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

Percentage Accurate: 60.7% → 99.3%

Time: 14.7s

Alternatives: 19

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - b \cdot y}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 2 \cdot 10^{+290}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_2}{y}} + \left(\frac{z}{\frac{t_2}{x}} + \left(y + t\right) \cdot \frac{a}{t_2}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \frac{t_1 - b \cdot y}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ t x)))
        (t_3 (/ (- (+ (* z (+ y x)) t_1) (* b y)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+290)))
     (+ (/ (- z b) (/ t_2 y)) (+ (/ z (/ t_2 x)) (* (+ y t) (/ a t_2))))
     (+ (* z (+ (/ x t_2) (/ y t_2))) (/ (- t_1 (* b y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (t + x);
	double t_3 = (((z * (y + x)) + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+290)) {
		tmp = ((z - b) / (t_2 / y)) + ((z / (t_2 / x)) + ((y + t) * (a / t_2)));
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (t + x);
	double t_3 = (((z * (y + x)) + t_1) - (b * y)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 2e+290)) {
		tmp = ((z - b) / (t_2 / y)) + ((z / (t_2 / x)) + ((y + t) * (a / t_2)));
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (t + x)
	t_3 = (((z * (y + x)) + t_1) - (b * y)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 2e+290):
		tmp = ((z - b) / (t_2 / y)) + ((z / (t_2 / x)) + ((y + t) * (a / t_2)))
	else:
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(b * y)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+290))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_2 / y)) + Float64(Float64(z / Float64(t_2 / x)) + Float64(Float64(y + t) * Float64(a / t_2))));
	else
		tmp = Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(t_1 - Float64(b * y)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (t + x);
	t_3 = (((z * (y + x)) + t_1) - (b * y)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 2e+290)))
		tmp = ((z - b) / (t_2 / y)) + ((z / (t_2 / x)) + ((y + t) * (a / t_2)));
	else
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+290]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000012e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in a around inf 5.2%

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

      1. associate-/l* 30.5%

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

      2. +-commutative 30.5%

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

      3. associate-/l* 69.6%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

      1. associate-/r/ 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000012e290

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 99.3%

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

      1. associate--l+ 99.3%

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

      2. *-commutative 99.3%

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

      3. div-sub 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+290}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{z}{\frac{y + \left(t + x\right)}{x}} + \left(y + t\right) \cdot \frac{a}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}\right) + \frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(t + x\right)}\\ \end{array} \]

Alternative 2: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + t_1\right) - b \cdot y}{t_2}\\ t_4 := \frac{z - b}{\frac{t_2}{y}}\\ t_5 := \frac{z}{\frac{t_2}{x}}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4 + \left(t_5 + \frac{a}{1 + \frac{x}{t}}\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \frac{t_1 - b \cdot y}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_4 + \left(a + t_5\right)\\ \end{array} \end{array} \]

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) (* b y)) t_2))
        (t_4 (/ (- z b) (/ t_2 y)))
        (t_5 (/ z (/ t_2 x))))
   (if (<= t_3 (- INFINITY))
     (+ t_4 (+ t_5 (/ a (+ 1.0 (/ x t)))))
     (if (<= t_3 5e+130)
       (+ (* z (+ (/ x t_2) (/ y t_2))) (/ (- t_1 (* b y)) t_2))
       (+ t_4 (+ a t_5))))))

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) - (b * y)) / t_2;
	double t_4 = (z - b) / (t_2 / y);
	double t_5 = z / (t_2 / x);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4 + (t_5 + (a / (1.0 + (x / t))));
	} else if (t_3 <= 5e+130) {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2);
	} else {
		tmp = t_4 + (a + t_5);
	}
	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) - (b * y)) / t_2;
	double t_4 = (z - b) / (t_2 / y);
	double t_5 = z / (t_2 / x);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4 + (t_5 + (a / (1.0 + (x / t))));
	} else if (t_3 <= 5e+130) {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2);
	} else {
		tmp = t_4 + (a + t_5);
	}
	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) - (b * y)) / t_2
	t_4 = (z - b) / (t_2 / y)
	t_5 = z / (t_2 / x)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4 + (t_5 + (a / (1.0 + (x / t))))
	elif t_3 <= 5e+130:
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2)
	else:
		tmp = t_4 + (a + t_5)
	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(b * y)) / t_2)
	t_4 = Float64(Float64(z - b) / Float64(t_2 / y))
	t_5 = Float64(z / Float64(t_2 / x))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_4 + Float64(t_5 + Float64(a / Float64(1.0 + Float64(x / t)))));
	elseif (t_3 <= 5e+130)
		tmp = Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(t_1 - Float64(b * y)) / t_2));
	else
		tmp = Float64(t_4 + Float64(a + t_5));
	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) - (b * y)) / t_2;
	t_4 = (z - b) / (t_2 / y);
	t_5 = z / (t_2 / x);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4 + (t_5 + (a / (1.0 + (x / t))));
	elseif (t_3 <= 5e+130)
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_1 - (b * y)) / t_2);
	else
		tmp = t_4 + (a + t_5);
	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[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$4 + N[(t$95$5 + N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+130], N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$4 + N[(a + t$95$5), $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 5.7%

