x <= (-3.65d+127)) .or. (.not. (x <= 3.8d+167))) then
        tmp = t_2 + (z + ((a / t_1) * (y + t)))
    else
        tmp = t_2 + ((a / (t_1 / (y + t))) + ((x * z) / 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 t_2 = (z - b) / (t_1 / y);
	double tmp;
	if ((x <= -3.65e+127) || !(x <= 3.8e+167)) {
		tmp = t_2 + (z + ((a / t_1) * (y + t)));
	} else {
		tmp = t_2 + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z - b) / (t_1 / y)
	tmp = 0
	if (x <= -3.65e+127) or not (x <= 3.8e+167):
		tmp = t_2 + (z + ((a / t_1) * (y + t)))
	else:
		tmp = t_2 + ((a / (t_1 / (y + t))) + ((x * z) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z - b) / Float64(t_1 / y))
	tmp = 0.0
	if ((x <= -3.65e+127) || !(x <= 3.8e+167))
		tmp = Float64(t_2 + Float64(z + Float64(Float64(a / t_1) * Float64(y + t))));
	else
		tmp = Float64(t_2 + Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(x * z) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z - b) / (t_1 / y);
	tmp = 0.0;
	if ((x <= -3.65e+127) || ~((x <= 3.8e+167)))
		tmp = t_2 + (z + ((a / t_1) * (y + t)));
	else
		tmp = t_2 + ((a / (t_1 / (y + t))) + ((x * z) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -3.65e+127], N[Not[LessEqual[x, 3.8e+167]], $MachinePrecision]], N[(t$95$2 + N[(z + N[(N[(a / t$95$1), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6499999999999998e127 or 3.79999999999999994e167 < x

   1. Initial program 43.2%

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

   3. Simplified 43.5%

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

   4. Taylor expanded in a around inf 43.2%

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

      1. associate-/l* 46.1%

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

      2. +-commutative 46.1%

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

      3. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. associate-/r/ 58.2%

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

      2. +-commutative 58.2%

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

   8. Applied egg-rr 58.2%

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

   9. Taylor expanded in x around inf 86.0%

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

   if -3.6499999999999998e127 < x < 3.79999999999999994e167

   1. Initial program 68.2%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in a around inf 68.3%

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

      1. associate-/l* 79.0%

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

      2. +-commutative 79.0%

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

      3. associate-/l* 97.5%

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

   6. Simplified 97.5%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{+127} \lor \neg \left(x \leq 3.8 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(z + \frac{a}{y + \left(x + t\right)} \cdot \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq 5 \cdot 10^{+278}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_2}{y}} + \left(z + \frac{a}{t_2} \cdot \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + \left(t_1 - b \cdot y\right)}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) t_2)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 5e+278)))
     (+ (/ (- z b) (/ t_2 y)) (+ z (* (/ a t_2) (+ y t))))
     (/ (+ t_3 (- t_1 (* b y))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 5e+278)) {
		tmp = ((z - b) / (t_2 / y)) + (z + ((a / t_2) * (y + t)));
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 5e+278)) {
		tmp = ((z - b) / (t_2 / y)) + (z + ((a / t_2) * (y + t)));
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (b * y)) / t_2
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 5e+278):
		tmp = ((z - b) / (t_2 / y)) + (z + ((a / t_2) * (y + t)))
	else:
		tmp = (t_3 + (t_1 - (b * y))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 5e+278))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_2 / y)) + Float64(z + Float64(Float64(a / t_2) * Float64(y + t))));
	else
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * y))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 5e+278)))
		tmp = ((z - b) / (t_2 / y)) + (z + ((a / t_2) * (y + t)));
	else
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 5e+278]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] + N[(z + N[(N[(a / t$95$2), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000029e278 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Simplified 6.8%

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

   4. Taylor expanded in a around inf 6.5%

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

      1. associate-/l* 31.3%

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

      2. +-commutative 31.3%

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

      3. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

      1. associate-/r/ 73.2%

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

      2. +-commutative 73.2%

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

   8. Applied egg-rr 73.2%

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

   9. Taylor expanded in x around inf 80.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000029e278

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Applied egg-rr 99.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 5 \cdot 10^{+278}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(z + \frac{a}{y + \left(x + t\right)} \cdot \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(y + t\right) - b \cdot y\right)}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t_4 \leq 10^{+265}:\\ \;\;\;\;\frac{t_3 + \left(t_1 - b \cdot y\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\left(x + \left(y + t\right)\right) \cdot \frac{1}{y}} + \left(a + \frac{x \cdot z}{t_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) t_2)))
   (if (<= t_4 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_4 1e+265)
       (/ (+ t_3 (- t_1 (* b y))) t_2)
       (+ (/ (- z b) (* (+ x (+ y t)) (/ 1.0 y))) (+ a (/ (* x z) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_4 <= 1e+265) {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	} else {
		tmp = ((z - b) / ((x + (y + t)) * (1.0 / y))) + (a + ((x * z) / t_2));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + a) - b;
	} else if (t_4 <= 1e+265) {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	} else {
		tmp = ((z - b) / ((x + (y + t)) * (1.0 / y))) + (a + ((x * z) / t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (b * y)) / t_2
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (z + a) - b
	elif t_4 <= 1e+265:
		tmp = (t_3 + (t_1 - (b * y))) / t_2
	else:
		tmp = ((z - b) / ((x + (y + t)) * (1.0 / y))) + (a + ((x * z) / t_2))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_4 <= 1e+265)
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * y))) / t_2);
	else
		tmp = Float64(Float64(Float64(z - b) / Float64(Float64(x + Float64(y + t)) * Float64(1.0 / y))) + Float64(a + Float64(Float64(x * z) / t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (z + a) - b;
	elseif (t_4 <= 1e+265)
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	else
		tmp = ((z - b) / ((x + (y + t)) * (1.0 / y))) + (a + ((x * z) / t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$4, 1e+265], N[(N[(t$95$3 + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(N[(z - b), $MachinePrecision] / N[(N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a + N[(N[(x * z), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 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

