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

Percentage Accurate: 61.1% → 93.2%

Time: 16.8s

Alternatives: 20

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.1% 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: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{z - b}{\frac{t_1}{y}}\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{+17}:\\ \;\;\;\;t_2 + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{z \cdot x}{t_1}\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t_1} + \frac{y}{t_1}, z, \frac{y \cdot \left(a - b\right)}{t_1} + \frac{a}{\frac{t_1}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(a + x \cdot \left(\frac{z}{y + t} - \frac{a}{y + t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (/ (- z b) (/ t_1 y))))
   (if (<= y -1.28e+17)
     (+ t_2 (+ (/ a (/ t_1 (+ y t))) (/ (* z x) t_1)))
     (if (<= y 2.55e+66)
       (fma
        (+ (/ x t_1) (/ y t_1))
        z
        (+ (/ (* y (- a b)) t_1) (/ a (/ t_1 t))))
       (+ t_2 (+ a (* x (- (/ z (+ y t)) (/ a (+ y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (z - b) / (t_1 / y);
	double tmp;
	if (y <= -1.28e+17) {
		tmp = t_2 + ((a / (t_1 / (y + t))) + ((z * x) / t_1));
	} else if (y <= 2.55e+66) {
		tmp = fma(((x / t_1) + (y / t_1)), z, (((y * (a - b)) / t_1) + (a / (t_1 / t))));
	} else {
		tmp = t_2 + (a + (x * ((z / (y + t)) - (a / (y + t)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(z - b) / Float64(t_1 / y))
	tmp = 0.0
	if (y <= -1.28e+17)
		tmp = Float64(t_2 + Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(z * x) / t_1)));
	elseif (y <= 2.55e+66)
		tmp = fma(Float64(Float64(x / t_1) + Float64(y / t_1)), z, Float64(Float64(Float64(y * Float64(a - b)) / t_1) + Float64(a / Float64(t_1 / t))));
	else
		tmp = Float64(t_2 + Float64(a + Float64(x * Float64(Float64(z / Float64(y + t)) - Float64(a / Float64(y + t))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.28e+17], N[(t$95$2 + N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+66], N[(N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * z + N[(N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(a + N[(x * N[(N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(a / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.28e17

   1. Initial program 42.9%

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

   3. Simplified 43.7%

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

   4. Taylor expanded in 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* 65.1%

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

      2. +-commutative 65.1%

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

      3. associate-/l* 88.4%

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

   6. Simplified 88.4%

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

   if -1.28e17 < y < 2.55000000000000004e66

   1. Initial program 86.1%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around 0 92.8%

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

      1. fma-def 92.8%

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

      2. associate-/l* 99.1%

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

   6. Simplified 99.1%

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

   if 2.55000000000000004e66 < y

   1. Initial program 38.1%

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

   3. Simplified 38.7%

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

   4. Taylor expanded in a around inf 38.0%

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

      1. associate-/l* 70.8%

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

      2. +-commutative 70.8%

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

      3. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in x around 0 96.5%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+17}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{a}{\frac{y + \left(t + x\right)}{y + t}} + \frac{z \cdot x}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}, z, \frac{y \cdot \left(a - b\right)}{y + \left(t + x\right)} + \frac{a}{\frac{y + \left(t + x\right)}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(a + x \cdot \left(\frac{z}{y + t} - \frac{a}{y + t}\right)\right)\\ \end{array} \]

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - y \cdot b}{t_2}\\ t_4 := \frac{z - b}{\frac{t_2}{y}}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4 + \left(z + \frac{a}{\frac{t_2}{y + t}}\right)\\ \mathbf{elif}\;t_3 \leq 10^{+283}:\\ \;\;\;\;\frac{z \cdot x + \left(t_1 + y \cdot \left(z - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4 + \left(a + x \cdot \left(\frac{z}{y + t} - \frac{a}{y + t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ t x)))
        (t_3 (/ (- (+ (* z (+ y x)) t_1) (* y b)) t_2))
        (t_4 (/ (- z b) (/ t_2 y))))
   (if (<= t_3 (- INFINITY))
     (+ t_4 (+ z (/ a (/ t_2 (+ y t)))))
     (if (<= t_3 1e+283)
       (/ (+ (* z x) (+ t_1 (* y (- z b)))) (+ x (+ y t)))
       (+ t_4 (+ a (* x (- (/ z (+ y t)) (/ a (+ y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (t + x);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double t_4 = (z - b) / (t_2 / y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4 + (z + (a / (t_2 / (y + t))));
	} else if (t_3 <= 1e+283) {
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	} else {
		tmp = t_4 + (a + (x * ((z / (y + t)) - (a / (y + t)))));
	}
	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 + (t + x);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double t_4 = (z - b) / (t_2 / y);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4 + (z + (a / (t_2 / (y + t))));
	} else if (t_3 <= 1e+283) {
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	} else {
		tmp = t_4 + (a + (x * ((z / (y + t)) - (a / (y + t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (t + x)
	t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2
	t_4 = (z - b) / (t_2 / y)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4 + (z + (a / (t_2 / (y + t))))
	elif t_3 <= 1e+283:
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t))
	else:
		tmp = t_4 + (a + (x * ((z / (y + t)) - (a / (y + t)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z - b) / Float64(t_2 / y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_4 + Float64(z + Float64(a / Float64(t_2 / Float64(y + t)))));
	elseif (t_3 <= 1e+283)
		tmp = Float64(Float64(Float64(z * x) + Float64(t_1 + Float64(y * Float64(z - b)))) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(t_4 + Float64(a + Float64(x * Float64(Float64(z / Float64(y + t)) - Float64(a / Float64(y + t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (t + x);
	t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	t_4 = (z - b) / (t_2 / y);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4 + (z + (a / (t_2 / (y + t))));
	elseif (t_3 <= 1e+283)
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	else
		tmp = t_4 + (a + (x * ((z / (y + t)) - (a / (y + t)))));
	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[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$4 + N[(z + N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+283], N[(N[(N[(z * x), $MachinePrecision] + N[(t$95$1 + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(a + N[(x * N[(N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(a / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 6.5%

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

   3. Simplified 6.1%

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

   4. Taylor expanded in a around inf 6.0%

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

      1. associate-/l* 41.1%

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

      2. +-commutative 41.1%

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

      3. associate-/l* 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in x around inf 83.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999955e282

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in a around 0 99.1%

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

   if 9.99999999999999955e282 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.4%

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

   3. Simplified 8.3%

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

   4. Taylor expanded in a around inf 6.8%

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

      1. associate-/l* 39.2%

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

      2. +-commutative 39.2%

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

      3. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in x around 0 81.9%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + \frac{a}{\frac{y + \left(t + x\right)}{y + t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 10^{+283}:\\ \;\;\;\;\frac{z \cdot x + \left(a \cdot \left(y + t\right) + y \cdot \left(z - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(a + x \cdot \left(\frac{z}{y + t} - \frac{a}{y + t}\right)\right)\\ \end{array} \]

Alternative 3: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+259}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x + \left(t_1 + y \cdot \left(z - b\right)\right)}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (/ (- (+ (* z (+ y x)) t_1) (* y b)) (+ y (+ t x)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+259)))
     (- (+ z a) b)
     (/ (+ (* z x) (+ t_1 (* y (- z b)))) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (((z * (y + x)) + t_1) - (y * b)) / (y + (t + x));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+259)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	}
	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 = (((z * (y + x)) + t_1) - (y * b)) / (y + (t + x));
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+259)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = (((z * (y + x)) + t_1) - (y * b)) / (y + (t + x))
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+259):
		tmp = (z + a) - b
	else:
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(y * b)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+259))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(z * x) + Float64(t_1 + Float64(y * Float64(z - b)))) / Float64(x + Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = (((z * (y + x)) + t_1) - (y * b)) / (y + (t + x));
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+259)))
		tmp = (z + a) - b;
	else
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	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[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+259]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] + N[(t$95$1 + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2e259 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.5%

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

   2. Taylor expanded in y around inf 75.2%

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

      1. +-commutative 75.2%

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

   4. Simplified 75.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e259

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in a around 0 99.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 2 \cdot 10^{+259}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x + \left(a \cdot \left(y + t\right) + y \cdot \left(z - b\right)\right)}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 4: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{t_2}{y}} + \left(z + \frac{a}{\frac{t_2}{y + t}}\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot x + \left(t_1 + y \cdot \left(z - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ t x)))
        (t_3 (/ (- (+ (* z (+ y x)) t_1) (* y b)) t_2)))
   (if (<= t_3 (- INFINITY))
     (+ (/ (- z b) (/ t_2 y)) (+ z (/ a (/ t_2 (+ y t)))))
     (if (<= t_3 2e+259)
       (/ (+ (* z x) (+ t_1 (* y (- z b)))) (+ x (+ y t)))
       (- (+ 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 + (t + x);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((z - b) / (t_2 / y)) + (z + (a / (t_2 / (y + t))));
	} else if (t_3 <= 2e+259) {
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	} else {
		tmp = (z + a) - b;
	}
	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 + (t + x);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z - b) / (t_2 / y)) + (z + (a / (t_2 / (y + t))));
	} else if (t_3 <= 2e+259) {
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (t + x)
	t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = ((z - b) / (t_2 / y)) + (z + (a / (t_2 / (y + t))))
	elif t_3 <= 2e+259:
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t))
	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(t + x))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_2 / y)) + Float64(z + Float64(a / Float64(t_2 / Float64(y + t)))));
	elseif (t_3 <= 2e+259)
		tmp = Float64(Float64(Float64(z * x) + Float64(t_1 + Float64(y * Float64(z - b)))) / Float64(x + Float64(y + t)));
	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 + (t + x);
	t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = ((z - b) / (t_2 / y)) + (z + (a / (t_2 / (y + t))));
	elseif (t_3 <= 2e+259)
		tmp = ((z * x) + (t_1 + (y * (z - b)))) / (x + (y + t));
	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[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] + N[(z + N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+259], N[(N[(N[(z * x), $MachinePrecision] + N[(t$95$1 + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $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 6.5%

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

   3. Simplified 6.1%

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

   4. Taylor expanded in a around inf 6.0%

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

      1. associate-/l* 41.1%

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

      2. +-commutative 41.1%

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

      3. associate-/l* 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in x around inf 83.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e259

   1. Initial program 99.1%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in a around 0 99.1%

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

   if 2e259 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.8%

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

   2. Taylor expanded in y around inf 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 3 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + \frac{a}{\frac{y + \left(t + x\right)}{y + t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(t + x\right)} \leq 2 \cdot 10^{+259}:\\ \;\;\;\;\frac{z \cdot x + \left(a \cdot \left(y + t\right) + y \cdot \left(z - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \frac{z - b}{\frac{t_1}{y}}\\ \mathbf{if}\;x \leq -4 \cdot 10^{+119} \lor \neg \left(x \leq 5.5 \cdot 10^{+46}\right):\\ \;\;\;\;t_3 + \left(z + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(t_2 + \frac{z \cdot x}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ a (/ t_1 (+ y t))))
        (t_3 (/ (- z b) (/ t_1 y))))
   (if (or (<= x -4e+119) (not (<= x 5.5e+46)))
     (+ t_3 (+ z t_2))
     (+ t_3 (+ t_2 (/ (* z x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z - b) / (t_1 / y);
	double tmp;
	if ((x <= -4e+119) || !(x <= 5.5e+46)) {
		tmp = t_3 + (z + t_2);
	} else {
		tmp = t_3 + (t_2 + ((z * x) / 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) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z - b) / (t_1 / y)
    if ((x <= (-4d+119)) .or. (.not. (x <= 5.5d+46))) then
        tmp = t_3 + (z + t_2)
    else
        tmp = t_3 + (t_2 + ((z * x) / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z - b) / (t_1 / y);
	double tmp;
	if ((x <= -4e+119) || !(x <= 5.5e+46)) {
		tmp = t_3 + (z + t_2);
	} else {
		tmp = t_3 + (t_2 + ((z * x) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z - b) / (t_1 / y)
	tmp = 0
	if (x <= -4e+119) or not (x <= 5.5e+46):
		tmp = t_3 + (z + t_2)
	else:
		tmp = t_3 + (t_2 + ((z * x) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z - b) / Float64(t_1 / y))
	tmp = 0.0
	if ((x <= -4e+119) || !(x <= 5.5e+46))
		tmp = Float64(t_3 + Float64(z + t_2));
	else
		tmp = Float64(t_3 + Float64(t_2 + Float64(Float64(z * x) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z - b) / (t_1 / y);
	tmp = 0.0;
	if ((x <= -4e+119) || ~((x <= 5.5e+46)))
		tmp = t_3 + (z + t_2);
	else
		tmp = t_3 + (t_2 + ((z * x) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -4e+119], N[Not[LessEqual[x, 5.5e+46]], $MachinePrecision]], N[(t$95$3 + N[(z + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + N[(t$95$2 + N[(N[(z * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999978e119 or 5.4999999999999998e46 < x

   1. Initial program 60.2%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in a around inf 59.8%

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

      1. associate-/l* 63.4%

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

      2. +-commutative 63.4%

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

      3. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in x around inf 88.4%

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

   if -3.99999999999999978e119 < x < 5.4999999999999998e46

   1. Initial program 69.2%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 82.8%

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

      2. +-commutative 82.8%

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

      3. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+119} \lor \neg \left(x \leq 5.5 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + \frac{a}{\frac{y + \left(t + x\right)}{y + t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{a}{\frac{y + \left(t + x\right)}{y + t}} + \frac{z \cdot x}{y + \left(t + x\right)}\right)\\ \end{array} \]