   1. Initial program 6.6%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. +-commutative 71.4%

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

   4. Simplified 71.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000007e265

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Applied egg-rr 99.7%

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

   if 1.00000000000000007e265 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.2%

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

   3. Simplified 10.3%

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

   4. Taylor expanded in a around inf 9.7%

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

      1. associate-/l* 36.6%

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

      2. +-commutative 36.6%

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

      3. associate-/l* 74.5%

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

   6. Simplified 74.5%

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

      1. div-inv 74.2%

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

      2. +-commutative 74.2%

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

   8. Applied egg-rr 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r+ 74.2%

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

   10. Simplified 74.2%

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

   11. Taylor expanded in y around inf 69.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 10^{+265}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(y + t\right) - b \cdot y\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\left(x + \left(y + t\right)\right) \cdot \frac{1}{y}} + \left(a + \frac{x \cdot z}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 4: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq 10^{+265}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + \left(t_1 - b \cdot y\right)}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) t_2)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 1e+265)))
     (- (+ z a) b)
     (/ (+ t_3 (- t_1 (* b y))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 1e+265)) {
		tmp = (z + a) - b;
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 1e+265)) {
		tmp = (z + a) - b;
	} else {
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (b * y)) / t_2
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 1e+265):
		tmp = (z + a) - b
	else:
		tmp = (t_3 + (t_1 - (b * y))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 1e+265))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(b * y))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 1e+265)))
		tmp = (z + a) - b;
	else
		tmp = (t_3 + (t_1 - (b * y))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 1e+265]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(t$95$3 + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $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 1.00000000000000007e265 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.1%

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

   2. Taylor expanded in y around inf 67.4%

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

      1. +-commutative 67.4%

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

   4. Simplified 67.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000007e265

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Applied egg-rr 99.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(x + t\right)} \leq 10^{+265}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(y + t\right) - b \cdot y\right)}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ t_3 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{a}{\frac{t_3}{y + t}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-266}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot z}{t_3}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-263}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y))))
        (t_2 (- (+ z a) b))
        (t_3 (+ y (+ x t))))
   (if (<= y -5.1e+51)
     t_2
     (if (<= y -1.5e-191)
       t_1
       (if (<= y -1.4e-236)
         (/ a (/ t_3 (+ y t)))
         (if (<= y -3.9e-266)
           (+ z (* y (- (/ a x) (/ b x))))
           (if (<= y 4.1e-272)
             (/ (* x z) t_3)
             (if (<= y 3.7e-263)
               (/ t (/ (+ x t) a))
               (if (<= y 2.3e+36) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -5.1e+51) {
		tmp = t_2;
	} else if (y <= -1.5e-191) {
		tmp = t_1;
	} else if (y <= -1.4e-236) {
		tmp = a / (t_3 / (y + t));
	} else if (y <= -3.9e-266) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= 4.1e-272) {
		tmp = (x * z) / t_3;
	} else if (y <= 3.7e-263) {
		tmp = t / ((x + t) / a);
	} else if (y <= 2.3e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    t_3 = y + (x + t)
    if (y <= (-5.1d+51)) then
        tmp = t_2
    else if (y <= (-1.5d-191)) then
        tmp = t_1
    else if (y <= (-1.4d-236)) then
        tmp = a / (t_3 / (y + t))
    else if (y <= (-3.9d-266)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (y <= 4.1d-272) then
        tmp = (x * z) / t_3
    else if (y <= 3.7d-263) then
        tmp = t / ((x + t) / a)
    else if (y <= 2.3d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -5.1e+51) {
		tmp = t_2;
	} else if (y <= -1.5e-191) {
		tmp = t_1;
	} else if (y <= -1.4e-236) {
		tmp = a / (t_3 / (y + t));
	} else if (y <= -3.9e-266) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= 4.1e-272) {
		tmp = (x * z) / t_3;
	} else if (y <= 3.7e-263) {
		tmp = t / ((x + t) / a);
	} else if (y <= 2.3e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	t_3 = y + (x + t)
	tmp = 0
	if y <= -5.1e+51:
		tmp = t_2
	elif y <= -1.5e-191:
		tmp = t_1
	elif y <= -1.4e-236:
		tmp = a / (t_3 / (y + t))
	elif y <= -3.9e-266:
		tmp = z + (y * ((a / x) - (b / x)))
	elif y <= 4.1e-272:
		tmp = (x * z) / t_3
	elif y <= 3.7e-263:
		tmp = t / ((x + t) / a)
	elif y <= 2.3e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -5.1e+51)
		tmp = t_2;
	elseif (y <= -1.5e-191)
		tmp = t_1;
	elseif (y <= -1.4e-236)
		tmp = Float64(a / Float64(t_3 / Float64(y + t)));
	elseif (y <= -3.9e-266)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (y <= 4.1e-272)
		tmp = Float64(Float64(x * z) / t_3);
	elseif (y <= 3.7e-263)
		tmp = Float64(t / Float64(Float64(x + t) / a));
	elseif (y <= 2.3e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	t_3 = y + (x + t);
	tmp = 0.0;
	if (y <= -5.1e+51)
		tmp = t_2;
	elseif (y <= -1.5e-191)
		tmp = t_1;
	elseif (y <= -1.4e-236)
		tmp = a / (t_3 / (y + t));
	elseif (y <= -3.9e-266)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (y <= 4.1e-272)
		tmp = (x * z) / t_3;
	elseif (y <= 3.7e-263)
		tmp = t / ((x + t) / a);
	elseif (y <= 2.3e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e+51], t$95$2, If[LessEqual[y, -1.5e-191], t$95$1, If[LessEqual[y, -1.4e-236], N[(a / N[(t$95$3 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e-266], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-272], N[(N[(x * z), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[y, 3.7e-263], N[(t / N[(N[(x + t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+36], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.1000000000000001e51 or 2.29999999999999996e36 < y

   1. Initial program 36.2%

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

   2. Taylor expanded in y around inf 73.2%

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

      1. +-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -5.1000000000000001e51 < y < -1.5e-191 or 3.6999999999999997e-263 < y < 2.29999999999999996e36