Alternative 6: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-291}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot t_2}{t_1}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+57}:\\ \;\;\;\;z + y \cdot \frac{z - b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (- (+ z a) b))
        (t_3 (/ (+ (* z x) (* t a)) (+ t x))))
   (if (<= y -1.6e+22)
     t_2
     (if (<= y -3.9e-40)
       (/ a (/ t_1 (+ y t)))
       (if (<= y -4.9e-95)
         t_2
         (if (<= y -1e-291)
           t_3
           (if (<= y 2.7e-212)
             (+ z (/ (* t a) (+ t x)))
             (if (<= y 3.1e-58)
               t_3
               (if (<= y 2.6e+15)
                 (/ (* y t_2) t_1)
                 (if (<= y 3.1e+57) (+ z (* y (/ (- z b) t_1))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (z + a) - b;
	double t_3 = ((z * x) + (t * a)) / (t + x);
	double tmp;
	if (y <= -1.6e+22) {
		tmp = t_2;
	} else if (y <= -3.9e-40) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= -4.9e-95) {
		tmp = t_2;
	} else if (y <= -1e-291) {
		tmp = t_3;
	} else if (y <= 2.7e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 3.1e-58) {
		tmp = t_3;
	} else if (y <= 2.6e+15) {
		tmp = (y * t_2) / t_1;
	} else if (y <= 3.1e+57) {
		tmp = z + (y * ((z - b) / 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 = y + (t + x)
    t_2 = (z + a) - b
    t_3 = ((z * x) + (t * a)) / (t + x)
    if (y <= (-1.6d+22)) then
        tmp = t_2
    else if (y <= (-3.9d-40)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= (-4.9d-95)) then
        tmp = t_2
    else if (y <= (-1d-291)) then
        tmp = t_3
    else if (y <= 2.7d-212) then
        tmp = z + ((t * a) / (t + x))
    else if (y <= 3.1d-58) then
        tmp = t_3
    else if (y <= 2.6d+15) then
        tmp = (y * t_2) / t_1
    else if (y <= 3.1d+57) then
        tmp = z + (y * ((z - b) / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (z + a) - b;
	double t_3 = ((z * x) + (t * a)) / (t + x);
	double tmp;
	if (y <= -1.6e+22) {
		tmp = t_2;
	} else if (y <= -3.9e-40) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= -4.9e-95) {
		tmp = t_2;
	} else if (y <= -1e-291) {
		tmp = t_3;
	} else if (y <= 2.7e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 3.1e-58) {
		tmp = t_3;
	} else if (y <= 2.6e+15) {
		tmp = (y * t_2) / t_1;
	} else if (y <= 3.1e+57) {
		tmp = z + (y * ((z - b) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (z + a) - b
	t_3 = ((z * x) + (t * a)) / (t + x)
	tmp = 0
	if y <= -1.6e+22:
		tmp = t_2
	elif y <= -3.9e-40:
		tmp = a / (t_1 / (y + t))
	elif y <= -4.9e-95:
		tmp = t_2
	elif y <= -1e-291:
		tmp = t_3
	elif y <= 2.7e-212:
		tmp = z + ((t * a) / (t + x))
	elif y <= 3.1e-58:
		tmp = t_3
	elif y <= 2.6e+15:
		tmp = (y * t_2) / t_1
	elif y <= 3.1e+57:
		tmp = z + (y * ((z - b) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x))
	tmp = 0.0
	if (y <= -1.6e+22)
		tmp = t_2;
	elseif (y <= -3.9e-40)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= -4.9e-95)
		tmp = t_2;
	elseif (y <= -1e-291)
		tmp = t_3;
	elseif (y <= 2.7e-212)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	elseif (y <= 3.1e-58)
		tmp = t_3;
	elseif (y <= 2.6e+15)
		tmp = Float64(Float64(y * t_2) / t_1);
	elseif (y <= 3.1e+57)
		tmp = Float64(z + Float64(y * Float64(Float64(z - b) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = (z + a) - b;
	t_3 = ((z * x) + (t * a)) / (t + x);
	tmp = 0.0;
	if (y <= -1.6e+22)
		tmp = t_2;
	elseif (y <= -3.9e-40)
		tmp = a / (t_1 / (y + t));
	elseif (y <= -4.9e-95)
		tmp = t_2;
	elseif (y <= -1e-291)
		tmp = t_3;
	elseif (y <= 2.7e-212)
		tmp = z + ((t * a) / (t + x));
	elseif (y <= 3.1e-58)
		tmp = t_3;
	elseif (y <= 2.6e+15)
		tmp = (y * t_2) / t_1;
	elseif (y <= 3.1e+57)
		tmp = z + (y * ((z - b) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+22], t$95$2, If[LessEqual[y, -3.9e-40], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.9e-95], t$95$2, If[LessEqual[y, -1e-291], t$95$3, If[LessEqual[y, 2.7e-212], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-58], t$95$3, If[LessEqual[y, 2.6e+15], N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3.1e+57], N[(z + N[(y * N[(N[(z - b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.6e22 or -3.89999999999999981e-40 < y < -4.9e-95 or 3.10000000000000013e57 < y

   1. Initial program 44.3%

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

   2. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

   4. Simplified 76.3%

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

   if -1.6e22 < y < -3.89999999999999981e-40

   1. Initial program 85.9%

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

   2. Taylor expanded in a around inf 56.8%

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

      1. associate-/l* 70.8%

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

   4. Simplified 70.8%

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

   if -4.9e-95 < y < -9.99999999999999962e-292 or 2.69999999999999981e-212 < y < 3.0999999999999999e-58

   1. Initial program 90.2%

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

   2. Taylor expanded in y around 0 68.8%

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

   if -9.99999999999999962e-292 < y < 2.69999999999999981e-212

   1. Initial program 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in a around inf 77.3%

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

      1. associate-/l* 74.1%

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

      2. +-commutative 74.1%

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

      3. associate-/l* 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in x around inf 89.3%

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

   8. Taylor expanded in y around 0 76.9%

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

   if 3.0999999999999999e-58 < y < 2.6e15

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 64.2%

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

      1. +-commutative 64.2%

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

   4. Simplified 64.2%

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

   if 2.6e15 < y < 3.10000000000000013e57

   1. Initial program 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in a around inf 82.4%

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

      1. associate-/l* 82.4%

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

      2. +-commutative 82.4%

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

      3. associate-/l* 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in x around inf 91.4%

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

   8. Taylor expanded in a around 0 56.3%

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

      1. associate-/l* 64.9%

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

      2. +-commutative 64.9%

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

      3. associate-/r/ 64.9%

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

      4. +-commutative 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-95}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-291}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+57}:\\ \;\;\;\;z + y \cdot \frac{z - b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 7: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-124}:\\ \;\;\;\;\frac{y + x}{\frac{t_1}{z}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (/ a (/ t_1 (+ y t)))) (t_3 (- (+ z a) b)))
   (if (<= y -2.5e+21)
     t_3
     (if (<= y -7.7e-87)
       t_2
       (if (<= y -7.3e-124)
         (/ (+ y x) (/ t_1 z))
         (if (<= y -4.2e-153)
           t_2
           (if (<= y 3.4e-212)
             (+ z (/ (* t a) (+ t x)))
             (if (<= y 6.8e-122)
               t_2
               (if (<= y 1.55e+41) (/ (* z (+ y x)) t_1) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -2.5e+21) {
		tmp = t_3;
	} else if (y <= -7.7e-87) {
		tmp = t_2;
	} else if (y <= -7.3e-124) {
		tmp = (y + x) / (t_1 / z);
	} else if (y <= -4.2e-153) {
		tmp = t_2;
	} else if (y <= 3.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 6.8e-122) {
		tmp = t_2;
	} else if (y <= 1.55e+41) {
		tmp = (z * (y + x)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z + a) - b
    if (y <= (-2.5d+21)) then
        tmp = t_3
    else if (y <= (-7.7d-87)) then
        tmp = t_2
    else if (y <= (-7.3d-124)) then
        tmp = (y + x) / (t_1 / z)
    else if (y <= (-4.2d-153)) then
        tmp = t_2
    else if (y <= 3.4d-212) then
        tmp = z + ((t * a) / (t + x))
    else if (y <= 6.8d-122) then
        tmp = t_2
    else if (y <= 1.55d+41) then
        tmp = (z * (y + x)) / t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -2.5e+21) {
		tmp = t_3;
	} else if (y <= -7.7e-87) {
		tmp = t_2;
	} else if (y <= -7.3e-124) {
		tmp = (y + x) / (t_1 / z);
	} else if (y <= -4.2e-153) {
		tmp = t_2;
	} else if (y <= 3.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 6.8e-122) {
		tmp = t_2;
	} else if (y <= 1.55e+41) {
		tmp = (z * (y + x)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -2.5e+21:
		tmp = t_3
	elif y <= -7.7e-87:
		tmp = t_2
	elif y <= -7.3e-124:
		tmp = (y + x) / (t_1 / z)
	elif y <= -4.2e-153:
		tmp = t_2
	elif y <= 3.4e-212:
		tmp = z + ((t * a) / (t + x))
	elif y <= 6.8e-122:
		tmp = t_2
	elif y <= 1.55e+41:
		tmp = (z * (y + x)) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.5e+21)
		tmp = t_3;
	elseif (y <= -7.7e-87)
		tmp = t_2;
	elseif (y <= -7.3e-124)
		tmp = Float64(Float64(y + x) / Float64(t_1 / z));
	elseif (y <= -4.2e-153)
		tmp = t_2;
	elseif (y <= 3.4e-212)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	elseif (y <= 6.8e-122)
		tmp = t_2;
	elseif (y <= 1.55e+41)
		tmp = Float64(Float64(z * Float64(y + x)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.5e+21)
		tmp = t_3;
	elseif (y <= -7.7e-87)
		tmp = t_2;
	elseif (y <= -7.3e-124)
		tmp = (y + x) / (t_1 / z);
	elseif (y <= -4.2e-153)
		tmp = t_2;
	elseif (y <= 3.4e-212)
		tmp = z + ((t * a) / (t + x));
	elseif (y <= 6.8e-122)
		tmp = t_2;
	elseif (y <= 1.55e+41)
		tmp = (z * (y + x)) / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.5e+21], t$95$3, If[LessEqual[y, -7.7e-87], t$95$2, If[LessEqual[y, -7.3e-124], N[(N[(y + x), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-153], t$95$2, If[LessEqual[y, 3.4e-212], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-122], t$95$2, If[LessEqual[y, 1.55e+41], N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.5e21 or 1.55e41 < y