   1. Initial program 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around 0 53.2%

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

   5. Taylor expanded in z around 0 64.6%

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

   if -1.5e-191 < y < -1.39999999999999993e-236

   1. Initial program 76.6%

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

   2. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

   if -1.39999999999999993e-236 < y < -3.90000000000000028e-266

   1. Initial program 59.5%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in t around 0 45.1%

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

   5. Taylor expanded in y around 0 72.5%

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

   if -3.90000000000000028e-266 < y < 4.0999999999999997e-272

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 60.7%

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

   if 4.0999999999999997e-272 < y < 3.6999999999999997e-263

   1. Initial program 76.5%

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

   2. Taylor expanded in z around 0 76.5%

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

   3. Taylor expanded in y around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{t + x}{a}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-191}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-266}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-263}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ t_3 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-236}:\\ \;\;\;\;\frac{a}{\frac{t_3}{y + t}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-272}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{t_3}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-264}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y))))
        (t_2 (- (+ z a) b))
        (t_3 (+ y (+ x t))))
   (if (<= y -5.5e+51)
     t_2
     (if (<= y -4.2e-192)
       t_1
       (if (<= y -6.5e-236)
         (/ a (/ t_3 (+ y t)))
         (if (<= y -3.7e-266)
           (+ z (* y (- (/ a x) (/ b x))))
           (if (<= y 1.9e-272)
             (/ (* z (+ x y)) t_3)
             (if (<= y 5e-264)
               (/ t (/ (+ x t) a))
               (if (<= y 1.95e+31) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -5.5e+51) {
		tmp = t_2;
	} else if (y <= -4.2e-192) {
		tmp = t_1;
	} else if (y <= -6.5e-236) {
		tmp = a / (t_3 / (y + t));
	} else if (y <= -3.7e-266) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= 1.9e-272) {
		tmp = (z * (x + y)) / t_3;
	} else if (y <= 5e-264) {
		tmp = t / ((x + t) / a);
	} else if (y <= 1.95e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    t_3 = y + (x + t)
    if (y <= (-5.5d+51)) then
        tmp = t_2
    else if (y <= (-4.2d-192)) then
        tmp = t_1
    else if (y <= (-6.5d-236)) then
        tmp = a / (t_3 / (y + t))
    else if (y <= (-3.7d-266)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (y <= 1.9d-272) then
        tmp = (z * (x + y)) / t_3
    else if (y <= 5d-264) then
        tmp = t / ((x + t) / a)
    else if (y <= 1.95d+31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -5.5e+51) {
		tmp = t_2;
	} else if (y <= -4.2e-192) {
		tmp = t_1;
	} else if (y <= -6.5e-236) {
		tmp = a / (t_3 / (y + t));
	} else if (y <= -3.7e-266) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= 1.9e-272) {
		tmp = (z * (x + y)) / t_3;
	} else if (y <= 5e-264) {
		tmp = t / ((x + t) / a);
	} else if (y <= 1.95e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	t_3 = y + (x + t)
	tmp = 0
	if y <= -5.5e+51:
		tmp = t_2
	elif y <= -4.2e-192:
		tmp = t_1
	elif y <= -6.5e-236:
		tmp = a / (t_3 / (y + t))
	elif y <= -3.7e-266:
		tmp = z + (y * ((a / x) - (b / x)))
	elif y <= 1.9e-272:
		tmp = (z * (x + y)) / t_3
	elif y <= 5e-264:
		tmp = t / ((x + t) / a)
	elif y <= 1.95e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -5.5e+51)
		tmp = t_2;
	elseif (y <= -4.2e-192)
		tmp = t_1;
	elseif (y <= -6.5e-236)
		tmp = Float64(a / Float64(t_3 / Float64(y + t)));
	elseif (y <= -3.7e-266)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (y <= 1.9e-272)
		tmp = Float64(Float64(z * Float64(x + y)) / t_3);
	elseif (y <= 5e-264)
		tmp = Float64(t / Float64(Float64(x + t) / a));
	elseif (y <= 1.95e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	t_3 = y + (x + t);
	tmp = 0.0;
	if (y <= -5.5e+51)
		tmp = t_2;
	elseif (y <= -4.2e-192)
		tmp = t_1;
	elseif (y <= -6.5e-236)
		tmp = a / (t_3 / (y + t));
	elseif (y <= -3.7e-266)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (y <= 1.9e-272)
		tmp = (z * (x + y)) / t_3;
	elseif (y <= 5e-264)
		tmp = t / ((x + t) / a);
	elseif (y <= 1.95e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+51], t$95$2, If[LessEqual[y, -4.2e-192], t$95$1, If[LessEqual[y, -6.5e-236], N[(a / N[(t$95$3 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-266], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-272], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[y, 5e-264], N[(t / N[(N[(x + t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+31], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.5e51 or 1.95e31 < y

   1. Initial program 36.2%

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

   2. Taylor expanded in y around inf 73.2%

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

      1. +-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -5.5e51 < y < -4.19999999999999986e-192 or 5.0000000000000001e-264 < y < 1.95e31