   1. Initial program 43.5%

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

   2. Taylor expanded in y around 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%

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

   if -2.5e21 < y < -7.6999999999999998e-87 or -7.3e-124 < y < -4.20000000000000008e-153 or 3.39999999999999998e-212 < y < 6.7999999999999996e-122

   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 a around inf 47.8%

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

      1. associate-/l* 66.1%

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

   4. Simplified 66.1%

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

   if -7.6999999999999998e-87 < y < -7.3e-124

   1. Initial program 88.6%

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

   2. Taylor expanded in z around inf 59.3%

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

      1. associate-/l* 70.5%

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

   4. Simplified 70.5%

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

   if -4.20000000000000008e-153 < y < 3.39999999999999998e-212

   1. Initial program 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in a around inf 86.7%

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

      1. associate-/l* 81.6%

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

      2. +-commutative 81.6%

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

      3. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in x around inf 79.5%

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

   8. Taylor expanded in y around 0 71.5%

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

   if 6.7999999999999996e-122 < y < 1.55e41

   1. Initial program 93.0%

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

   2. Taylor expanded in z around inf 52.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-87}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-124}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(t + x\right)}{z}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right)}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 64.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{t_1}\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-228}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{z \cdot x + y \cdot \left(\left(z + a\right) - b\right)}{y + x}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (* y (* (+ z (- a b)) (/ 1.0 t_1)))))
   (if (<= y -6.5e+18)
     t_2
     (if (<= y -1.15e-228)
       (/ (- (* a (+ y t)) (* y b)) t_1)
       (if (<= y 2.4e-212)
         (+ z (/ (* t a) (+ t x)))
         (if (<= y 1.3e-93)
           (/ (+ (* z x) (* t a)) (+ t x))
           (if (<= y 4.6e+54)
             (/ (+ (* z x) (* y (- (+ z a) b))) (+ y x))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y * ((z + (a - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -6.5e+18) {
		tmp = t_2;
	} else if (y <= -1.15e-228) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 2.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 1.3e-93) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 4.6e+54) {
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = y * ((z + (a - b)) * (1.0d0 / t_1))
    if (y <= (-6.5d+18)) then
        tmp = t_2
    else if (y <= (-1.15d-228)) then
        tmp = ((a * (y + t)) - (y * b)) / t_1
    else if (y <= 2.4d-212) then
        tmp = z + ((t * a) / (t + x))
    else if (y <= 1.3d-93) then
        tmp = ((z * x) + (t * a)) / (t + x)
    else if (y <= 4.6d+54) then
        tmp = ((z * x) + (y * ((z + a) - b))) / (y + x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y * ((z + (a - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -6.5e+18) {
		tmp = t_2;
	} else if (y <= -1.15e-228) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (y <= 2.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 1.3e-93) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 4.6e+54) {
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = y * ((z + (a - b)) * (1.0 / t_1))
	tmp = 0
	if y <= -6.5e+18:
		tmp = t_2
	elif y <= -1.15e-228:
		tmp = ((a * (y + t)) - (y * b)) / t_1
	elif y <= 2.4e-212:
		tmp = z + ((t * a) / (t + x))
	elif y <= 1.3e-93:
		tmp = ((z * x) + (t * a)) / (t + x)
	elif y <= 4.6e+54:
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(y * Float64(Float64(z + Float64(a - b)) * Float64(1.0 / t_1)))
	tmp = 0.0
	if (y <= -6.5e+18)
		tmp = t_2;
	elseif (y <= -1.15e-228)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1);
	elseif (y <= 2.4e-212)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	elseif (y <= 1.3e-93)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x));
	elseif (y <= 4.6e+54)
		tmp = Float64(Float64(Float64(z * x) + Float64(y * Float64(Float64(z + a) - b))) / Float64(y + x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = y * ((z + (a - b)) * (1.0 / t_1));
	tmp = 0.0;
	if (y <= -6.5e+18)
		tmp = t_2;
	elseif (y <= -1.15e-228)
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	elseif (y <= 2.4e-212)
		tmp = z + ((t * a) / (t + x));
	elseif (y <= 1.3e-93)
		tmp = ((z * x) + (t * a)) / (t + x);
	elseif (y <= 4.6e+54)
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+18], t$95$2, If[LessEqual[y, -1.15e-228], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.4e-212], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-93], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+54], N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.5e18 or 4.59999999999999988e54 < y

   1. Initial program 41.1%

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

   2. Taylor expanded in y around inf 37.1%

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

      1. +-commutative 37.1%

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

   4. Simplified 37.1%

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

      1. div-inv 37.1%

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

      2. associate--l+ 37.1%

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

      3. +-commutative 37.1%

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

      4. +-commutative 37.1%

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

      5. +-commutative 37.1%

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

   6. Applied egg-rr 37.1%

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

      1. associate-*l* 82.0%

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

   8. Simplified 82.0%

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

   if -6.5e18 < y < -1.1499999999999999e-228

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 62.5%

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

   if -1.1499999999999999e-228 < y < 2.39999999999999989e-212

   1. Initial program 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in a around inf 83.1%

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

      1. associate-/l* 80.7%

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

      2. +-commutative 80.7%

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

      3. associate-/l* 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around inf 84.6%

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

   8. Taylor expanded in y around 0 75.4%

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

   if 2.39999999999999989e-212 < y < 1.2999999999999999e-93

   1. Initial program 87.8%

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

   2. Taylor expanded in y around 0 68.7%

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

   if 1.2999999999999999e-93 < y < 4.59999999999999988e54

   1. Initial program 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around 0 77.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-228}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{z \cdot x + y \cdot \left(\left(z + a\right) - b\right)}{y + x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \end{array} \]