   1. Initial program 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around 0 53.2%

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

   5. Taylor expanded in z around 0 64.6%

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

   if -4.19999999999999986e-192 < y < -6.5000000000000001e-236

   1. Initial program 76.6%

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

   2. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

   if -6.5000000000000001e-236 < y < -3.7000000000000003e-266

   1. Initial program 59.5%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in t around 0 45.1%

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

   5. Taylor expanded in y around 0 72.5%

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

   if -3.7000000000000003e-266 < y < 1.89999999999999985e-272

   1. Initial program 91.0%

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

   2. Taylor expanded in z around inf 62.0%

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

   if 1.89999999999999985e-272 < y < 5.0000000000000001e-264

   1. Initial program 76.5%

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

   2. Taylor expanded in z around 0 76.5%

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

   3. Taylor expanded in y around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{t + x}{a}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-192}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-236}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-266}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-272}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-264}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+31}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 7: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ t_3 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-237}:\\ \;\;\;\;\frac{a}{\frac{t_3}{y + t}}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-265}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + y}{\frac{t_3}{z}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y))))
        (t_2 (- (+ z a) b))
        (t_3 (+ y (+ x t))))
   (if (<= y -4.8e+51)
     t_2
     (if (<= y -2.8e-192)
       t_1
       (if (<= y -4.8e-237)
         (/ a (/ t_3 (+ y t)))
         (if (<= y -4.4e-265)
           (+ z (* y (- (/ a x) (/ b x))))
           (if (<= y 6.5e-273)
             (/ (+ x y) (/ t_3 z))
             (if (<= y 3.2e-262)
               (/ t (/ (+ x t) a))
               (if (<= y 1.6e+36) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -4.8e+51) {
		tmp = t_2;
	} else if (y <= -2.8e-192) {
		tmp = t_1;
	} else if (y <= -4.8e-237) {
		tmp = a / (t_3 / (y + t));
	} else if (y <= -4.4e-265) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= 6.5e-273) {
		tmp = (x + y) / (t_3 / z);
	} else if (y <= 3.2e-262) {
		tmp = t / ((x + t) / a);
	} else if (y <= 1.6e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    t_3 = y + (x + t)
    if (y <= (-4.8d+51)) then
        tmp = t_2
    else if (y <= (-2.8d-192)) then
        tmp = t_1
    else if (y <= (-4.8d-237)) then
        tmp = a / (t_3 / (y + t))
    else if (y <= (-4.4d-265)) then
        tmp = z + (y * ((a / x) - (b / x)))
    else if (y <= 6.5d-273) then
        tmp = (x + y) / (t_3 / z)
    else if (y <= 3.2d-262) then
        tmp = t / ((x + t) / a)
    else if (y <= 1.6d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double t_3 = y + (x + t);
	double tmp;
	if (y <= -4.8e+51) {
		tmp = t_2;
	} else if (y <= -2.8e-192) {
		tmp = t_1;
	} else if (y <= -4.8e-237) {
		tmp = a / (t_3 / (y + t));
	} else if (y <= -4.4e-265) {
		tmp = z + (y * ((a / x) - (b / x)));
	} else if (y <= 6.5e-273) {
		tmp = (x + y) / (t_3 / z);
	} else if (y <= 3.2e-262) {
		tmp = t / ((x + t) / a);
	} else if (y <= 1.6e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	t_3 = y + (x + t)
	tmp = 0
	if y <= -4.8e+51:
		tmp = t_2
	elif y <= -2.8e-192:
		tmp = t_1
	elif y <= -4.8e-237:
		tmp = a / (t_3 / (y + t))
	elif y <= -4.4e-265:
		tmp = z + (y * ((a / x) - (b / x)))
	elif y <= 6.5e-273:
		tmp = (x + y) / (t_3 / z)
	elif y <= 3.2e-262:
		tmp = t / ((x + t) / a)
	elif y <= 1.6e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -4.8e+51)
		tmp = t_2;
	elseif (y <= -2.8e-192)
		tmp = t_1;
	elseif (y <= -4.8e-237)
		tmp = Float64(a / Float64(t_3 / Float64(y + t)));
	elseif (y <= -4.4e-265)
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	elseif (y <= 6.5e-273)
		tmp = Float64(Float64(x + y) / Float64(t_3 / z));
	elseif (y <= 3.2e-262)
		tmp = Float64(t / Float64(Float64(x + t) / a));
	elseif (y <= 1.6e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	t_3 = y + (x + t);
	tmp = 0.0;
	if (y <= -4.8e+51)
		tmp = t_2;
	elseif (y <= -2.8e-192)
		tmp = t_1;
	elseif (y <= -4.8e-237)
		tmp = a / (t_3 / (y + t));
	elseif (y <= -4.4e-265)
		tmp = z + (y * ((a / x) - (b / x)));
	elseif (y <= 6.5e-273)
		tmp = (x + y) / (t_3 / z);
	elseif (y <= 3.2e-262)
		tmp = t / ((x + t) / a);
	elseif (y <= 1.6e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+51], t$95$2, If[LessEqual[y, -2.8e-192], t$95$1, If[LessEqual[y, -4.8e-237], N[(a / N[(t$95$3 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e-265], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-273], N[(N[(x + y), $MachinePrecision] / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-262], N[(t / N[(N[(x + t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+36], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.7999999999999997e51 or 1.5999999999999999e36 < y

   1. Initial program 36.2%

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

   2. Taylor expanded in y around inf 73.2%

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

      1. +-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -4.7999999999999997e51 < y < -2.80000000000000004e-192 or 3.2e-262 < y < 1.5999999999999999e36

   1. Initial program 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around 0 53.2%

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

   5. Taylor expanded in z around 0 64.6%

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

   if -2.80000000000000004e-192 < y < -4.8e-237

   1. Initial program 76.6%

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

   2. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

   if -4.8e-237 < y < -4.40000000000000021e-265

   1. Initial program 68.6%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 67.9%

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

   if -4.40000000000000021e-265 < y < 6.49999999999999979e-273

   1. Initial program 83.8%

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

   2. Taylor expanded in z around inf 57.2%

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

      1. associate-/l* 68.3%

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

   4. Simplified 68.3%

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

   if 6.49999999999999979e-273 < y < 3.2e-262

   1. Initial program 76.5%

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

   2. Taylor expanded in z around 0 76.5%

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

   3. Taylor expanded in y around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{t + x}{a}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+51}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-192}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-237}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-265}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-273}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 61.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-236}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-264}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y)))) (t_2 (- (+ z a) b)))
   (if (<= y -9.6e+44)
     t_2
     (if (<= y -6.8e-203)
       t_1
       (if (<= y -1.1e-236)
         (/ t (/ (+ x t) a))
         (if (<= y -1e-308)
           (/ (* x z) (+ y (+ x t)))
           (if (<= y 6.1e-264) (+ z a) (if (<= y 2.2e+36) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -9.6e+44) {
		tmp = t_2;
	} else if (y <= -6.8e-203) {
		tmp = t_1;
	} else if (y <= -1.1e-236) {
		tmp = t / ((x + t) / a);
	} else if (y <= -1e-308) {
		tmp = (x * z) / (y + (x + t));
	} else if (y <= 6.1e-264) {
		tmp = z + a;
	} else if (y <= 2.2e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    if (y <= (-9.6d+44)) then
        tmp = t_2
    else if (y <= (-6.8d-203)) then
        tmp = t_1
    else if (y <= (-1.1d-236)) then
        tmp = t / ((x + t) / a)
    else if (y <= (-1d-308)) then
        tmp = (x * z) / (y + (x + t))
    else if (y <= 6.1d-264) then
        tmp = z + a
    else if (y <= 2.2d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -9.6e+44) {
		tmp = t_2;
	} else if (y <= -6.8e-203) {
		tmp = t_1;
	} else if (y <= -1.1e-236) {
		tmp = t / ((x + t) / a);
	} else if (y <= -1e-308) {
		tmp = (x * z) / (y + (x + t));
	} else if (y <= 6.1e-264) {
		tmp = z + a;
	} else if (y <= 2.2e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -9.6e+44:
		tmp = t_2
	elif y <= -6.8e-203:
		tmp = t_1
	elif y <= -1.1e-236:
		tmp = t / ((x + t) / a)
	elif y <= -1e-308:
		tmp = (x * z) / (y + (x + t))
	elif y <= 6.1e-264:
		tmp = z + a
	elif y <= 2.2e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9.6e+44)
		tmp = t_2;
	elseif (y <= -6.8e-203)
		tmp = t_1;
	elseif (y <= -1.1e-236)
		tmp = Float64(t / Float64(Float64(x + t) / a));
	elseif (y <= -1e-308)
		tmp = Float64(Float64(x * z) / Float64(y + Float64(x + t)));
	elseif (y <= 6.1e-264)
		tmp = Float64(z + a);
	elseif (y <= 2.2e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9.6e+44)
		tmp = t_2;
	elseif (y <= -6.8e-203)
		tmp = t_1;
	elseif (y <= -1.1e-236)
		tmp = t / ((x + t) / a);
	elseif (y <= -1e-308)
		tmp = (x * z) / (y + (x + t));
	elseif (y <= 6.1e-264)
		tmp = z + a;
	elseif (y <= 2.2e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.6e+44], t$95$2, If[LessEqual[y, -6.8e-203], t$95$1, If[LessEqual[y, -1.1e-236], N[(t / N[(N[(x + t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-308], N[(N[(x * z), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e-264], N[(z + a), $MachinePrecision], If[LessEqual[y, 2.2e+36], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.60000000000000053e44 or 2.2e36 < y

   1. Initial program 38.0%

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

   2. Taylor expanded in y around inf 73.9%

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

      1. +-commutative 73.9%

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

   4. Simplified 73.9%

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

   if -9.60000000000000053e44 < y < -6.7999999999999998e-203 or 6.10000000000000025e-264 < y < 2.2e36

   1. Initial program 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in t around 0 52.0%

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

   5. Taylor expanded in z around 0 63.5%

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

   if -6.7999999999999998e-203 < y < -1.09999999999999996e-236

   1. Initial program 73.4%

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

   2. Taylor expanded in z around 0 39.8%

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

   3. Taylor expanded in y around 0 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   if -1.09999999999999996e-236 < y < -9.9999999999999991e-309

   1. Initial program 78.0%

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

   2. Taylor expanded in x around inf 53.7%

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

   if -9.9999999999999991e-309 < y < 6.10000000000000025e-264

   1. Initial program 78.8%

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

   2. Taylor expanded in y around inf 55.5%

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

      1. +-commutative 55.5%

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

   4. Simplified 55.5%

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

   5. Taylor expanded in b around 0 66.2%

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

      1. +-commutative 66.2%

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

   7. Simplified 66.2%

      \[\leadsto \color{blue}{z + a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+44}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-236}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-264}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+36}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+86}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{t \cdot a + y \cdot t_1}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5.6e+86)
     (- (+ a (+ z (* x (- (/ b y) (/ a y))))) b)
     (if (<= y -2.55e-110)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= y 2.3e-160)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 2.2e-14) (/ (+ (* t a) (* y t_1)) (+ y t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e+86) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -2.55e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 2.3e-160) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.2e-14) {
		tmp = ((t * a) + (y * t_1)) / (y + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-5.6d+86)) then
        tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
    else if (y <= (-2.55d-110)) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (y <= 2.3d-160) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 2.2d-14) then
        tmp = ((t * a) + (y * t_1)) / (y + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e+86) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -2.55e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 2.3e-160) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 2.2e-14) {
		tmp = ((t * a) + (y * t_1)) / (y + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5.6e+86:
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
	elif y <= -2.55e-110:
		tmp = z + ((y * (a - b)) / (x + y))
	elif y <= 2.3e-160:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 2.2e-14:
		tmp = ((t * a) + (y * t_1)) / (y + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.6e+86)
		tmp = Float64(Float64(a + Float64(z + Float64(x * Float64(Float64(b / y) - Float64(a / y))))) - b);
	elseif (y <= -2.55e-110)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 2.3e-160)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 2.2e-14)
		tmp = Float64(Float64(Float64(t * a) + Float64(y * t_1)) / Float64(y + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.6e+86)
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	elseif (y <= -2.55e-110)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (y <= 2.3e-160)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 2.2e-14)
		tmp = ((t * a) + (y * t_1)) / (y + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.6e+86], N[(N[(a + N[(z + N[(x * N[(N[(b / y), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -2.55e-110], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-160], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-14], N[(N[(N[(t * a), $MachinePrecision] + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.60000000000000008e86

   1. Initial program 26.6%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in t around 0 24.8%

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

   5. Taylor expanded in x around 0 73.4%

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

   if -5.60000000000000008e86 < y < -2.5500000000000001e-110

   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. Step-by-step derivation

   3. Simplified 73.8%

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

   4. Taylor expanded in t around 0 62.7%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -2.5500000000000001e-110 < y < 2.29999999999999985e-160