Alternative 9: 62.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ (+ (* z x) (* t a)) (+ t x))))
   (if (<= y -1.55e+22)
     t_1
     (if (<= y -6.5e-41)
       (/ a (/ (+ y (+ t x)) (+ y t)))
       (if (<= y -1.75e-96)
         t_1
         (if (<= y -9.5e-292)
           t_2
           (if (<= y 2.7e-212)
             (+ z (/ (* t a) (+ t x)))
             (if (<= y 1.45e+41) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = ((z * x) + (t * a)) / (t + x);
	double tmp;
	if (y <= -1.55e+22) {
		tmp = t_1;
	} else if (y <= -6.5e-41) {
		tmp = a / ((y + (t + x)) / (y + t));
	} else if (y <= -1.75e-96) {
		tmp = t_1;
	} else if (y <= -9.5e-292) {
		tmp = t_2;
	} else if (y <= 2.7e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 1.45e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = ((z * x) + (t * a)) / (t + x)
    if (y <= (-1.55d+22)) then
        tmp = t_1
    else if (y <= (-6.5d-41)) then
        tmp = a / ((y + (t + x)) / (y + t))
    else if (y <= (-1.75d-96)) then
        tmp = t_1
    else if (y <= (-9.5d-292)) then
        tmp = t_2
    else if (y <= 2.7d-212) then
        tmp = z + ((t * a) / (t + x))
    else if (y <= 1.45d+41) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = ((z * x) + (t * a)) / (t + x);
	double tmp;
	if (y <= -1.55e+22) {
		tmp = t_1;
	} else if (y <= -6.5e-41) {
		tmp = a / ((y + (t + x)) / (y + t));
	} else if (y <= -1.75e-96) {
		tmp = t_1;
	} else if (y <= -9.5e-292) {
		tmp = t_2;
	} else if (y <= 2.7e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 1.45e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = ((z * x) + (t * a)) / (t + x)
	tmp = 0
	if y <= -1.55e+22:
		tmp = t_1
	elif y <= -6.5e-41:
		tmp = a / ((y + (t + x)) / (y + t))
	elif y <= -1.75e-96:
		tmp = t_1
	elif y <= -9.5e-292:
		tmp = t_2
	elif y <= 2.7e-212:
		tmp = z + ((t * a) / (t + x))
	elif y <= 1.45e+41:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x))
	tmp = 0.0
	if (y <= -1.55e+22)
		tmp = t_1;
	elseif (y <= -6.5e-41)
		tmp = Float64(a / Float64(Float64(y + Float64(t + x)) / Float64(y + t)));
	elseif (y <= -1.75e-96)
		tmp = t_1;
	elseif (y <= -9.5e-292)
		tmp = t_2;
	elseif (y <= 2.7e-212)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	elseif (y <= 1.45e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = ((z * x) + (t * a)) / (t + x);
	tmp = 0.0;
	if (y <= -1.55e+22)
		tmp = t_1;
	elseif (y <= -6.5e-41)
		tmp = a / ((y + (t + x)) / (y + t));
	elseif (y <= -1.75e-96)
		tmp = t_1;
	elseif (y <= -9.5e-292)
		tmp = t_2;
	elseif (y <= 2.7e-212)
		tmp = z + ((t * a) / (t + x));
	elseif (y <= 1.45e+41)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+22], t$95$1, If[LessEqual[y, -6.5e-41], N[(a / N[(N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-96], t$95$1, If[LessEqual[y, -9.5e-292], t$95$2, If[LessEqual[y, 2.7e-212], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+41], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5500000000000001e22 or -6.5000000000000004e-41 < y < -1.7499999999999999e-96 or 1.44999999999999994e41 < y

   1. Initial program 46.1%

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

   2. Taylor expanded in y around inf 75.2%

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

      1. +-commutative 75.2%

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

   4. Simplified 75.2%

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

   if -1.5500000000000001e22 < y < -6.5000000000000004e-41

   1. Initial program 85.9%

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

   2. Taylor expanded in a around inf 56.8%

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

      1. associate-/l* 70.8%

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

   4. Simplified 70.8%

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

   if -1.7499999999999999e-96 < y < -9.4999999999999994e-292 or 2.69999999999999981e-212 < y < 1.44999999999999994e41

   1. Initial program 89.8%

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

   2. Taylor expanded in y around 0 62.5%

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

   if -9.4999999999999994e-292 < y < 2.69999999999999981e-212

   1. Initial program 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in a around inf 77.3%

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

      1. associate-/l* 74.1%

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

      2. +-commutative 74.1%

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

      3. associate-/l* 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in x around inf 89.3%

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

   8. Taylor expanded in y around 0 76.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-96}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{t_1}\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{t_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+44}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (* y (* (+ z (- a b)) (/ 1.0 t_1)))))
   (if (<= y -1.7e-34)
     t_2
     (if (<= y 1.35e-58)
       (/ (+ (* z x) (* t a)) (+ t x))
       (if (<= y 1.8e+15)
         (/ (* y (- (+ z a) b)) t_1)
         (if (<= y 4e+44) (+ z (/ (* t a) (+ t x))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y * ((z + (a - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -1.7e-34) {
		tmp = t_2;
	} else if (y <= 1.35e-58) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 1.8e+15) {
		tmp = (y * ((z + a) - b)) / t_1;
	} else if (y <= 4e+44) {
		tmp = z + ((t * a) / (t + x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = y * ((z + (a - b)) * (1.0d0 / t_1))
    if (y <= (-1.7d-34)) then
        tmp = t_2
    else if (y <= 1.35d-58) then
        tmp = ((z * x) + (t * a)) / (t + x)
    else if (y <= 1.8d+15) then
        tmp = (y * ((z + a) - b)) / t_1
    else if (y <= 4d+44) then
        tmp = z + ((t * a) / (t + x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y * ((z + (a - b)) * (1.0 / t_1));
	double tmp;
	if (y <= -1.7e-34) {
		tmp = t_2;
	} else if (y <= 1.35e-58) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 1.8e+15) {
		tmp = (y * ((z + a) - b)) / t_1;
	} else if (y <= 4e+44) {
		tmp = z + ((t * a) / (t + x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = y * ((z + (a - b)) * (1.0 / t_1))
	tmp = 0
	if y <= -1.7e-34:
		tmp = t_2
	elif y <= 1.35e-58:
		tmp = ((z * x) + (t * a)) / (t + x)
	elif y <= 1.8e+15:
		tmp = (y * ((z + a) - b)) / t_1
	elif y <= 4e+44:
		tmp = z + ((t * a) / (t + x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(y * Float64(Float64(z + Float64(a - b)) * Float64(1.0 / t_1)))
	tmp = 0.0
	if (y <= -1.7e-34)
		tmp = t_2;
	elseif (y <= 1.35e-58)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x));
	elseif (y <= 1.8e+15)
		tmp = Float64(Float64(y * Float64(Float64(z + a) - b)) / t_1);
	elseif (y <= 4e+44)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = y * ((z + (a - b)) * (1.0 / t_1));
	tmp = 0.0;
	if (y <= -1.7e-34)
		tmp = t_2;
	elseif (y <= 1.35e-58)
		tmp = ((z * x) + (t * a)) / (t + x);
	elseif (y <= 1.8e+15)
		tmp = (y * ((z + a) - b)) / t_1;
	elseif (y <= 4e+44)
		tmp = z + ((t * a) / (t + x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-34], t$95$2, If[LessEqual[y, 1.35e-58], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+15], N[(N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4e+44], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7e-34 or 4.0000000000000004e44 < y

   1. Initial program 46.7%

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

   2. Taylor expanded in y around inf 40.1%

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

      1. +-commutative 40.1%

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

   4. Simplified 40.1%

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

      1. div-inv 40.0%

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

      2. associate--l+ 40.0%

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

      3. +-commutative 40.0%

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

      4. +-commutative 40.0%

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

      5. +-commutative 40.0%

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

   6. Applied egg-rr 40.0%

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

      1. associate-*l* 80.6%

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

   8. Simplified 80.6%

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

   if -1.7e-34 < y < 1.3499999999999999e-58

   1. Initial program 84.8%

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

   2. Taylor expanded in y around 0 63.7%

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

   if 1.3499999999999999e-58 < y < 1.8e15

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 64.2%

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

      1. +-commutative 64.2%

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

   4. Simplified 64.2%

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

   if 1.8e15 < y < 4.0000000000000004e44

   1. Initial program 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in a around inf 76.0%

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

      1. associate-/l* 76.0%

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

      2. +-commutative 76.0%

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

      3. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in x around inf 88.2%

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

   8. Taylor expanded in y around 0 70.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+44}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \end{array} \]

Alternative 11: 69.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+15} \lor \neg \left(y \leq 4.4 \cdot 10^{+42}\right):\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x + \left(a \cdot \left(y + t\right) + y \cdot z\right)}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e+15) (not (<= y 4.4e+42)))
   (* y (* (+ z (- a b)) (/ 1.0 (+ y (+ t x)))))
   (/ (+ (* z x) (+ (* a (+ y t)) (* y z))) (+ x (+ y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e+15) || !(y <= 4.4e+42)) {
		tmp = y * ((z + (a - b)) * (1.0 / (y + (t + x))));
	} else {
		tmp = ((z * x) + ((a * (y + t)) + (y * z))) / (x + (y + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.4d+15)) .or. (.not. (y <= 4.4d+42))) then
        tmp = y * ((z + (a - b)) * (1.0d0 / (y + (t + x))))
    else
        tmp = ((z * x) + ((a * (y + t)) + (y * z))) / (x + (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e+15) || !(y <= 4.4e+42)) {
		tmp = y * ((z + (a - b)) * (1.0 / (y + (t + x))));
	} else {
		tmp = ((z * x) + ((a * (y + t)) + (y * z))) / (x + (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.4e+15) or not (y <= 4.4e+42):
		tmp = y * ((z + (a - b)) * (1.0 / (y + (t + x))))
	else:
		tmp = ((z * x) + ((a * (y + t)) + (y * z))) / (x + (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.4e+15) || !(y <= 4.4e+42))
		tmp = Float64(y * Float64(Float64(z + Float64(a - b)) * Float64(1.0 / Float64(y + Float64(t + x)))));
	else
		tmp = Float64(Float64(Float64(z * x) + Float64(Float64(a * Float64(y + t)) + Float64(y * z))) / Float64(x + Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.4e+15) || ~((y <= 4.4e+42)))
		tmp = y * ((z + (a - b)) * (1.0 / (y + (t + x))));
	else
		tmp = ((z * x) + ((a * (y + t)) + (y * z))) / (x + (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.4e+15], N[Not[LessEqual[y, 4.4e+42]], $MachinePrecision]], N[(y * N[(N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] + N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e15 or 4.4000000000000003e42 < y

   1. Initial program 42.7%

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

   2. Taylor expanded in y around inf 38.2%

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

      1. +-commutative 38.2%

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

   4. Simplified 38.2%

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

      1. div-inv 38.1%

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

      2. associate--l+ 38.1%

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

      3. +-commutative 38.1%

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

      4. +-commutative 38.1%

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

      5. +-commutative 38.1%

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

   6. Applied egg-rr 38.1%

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

      1. associate-*l* 81.2%

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

   8. Simplified 81.2%

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

   if -4.4e15 < y < 4.4000000000000003e42

   1. Initial program 86.2%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in a around 0 86.2%

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

   5. Taylor expanded in b around 0 71.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+15} \lor \neg \left(y \leq 4.4 \cdot 10^{+42}\right):\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x + \left(a \cdot \left(y + t\right) + y \cdot z\right)}{x + \left(y + t\right)}\\ \end{array} \]

Alternative 12: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (/ a (/ t_1 (+ y t)))) (t_3 (- (+ z a) b)))
   (if (<= y -5.8e+20)
     t_3
     (if (<= y -4.8e-40)
       t_2
       (if (<= y 3.4e-212)
         (+ z (/ (* t a) (+ t x)))
         (if (<= y 8.5e-122)
           t_2
           (if (<= y 1.45e+41) (/ (* z (+ y x)) t_1) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -5.8e+20) {
		tmp = t_3;
	} else if (y <= -4.8e-40) {
		tmp = t_2;
	} else if (y <= 3.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 8.5e-122) {
		tmp = t_2;
	} else if (y <= 1.45e+41) {
		tmp = (z * (y + x)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z + a) - b
    if (y <= (-5.8d+20)) then
        tmp = t_3
    else if (y <= (-4.8d-40)) then
        tmp = t_2
    else if (y <= 3.4d-212) then
        tmp = z + ((t * a) / (t + x))
    else if (y <= 8.5d-122) then
        tmp = t_2
    else if (y <= 1.45d+41) then
        tmp = (z * (y + x)) / t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -5.8e+20) {
		tmp = t_3;
	} else if (y <= -4.8e-40) {
		tmp = t_2;
	} else if (y <= 3.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 8.5e-122) {
		tmp = t_2;
	} else if (y <= 1.45e+41) {
		tmp = (z * (y + x)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -5.8e+20:
		tmp = t_3
	elif y <= -4.8e-40:
		tmp = t_2
	elif y <= 3.4e-212:
		tmp = z + ((t * a) / (t + x))
	elif y <= 8.5e-122:
		tmp = t_2
	elif y <= 1.45e+41:
		tmp = (z * (y + x)) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.8e+20)
		tmp = t_3;
	elseif (y <= -4.8e-40)
		tmp = t_2;
	elseif (y <= 3.4e-212)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	elseif (y <= 8.5e-122)
		tmp = t_2;
	elseif (y <= 1.45e+41)
		tmp = Float64(Float64(z * Float64(y + x)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.8e+20)
		tmp = t_3;
	elseif (y <= -4.8e-40)
		tmp = t_2;
	elseif (y <= 3.4e-212)
		tmp = z + ((t * a) / (t + x));
	elseif (y <= 8.5e-122)
		tmp = t_2;
	elseif (y <= 1.45e+41)
		tmp = (z * (y + x)) / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.8e+20], t$95$3, If[LessEqual[y, -4.8e-40], t$95$2, If[LessEqual[y, 3.4e-212], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-122], t$95$2, If[LessEqual[y, 1.45e+41], N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8e20 or 1.44999999999999994e41 < y

   1. Initial program 43.5%

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

   2. Taylor expanded in y around 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%

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

   if -5.8e20 < y < -4.79999999999999982e-40 or 3.39999999999999998e-212 < y < 8.50000000000000003e-122