   1. Initial program 81.0%

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

   2. Taylor expanded in y around 0 71.3%

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

   if 2.29999999999999985e-160 < y < 2.2000000000000001e-14

   1. Initial program 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in x around 0 64.8%

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

   if 2.2000000000000001e-14 < y

   1. Initial program 50.9%

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

   2. Taylor expanded in y around inf 76.2%

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

      1. +-commutative 76.2%

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

   4. Simplified 76.2%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+86}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{t \cdot a + y \cdot \left(\left(z + a\right) - b\right)}{y + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.6e+84)
   (- (+ a (+ z (* x (- (/ b y) (/ a y))))) b)
   (if (<= y -2.35e-110)
     (+ z (/ (* y (- a b)) (+ x y)))
     (if (<= y 5.8e-170)
       (/ (+ (* x z) (* t a)) (+ x t))
       (if (<= y 3.1e-15)
         (/ (- (* a (+ y t)) (* b y)) (+ y (+ x t)))
         (- (+ z a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e+84) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -2.35e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 5.8e-170) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.1e-15) {
		tmp = ((a * (y + t)) - (b * y)) / (y + (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.6d+84)) then
        tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
    else if (y <= (-2.35d-110)) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (y <= 5.8d-170) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 3.1d-15) then
        tmp = ((a * (y + t)) - (b * y)) / (y + (x + t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.6e+84) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -2.35e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 5.8e-170) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.1e-15) {
		tmp = ((a * (y + t)) - (b * y)) / (y + (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.6e+84:
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
	elif y <= -2.35e-110:
		tmp = z + ((y * (a - b)) / (x + y))
	elif y <= 5.8e-170:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 3.1e-15:
		tmp = ((a * (y + t)) - (b * y)) / (y + (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.6e+84)
		tmp = Float64(Float64(a + Float64(z + Float64(x * Float64(Float64(b / y) - Float64(a / y))))) - b);
	elseif (y <= -2.35e-110)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 5.8e-170)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 3.1e-15)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(b * y)) / Float64(y + Float64(x + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.6e+84)
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	elseif (y <= -2.35e-110)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (y <= 5.8e-170)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 3.1e-15)
		tmp = ((a * (y + t)) - (b * y)) / (y + (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.6e+84], N[(N[(a + N[(z + N[(x * N[(N[(b / y), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -2.35e-110], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-170], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-15], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.59999999999999963e84

   1. Initial program 26.6%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in t around 0 24.8%

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

   5. Taylor expanded in x around 0 73.4%

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

   if -5.59999999999999963e84 < y < -2.34999999999999996e-110

   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. Step-by-step derivation

   3. Simplified 73.8%

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

   4. Taylor expanded in t around 0 62.7%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -2.34999999999999996e-110 < y < 5.8000000000000001e-170

   1. Initial program 80.5%

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

   2. Taylor expanded in y around 0 71.9%

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

   if 5.8000000000000001e-170 < y < 3.0999999999999999e-15

   1. Initial program 79.0%

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

   2. Taylor expanded in z around 0 66.9%

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

   if 3.0999999999999999e-15 < y

   1. Initial program 50.9%

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

   2. Taylor expanded in y around inf 76.2%

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

      1. +-commutative 76.2%

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

   4. Simplified 76.2%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + t_1}{t_2}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-14}:\\ \;\;\;\;\frac{t_1 - b \cdot y}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t))) (t_2 (+ y (+ x t))))
   (if (<= y -1.25e+86)
     (- (+ a (+ z (* x (- (/ b y) (/ a y))))) b)
     (if (<= y -3.1e-110)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= y 4.1e-131)
         (/ (+ (* z (+ x y)) t_1) t_2)
         (if (<= y 1.9e-14) (/ (- t_1 (* b y)) t_2) (- (+ z a) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -1.25e+86) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -3.1e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 4.1e-131) {
		tmp = ((z * (x + y)) + t_1) / t_2;
	} else if (y <= 1.9e-14) {
		tmp = (t_1 - (b * y)) / t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y + t)
    t_2 = y + (x + t)
    if (y <= (-1.25d+86)) then
        tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
    else if (y <= (-3.1d-110)) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (y <= 4.1d-131) then
        tmp = ((z * (x + y)) + t_1) / t_2
    else if (y <= 1.9d-14) then
        tmp = (t_1 - (b * y)) / t_2
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -1.25e+86) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -3.1e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 4.1e-131) {
		tmp = ((z * (x + y)) + t_1) / t_2;
	} else if (y <= 1.9e-14) {
		tmp = (t_1 - (b * y)) / t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	tmp = 0
	if y <= -1.25e+86:
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
	elif y <= -3.1e-110:
		tmp = z + ((y * (a - b)) / (x + y))
	elif y <= 4.1e-131:
		tmp = ((z * (x + y)) + t_1) / t_2
	elif y <= 1.9e-14:
		tmp = (t_1 - (b * y)) / t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -1.25e+86)
		tmp = Float64(Float64(a + Float64(z + Float64(x * Float64(Float64(b / y) - Float64(a / y))))) - b);
	elseif (y <= -3.1e-110)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 4.1e-131)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) + t_1) / t_2);
	elseif (y <= 1.9e-14)
		tmp = Float64(Float64(t_1 - Float64(b * y)) / t_2);
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	tmp = 0.0;
	if (y <= -1.25e+86)
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	elseif (y <= -3.1e-110)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (y <= 4.1e-131)
		tmp = ((z * (x + y)) + t_1) / t_2;
	elseif (y <= 1.9e-14)
		tmp = (t_1 - (b * y)) / t_2;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+86], N[(N[(a + N[(z + N[(x * N[(N[(b / y), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -3.1e-110], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-131], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.9e-14], N[(N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.2499999999999999e86

   1. Initial program 26.6%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in t around 0 24.8%

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

   5. Taylor expanded in x around 0 73.4%

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

   if -1.2499999999999999e86 < y < -3.10000000000000007e-110

   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. Step-by-step derivation

   3. Simplified 73.8%

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

   4. Taylor expanded in t around 0 62.7%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -3.10000000000000007e-110 < y < 4.1000000000000002e-131