   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 a around inf 54.4%

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

      1. associate-/l* 70.3%

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

   4. Simplified 70.3%

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

   if -4.79999999999999982e-40 < y < 3.39999999999999998e-212

   1. Initial program 83.6%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in a around inf 83.6%

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

      1. associate-/l* 78.9%

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

      2. +-commutative 78.9%

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

      3. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in x around inf 78.6%

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

   8. Taylor expanded in y around 0 63.9%

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

   if 8.50000000000000003e-122 < y < 1.44999999999999994e41

   1. Initial program 93.0%

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

   2. Taylor expanded in z around inf 52.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right)}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 13: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot x + y \cdot \left(\left(z + a\right) - b\right)}{y + x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* (+ z (- a b)) (/ 1.0 (+ y (+ t x)))))))
   (if (<= y -2.1e-35)
     t_1
     (if (<= y 1.15e-93)
       (/ (+ (* z x) (* t a)) (+ t x))
       (if (<= y 7e+57) (/ (+ (* z x) (* y (- (+ z a) b))) (+ y x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * ((z + (a - b)) * (1.0 / (y + (t + x))));
	double tmp;
	if (y <= -2.1e-35) {
		tmp = t_1;
	} else if (y <= 1.15e-93) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 7e+57) {
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z + (a - b)) * (1.0d0 / (y + (t + x))))
    if (y <= (-2.1d-35)) then
        tmp = t_1
    else if (y <= 1.15d-93) then
        tmp = ((z * x) + (t * a)) / (t + x)
    else if (y <= 7d+57) then
        tmp = ((z * x) + (y * ((z + a) - b))) / (y + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * ((z + (a - b)) * (1.0 / (y + (t + x))));
	double tmp;
	if (y <= -2.1e-35) {
		tmp = t_1;
	} else if (y <= 1.15e-93) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 7e+57) {
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * ((z + (a - b)) * (1.0 / (y + (t + x))))
	tmp = 0
	if y <= -2.1e-35:
		tmp = t_1
	elif y <= 1.15e-93:
		tmp = ((z * x) + (t * a)) / (t + x)
	elif y <= 7e+57:
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(Float64(z + Float64(a - b)) * Float64(1.0 / Float64(y + Float64(t + x)))))
	tmp = 0.0
	if (y <= -2.1e-35)
		tmp = t_1;
	elseif (y <= 1.15e-93)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x));
	elseif (y <= 7e+57)
		tmp = Float64(Float64(Float64(z * x) + Float64(y * Float64(Float64(z + a) - b))) / Float64(y + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * ((z + (a - b)) * (1.0 / (y + (t + x))));
	tmp = 0.0;
	if (y <= -2.1e-35)
		tmp = t_1;
	elseif (y <= 1.15e-93)
		tmp = ((z * x) + (t * a)) / (t + x);
	elseif (y <= 7e+57)
		tmp = ((z * x) + (y * ((z + a) - b))) / (y + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e-35], t$95$1, If[LessEqual[y, 1.15e-93], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+57], N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e-35 or 6.9999999999999995e57 < y

   1. Initial program 45.4%

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

   2. Taylor expanded in y around inf 39.4%

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

      1. +-commutative 39.4%

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

   4. Simplified 39.4%

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

      1. div-inv 39.3%

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

      2. associate--l+ 39.3%

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

      3. +-commutative 39.3%

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

      4. +-commutative 39.3%

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

      5. +-commutative 39.3%

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

   6. Applied egg-rr 39.3%

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

      1. associate-*l* 80.9%

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

   8. Simplified 80.9%

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

   if -2.1e-35 < y < 1.1499999999999999e-93

   1. Initial program 84.1%

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

   2. Taylor expanded in y around 0 63.5%

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

   if 1.1499999999999999e-93 < y < 6.9999999999999995e57

   1. Initial program 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around 0 77.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot x + y \cdot \left(\left(z + a\right) - b\right)}{y + x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z + \left(a - b\right)\right) \cdot \frac{1}{y + \left(t + x\right)}\right)\\ \end{array} \]

Alternative 14: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{z \cdot x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (/ a (/ t_1 (+ y t)))) (t_3 (- (+ z a) b)))
   (if (<= y -3.4e+20)
     t_3
     (if (<= y -3e-40)
       t_2
       (if (<= y 3.4e-212)
         (+ z (/ (* t a) (+ t x)))
         (if (<= y 3.2e-122) t_2 (if (<= y 4.8e-59) (/ (* z x) t_1) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.4e+20) {
		tmp = t_3;
	} else if (y <= -3e-40) {
		tmp = t_2;
	} else if (y <= 3.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 3.2e-122) {
		tmp = t_2;
	} else if (y <= 4.8e-59) {
		tmp = (z * x) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z + a) - b
    if (y <= (-3.4d+20)) then
        tmp = t_3
    else if (y <= (-3d-40)) then
        tmp = t_2
    else if (y <= 3.4d-212) then
        tmp = z + ((t * a) / (t + x))
    else if (y <= 3.2d-122) then
        tmp = t_2
    else if (y <= 4.8d-59) then
        tmp = (z * x) / t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.4e+20) {
		tmp = t_3;
	} else if (y <= -3e-40) {
		tmp = t_2;
	} else if (y <= 3.4e-212) {
		tmp = z + ((t * a) / (t + x));
	} else if (y <= 3.2e-122) {
		tmp = t_2;
	} else if (y <= 4.8e-59) {
		tmp = (z * x) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -3.4e+20:
		tmp = t_3
	elif y <= -3e-40:
		tmp = t_2
	elif y <= 3.4e-212:
		tmp = z + ((t * a) / (t + x))
	elif y <= 3.2e-122:
		tmp = t_2
	elif y <= 4.8e-59:
		tmp = (z * x) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.4e+20)
		tmp = t_3;
	elseif (y <= -3e-40)
		tmp = t_2;
	elseif (y <= 3.4e-212)
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	elseif (y <= 3.2e-122)
		tmp = t_2;
	elseif (y <= 4.8e-59)
		tmp = Float64(Float64(z * x) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.4e+20)
		tmp = t_3;
	elseif (y <= -3e-40)
		tmp = t_2;
	elseif (y <= 3.4e-212)
		tmp = z + ((t * a) / (t + x));
	elseif (y <= 3.2e-122)
		tmp = t_2;
	elseif (y <= 4.8e-59)
		tmp = (z * x) / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.4e+20], t$95$3, If[LessEqual[y, -3e-40], t$95$2, If[LessEqual[y, 3.4e-212], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-122], t$95$2, If[LessEqual[y, 4.8e-59], N[(N[(z * x), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4e20 or 4.8000000000000003e-59 < y

   1. Initial program 48.8%

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

   2. Taylor expanded in y around inf 71.2%

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

      1. +-commutative 71.2%

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

   4. Simplified 71.2%

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

   if -3.4e20 < y < -3.0000000000000002e-40 or 3.39999999999999998e-212 < y < 3.2000000000000002e-122