   1. Initial program 78.8%

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

   2. Taylor expanded in b around 0 73.2%

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

   if 4.1000000000000002e-131 < y < 1.9000000000000001e-14

   1. Initial program 84.0%

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

   2. Taylor expanded in z around 0 75.3%

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

   if 1.9000000000000001e-14 < y

   1. Initial program 50.9%

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

   2. Taylor expanded in y around inf 76.2%

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

      1. +-commutative 76.2%

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

   4. Simplified 76.2%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + a \cdot \left(y + t\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-14}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{y \cdot t_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5.6e+42)
     t_1
     (if (<= y -2.9e-110)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= y 2e-164)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 3.6e-32)
           (/ (* y t_1) (+ y (+ x t)))
           (if (<= y 3.8e-32) a t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e+42) {
		tmp = t_1;
	} else if (y <= -2.9e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 2e-164) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.6e-32) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= 3.8e-32) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-5.6d+42)) then
        tmp = t_1
    else if (y <= (-2.9d-110)) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (y <= 2d-164) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 3.6d-32) then
        tmp = (y * t_1) / (y + (x + t))
    else if (y <= 3.8d-32) then
        tmp = a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5.6e+42) {
		tmp = t_1;
	} else if (y <= -2.9e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 2e-164) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.6e-32) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= 3.8e-32) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5.6e+42:
		tmp = t_1
	elif y <= -2.9e-110:
		tmp = z + ((y * (a - b)) / (x + y))
	elif y <= 2e-164:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 3.6e-32:
		tmp = (y * t_1) / (y + (x + t))
	elif y <= 3.8e-32:
		tmp = a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.6e+42)
		tmp = t_1;
	elseif (y <= -2.9e-110)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 2e-164)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 3.6e-32)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (y <= 3.8e-32)
		tmp = a;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.6e+42)
		tmp = t_1;
	elseif (y <= -2.9e-110)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (y <= 2e-164)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 3.6e-32)
		tmp = (y * t_1) / (y + (x + t));
	elseif (y <= 3.8e-32)
		tmp = a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.6e+42], t$95$1, If[LessEqual[y, -2.9e-110], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-164], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-32], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-32], a, t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.5999999999999999e42 or 3.80000000000000008e-32 < y

   1. Initial program 45.7%

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

   2. Taylor expanded in y around inf 74.2%

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

      1. +-commutative 74.2%

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

   4. Simplified 74.2%

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

   if -5.5999999999999999e42 < y < -2.9000000000000002e-110

   1. Initial program 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around 0 62.1%

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

   5. Taylor expanded in z around 0 70.4%

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

   if -2.9000000000000002e-110 < y < 1.99999999999999992e-164

   1. Initial program 80.5%

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

   2. Taylor expanded in y around 0 71.9%

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

   if 1.99999999999999992e-164 < y < 3.59999999999999993e-32

   1. Initial program 75.0%

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

   2. Taylor expanded in y around inf 49.4%

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

      1. +-commutative 49.4%

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

   4. Simplified 49.4%

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

   if 3.59999999999999993e-32 < y < 3.80000000000000008e-32

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 96.4%

      \[\leadsto \color{blue}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 13: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+84}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{y \cdot t_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.4e+84)
     (- (+ a (+ z (* x (- (/ b y) (/ a y))))) b)
     (if (<= y -3e-110)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= y 1.55e-164)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 3.2e-32)
           (/ (* y t_1) (+ y (+ x t)))
           (if (<= y 3.8e-32) a 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 <= -2.4e+84) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -3e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 1.55e-164) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.2e-32) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= 3.8e-32) {
		tmp = a;
	} 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 <= (-2.4d+84)) then
        tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
    else if (y <= (-3d-110)) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (y <= 1.55d-164) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 3.2d-32) then
        tmp = (y * t_1) / (y + (x + t))
    else if (y <= 3.8d-32) then
        tmp = a
    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 <= -2.4e+84) {
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	} else if (y <= -3e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 1.55e-164) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.2e-32) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= 3.8e-32) {
		tmp = a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.4e+84:
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b
	elif y <= -3e-110:
		tmp = z + ((y * (a - b)) / (x + y))
	elif y <= 1.55e-164:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 3.2e-32:
		tmp = (y * t_1) / (y + (x + t))
	elif y <= 3.8e-32:
		tmp = a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.4e+84)
		tmp = Float64(Float64(a + Float64(z + Float64(x * Float64(Float64(b / y) - Float64(a / y))))) - b);
	elseif (y <= -3e-110)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 1.55e-164)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 3.2e-32)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (y <= 3.8e-32)
		tmp = a;
	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 <= -2.4e+84)
		tmp = (a + (z + (x * ((b / y) - (a / y))))) - b;
	elseif (y <= -3e-110)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (y <= 1.55e-164)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 3.2e-32)
		tmp = (y * t_1) / (y + (x + t));
	elseif (y <= 3.8e-32)
		tmp = a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.4e+84], N[(N[(a + N[(z + N[(x * N[(N[(b / y), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -3e-110], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-164], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-32], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-32], a, t$95$1]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.4e84