   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 a around inf 54.4%

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

      1. associate-/l* 70.3%

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

   4. Simplified 70.3%

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

   if -3.0000000000000002e-40 < y < 3.39999999999999998e-212

   1. Initial program 83.6%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in a around inf 83.6%

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

      1. associate-/l* 78.9%

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

      2. +-commutative 78.9%

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

      3. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in x around inf 78.6%

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

   8. Taylor expanded in y around 0 63.9%

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

   if 3.2000000000000002e-122 < y < 4.8000000000000003e-59

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 67.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-40}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{z \cdot x}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 15: 61.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + \frac{z - b}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-266}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ a (/ (- z b) (/ t y)))))
   (if (<= t -2.4e+106)
     t_2
     (if (<= t -2.8e-236)
       t_1
       (if (<= t 8.4e-266) z (if (<= t 4.5e+140) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + ((z - b) / (t / y));
	double tmp;
	if (t <= -2.4e+106) {
		tmp = t_2;
	} else if (t <= -2.8e-236) {
		tmp = t_1;
	} else if (t <= 8.4e-266) {
		tmp = z;
	} else if (t <= 4.5e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a + ((z - b) / (t / y))
    if (t <= (-2.4d+106)) then
        tmp = t_2
    else if (t <= (-2.8d-236)) then
        tmp = t_1
    else if (t <= 8.4d-266) then
        tmp = z
    else if (t <= 4.5d+140) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a + ((z - b) / (t / y));
	double tmp;
	if (t <= -2.4e+106) {
		tmp = t_2;
	} else if (t <= -2.8e-236) {
		tmp = t_1;
	} else if (t <= 8.4e-266) {
		tmp = z;
	} else if (t <= 4.5e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a + ((z - b) / (t / y))
	tmp = 0
	if t <= -2.4e+106:
		tmp = t_2
	elif t <= -2.8e-236:
		tmp = t_1
	elif t <= 8.4e-266:
		tmp = z
	elif t <= 4.5e+140:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a + Float64(Float64(z - b) / Float64(t / y)))
	tmp = 0.0
	if (t <= -2.4e+106)
		tmp = t_2;
	elseif (t <= -2.8e-236)
		tmp = t_1;
	elseif (t <= 8.4e-266)
		tmp = z;
	elseif (t <= 4.5e+140)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a + ((z - b) / (t / y));
	tmp = 0.0;
	if (t <= -2.4e+106)
		tmp = t_2;
	elseif (t <= -2.8e-236)
		tmp = t_1;
	elseif (t <= 8.4e-266)
		tmp = z;
	elseif (t <= 4.5e+140)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(z - b), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+106], t$95$2, If[LessEqual[t, -2.8e-236], t$95$1, If[LessEqual[t, 8.4e-266], z, If[LessEqual[t, 4.5e+140], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4000000000000001e106 or 4.5000000000000002e140 < t

   1. Initial program 61.9%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in a around 0 61.8%

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

   5. Taylor expanded in x around 0 47.2%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-/l* 68.4%

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

   8. Simplified 68.4%

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

   if -2.4000000000000001e106 < t < -2.79999999999999986e-236 or 8.39999999999999987e-266 < t < 4.5000000000000002e140

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 63.5%

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

      1. +-commutative 63.5%

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

   4. Simplified 63.5%

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

   if -2.79999999999999986e-236 < t < 8.39999999999999987e-266

   1. Initial program 72.2%

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

   2. Taylor expanded in x around inf 51.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+106}:\\ \;\;\;\;a + \frac{z - b}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-236}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-266}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+140}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z - b}{\frac{t}{y}}\\ \end{array} \]

Alternative 16: 62.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-33} \lor \neg \left(y \leq 4.4 \cdot 10^{+54}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e-33) (not (<= y 4.4e+54)))
   (- (+ z a) b)
   (+ z (/ (* t a) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e-33) || !(y <= 4.4e+54)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + ((t * a) / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.6d-33)) .or. (.not. (y <= 4.4d+54))) then
        tmp = (z + a) - b
    else
        tmp = z + ((t * a) / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e-33) || !(y <= 4.4e+54)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + ((t * a) / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e-33) or not (y <= 4.4e+54):
		tmp = (z + a) - b
	else:
		tmp = z + ((t * a) / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e-33) || !(y <= 4.4e+54))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(Float64(t * a) / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e-33) || ~((y <= 4.4e+54)))
		tmp = (z + a) - b;
	else
		tmp = z + ((t * a) / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e-33], N[Not[LessEqual[y, 4.4e+54]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(N[(t * a), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999988e-33 or 4.3999999999999998e54 < y

   1. Initial program 44.9%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. +-commutative 74.8%

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

   4. Simplified 74.8%

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

   if -1.59999999999999988e-33 < y < 4.3999999999999998e54

   1. Initial program 85.2%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in a around inf 85.2%

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

      1. associate-/l* 81.7%

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

      2. +-commutative 81.7%

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

      3. associate-/l* 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around inf 79.9%

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

   8. Taylor expanded in y around 0 55.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-33} \lor \neg \left(y \leq 4.4 \cdot 10^{+54}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{t \cdot a}{t + x}\\ \end{array} \]

Alternative 17: 58.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+145) z (if (<= x 5.2e+156) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+145) {
		tmp = z;
	} else if (x <= 5.2e+156) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.5d+145)) then
        tmp = z
    else if (x <= 5.2d+156) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+145) {
		tmp = z;
	} else if (x <= 5.2e+156) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+145:
		tmp = z
	elif x <= 5.2e+156:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+145)
		tmp = z;
	elseif (x <= 5.2e+156)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e+145)
		tmp = z;
	elseif (x <= 5.2e+156)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+145], z, If[LessEqual[x, 5.2e+156], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999948e145 or 5.20000000000000037e156 < x

   1. Initial program 57.2%

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

   2. Taylor expanded in x around inf 56.6%

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

   if -9.49999999999999948e145 < x < 5.20000000000000037e156

   1. Initial program 68.8%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

   4. Simplified 58.6%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 18: 53.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+141}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.8e+141) z (if (<= x 6.5e+155) (+ z a) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.8e+141) {
		tmp = z;
	} else if (x <= 6.5e+155) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.8d+141)) then
        tmp = z
    else if (x <= 6.5d+155) then
        tmp = z + a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.8e+141) {
		tmp = z;
	} else if (x <= 6.5e+155) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.8e+141:
		tmp = z
	elif x <= 6.5e+155:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.8e+141)
		tmp = z;
	elseif (x <= 6.5e+155)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.8e+141)
		tmp = z;
	elseif (x <= 6.5e+155)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.8e+141], z, If[LessEqual[x, 6.5e+155], N[(z + a), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999996e141 or 6.50000000000000046e155 < x

   1. Initial program 55.5%

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

   2. Taylor expanded in x around inf 55.6%

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

   if -6.7999999999999996e141 < x < 6.50000000000000046e155

   1. Initial program 69.5%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in a around inf 69.7%

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

      1. associate-/l* 81.7%

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

      2. +-commutative 81.7%

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

      3. associate-/l* 96.1%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in x around inf 73.6%

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

   8. Taylor expanded in t around inf 53.4%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+141}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 19: 44.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+18}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9e+18) a (if (<= t 1.9e+54) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+18) {
		tmp = a;
	} else if (t <= 1.9e+54) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9d+18)) then
        tmp = a
    else if (t <= 1.9d+54) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+18) {
		tmp = a;
	} else if (t <= 1.9e+54) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9e+18:
		tmp = a
	elif t <= 1.9e+54:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9e+18)
		tmp = a;
	elseif (t <= 1.9e+54)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9e+18)
		tmp = a;
	elseif (t <= 1.9e+54)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9e+18], a, If[LessEqual[t, 1.9e+54], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -9e18 or 1.9000000000000001e54 < t

   1. Initial program 62.5%

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

   2. Taylor expanded in t around inf 47.7%

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

   if -9e18 < t < 1.9000000000000001e54

   1. Initial program 68.7%

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

   2. Taylor expanded in x around inf 45.5%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+18}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 20: 32.4% 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 66.2%

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

2. Taylor expanded in t around inf 31.7%

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

3. Final simplification 31.7%

   \[\leadsto a \]

Developer target: 82.7% 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 2023238 
(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)))