   1. Initial program 26.6%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in t around 0 24.8%

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

   5. Taylor expanded in x around 0 73.4%

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

   if -2.4e84 < y < -2.99999999999999986e-110

   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. Step-by-step derivation

   3. Simplified 73.8%

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

   4. Taylor expanded in t around 0 62.7%

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

   5. Taylor expanded in z around 0 69.2%

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

   if -2.99999999999999986e-110 < y < 1.55e-164

   1. Initial program 80.5%

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

   2. Taylor expanded in y around 0 71.9%

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

   if 1.55e-164 < y < 3.2000000000000002e-32

   1. Initial program 75.0%

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

   2. Taylor expanded in y around inf 49.4%

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

      1. +-commutative 49.4%

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

   4. Simplified 49.4%

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

   if 3.2000000000000002e-32 < y < 3.80000000000000008e-32

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 96.4%

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

   if 3.80000000000000008e-32 < y

   1. Initial program 55.3%

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

   2. Taylor expanded in y around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+84}:\\ \;\;\;\;\left(a + \left(z + x \cdot \left(\frac{b}{y} - \frac{a}{y}\right)\right)\right) - b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 14: 65.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2e+45)
     t_1
     (if (<= y -2.35e-110)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= y 7.4e-32) (/ (+ (* x z) (* t a)) (+ x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2e+45) {
		tmp = t_1;
	} else if (y <= -2.35e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 7.4e-32) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2d+45)) then
        tmp = t_1
    else if (y <= (-2.35d-110)) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (y <= 7.4d-32) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2e+45) {
		tmp = t_1;
	} else if (y <= -2.35e-110) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (y <= 7.4e-32) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2e+45:
		tmp = t_1
	elif y <= -2.35e-110:
		tmp = z + ((y * (a - b)) / (x + y))
	elif y <= 7.4e-32:
		tmp = ((x * z) + (t * a)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2e+45)
		tmp = t_1;
	elseif (y <= -2.35e-110)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (y <= 7.4e-32)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2e+45)
		tmp = t_1;
	elseif (y <= -2.35e-110)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (y <= 7.4e-32)
		tmp = ((x * z) + (t * a)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2e+45], t$95$1, If[LessEqual[y, -2.35e-110], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-32], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e45 or 7.4e-32 < y

   1. Initial program 45.7%

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

   2. Taylor expanded in y around inf 74.2%

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

      1. +-commutative 74.2%

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

   4. Simplified 74.2%

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

   if -1.9999999999999999e45 < y < -2.34999999999999996e-110

   1. Initial program 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around 0 62.1%

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

   5. Taylor expanded in z around 0 70.4%

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

   if -2.34999999999999996e-110 < y < 7.4e-32

   1. Initial program 79.4%

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

   2. Taylor expanded in y around 0 61.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+45}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-110}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 15: 59.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-105} \lor \neg \left(y \leq 8.6 \cdot 10^{-32}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e-105) (not (<= y 8.6e-32))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-105) || !(y <= 8.6e-32)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d-105)) .or. (.not. (y <= 8.6d-32))) then
        tmp = (z + a) - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-105) || !(y <= 8.6e-32)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e-105) or not (y <= 8.6e-32):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e-105) || !(y <= 8.6e-32))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e-105) || ~((y <= 8.6e-32)))
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e-105], N[Not[LessEqual[y, 8.6e-32]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999995e-105 or 8.5999999999999998e-32 < y

   1. Initial program 51.6%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. +-commutative 69.2%

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

   4. Simplified 69.2%

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

   if -8.9999999999999995e-105 < y < 8.5999999999999998e-32

   1. Initial program 78.8%

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

   2. Taylor expanded in y around inf 37.0%

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

      1. +-commutative 37.0%

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

   4. Simplified 37.0%

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

   5. Taylor expanded in b around 0 46.5%

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

      1. +-commutative 46.5%

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

   7. Simplified 46.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-105} \lor \neg \left(y \leq 8.6 \cdot 10^{-32}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 16: 49.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+133}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-77}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2e+133) z (if (<= x 1.65e-77) (- a b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2e+133) {
		tmp = z;
	} else if (x <= 1.65e-77) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2d+133)) then
        tmp = z
    else if (x <= 1.65d-77) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2e+133) {
		tmp = z;
	} else if (x <= 1.65e-77) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2e+133:
		tmp = z
	elif x <= 1.65e-77:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2e+133)
		tmp = z;
	elseif (x <= 1.65e-77)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2e+133)
		tmp = z;
	elseif (x <= 1.65e-77)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2e+133], z, If[LessEqual[x, 1.65e-77], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e133

   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. Taylor expanded in x around inf 51.7%

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

   if -2e133 < x < 1.64999999999999996e-77

   1. Initial program 66.7%

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

   2. Taylor expanded in y around inf 65.5%

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

      1. +-commutative 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in z around 0 58.5%

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

   if 1.64999999999999996e-77 < x

   1. Initial program 61.6%

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

   2. Taylor expanded in y around inf 47.8%

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

      1. +-commutative 47.8%

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

   4. Simplified 47.8%

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

   5. Taylor expanded in b around 0 48.2%

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

      1. +-commutative 48.2%

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

   7. Simplified 48.2%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+133}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-77}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 17: 43.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+118}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-61}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+118) z (if (<= x 6.5e-61) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+118) {
		tmp = z;
	} else if (x <= 6.5e-61) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6d+118)) then
        tmp = z
    else if (x <= 6.5d-61) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+118) {
		tmp = z;
	} else if (x <= 6.5e-61) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+118:
		tmp = z
	elif x <= 6.5e-61:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+118)
		tmp = z;
	elseif (x <= 6.5e-61)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6e+118)
		tmp = z;
	elseif (x <= 6.5e-61)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+118], z, If[LessEqual[x, 6.5e-61], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -6e118 or 6.4999999999999994e-61 < x

   1. Initial program 55.6%

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

   2. Taylor expanded in x around inf 43.4%

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

   if -6e118 < x < 6.4999999999999994e-61

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 45.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+118}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-61}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 18: 51.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{+209}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 2.4e+209) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.4e+209) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.4d+209) then
        tmp = z + a
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.4e+209) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.4e+209:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.4e+209)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.4e+209)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.4e+209], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 2.39999999999999996e209

   1. Initial program 62.6%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in b around 0 50.4%

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

      1. +-commutative 50.4%

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

   7. Simplified 50.4%

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

   if 2.39999999999999996e209 < b

   1. Initial program 57.7%

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

   2. Taylor expanded in y around inf 45.7%

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

      1. +-commutative 45.7%

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

   4. Simplified 45.7%

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

   5. Taylor expanded in b around inf 41.6%

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

      1. neg-mul-1 41.6%

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

   7. Simplified 41.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{+209}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]

Alternative 19: 33.5% 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 62.1%

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

2. Taylor expanded in t around inf 30.9%

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

3. Final simplification 30.9%

   \[\leadsto a \]

Developer target: 82.4% 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 2023195 
(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)))