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

   3. Simplified 5.7%

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

   4. Taylor expanded in a around inf 5.7%

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

      1. associate-/l* 32.8%

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

      2. +-commutative 32.8%

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

      3. associate-/l* 70.7%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in t around inf 98.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e130

   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. Taylor expanded in z around 0 99.3%

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

      1. associate--l+ 99.3%

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

      2. *-commutative 99.3%

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

      3. div-sub 99.3%

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

   4. Simplified 99.3%

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

   if 4.9999999999999996e130 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 29.3%

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

   3. Simplified 30.5%

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

   4. Taylor expanded in a around inf 29.6%

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

      1. associate-/l* 47.3%

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

      2. +-commutative 47.3%

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

      3. associate-/l* 76.8%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 96.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{z}{\frac{y + \left(t + x\right)}{x}} + \frac{a}{1 + \frac{x}{t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 5 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}\right) + \frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(a + \frac{z}{\frac{y + \left(t + x\right)}{x}}\right)\\ \end{array} \]

Alternative 3: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(a + \frac{z}{\frac{t_1}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* b y)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+130)))
     (+ (/ (- z b) (/ t_1 y)) (+ a (/ z (/ t_1 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 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+130)) {
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+130)) {
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+130):
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / 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(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(b * y)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+130))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(a + Float64(z / Float64(t_1 / 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 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+130)))
		tmp = ((z - b) / (t_1 / y)) + (a + (z / (t_1 / 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[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+130]], $MachinePrecision]], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999996e130 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 20.9%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in a around inf 21.1%

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

      1. associate-/l* 42.2%

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

      2. +-commutative 42.2%

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

      3. associate-/l* 74.7%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 93.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e130

   1. Initial program 99.1%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 5 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(a + \frac{z}{\frac{y + \left(t + x\right)}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \end{array} \]

Alternative 4: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{t_1}\\ t_3 := \frac{z - b}{\frac{t_1}{y}}\\ t_4 := \frac{z}{\frac{t_1}{x}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + \left(t_4 + \frac{a}{1 + \frac{x}{t}}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(a + t_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* b y)) t_1))
        (t_3 (/ (- z b) (/ t_1 y)))
        (t_4 (/ z (/ t_1 x))))
   (if (<= t_2 (- INFINITY))
     (+ t_3 (+ t_4 (/ a (+ 1.0 (/ x t)))))
     (if (<= t_2 5e+130) t_2 (+ t_3 (+ a t_4))))))

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 * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	double t_3 = (z - b) / (t_1 / y);
	double t_4 = z / (t_1 / x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3 + (t_4 + (a / (1.0 + (x / t))));
	} else if (t_2 <= 5e+130) {
		tmp = t_2;
	} else {
		tmp = t_3 + (a + t_4);
	}
	return tmp;
}

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 * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	double t_3 = (z - b) / (t_1 / y);
	double t_4 = z / (t_1 / x);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3 + (t_4 + (a / (1.0 + (x / t))));
	} else if (t_2 <= 5e+130) {
		tmp = t_2;
	} else {
		tmp = t_3 + (a + t_4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1
	t_3 = (z - b) / (t_1 / y)
	t_4 = z / (t_1 / x)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3 + (t_4 + (a / (1.0 + (x / t))))
	elif t_2 <= 5e+130:
		tmp = t_2
	else:
		tmp = t_3 + (a + t_4)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(z - b) / Float64(t_1 / y))
	t_4 = Float64(z / Float64(t_1 / x))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_3 + Float64(t_4 + Float64(a / Float64(1.0 + Float64(x / t)))));
	elseif (t_2 <= 5e+130)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(a + t_4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	t_3 = (z - b) / (t_1 / y);
	t_4 = z / (t_1 / x);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3 + (t_4 + (a / (1.0 + (x / t))));
	elseif (t_2 <= 5e+130)
		tmp = t_2;
	else
		tmp = t_3 + (a + t_4);
	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[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$3 + N[(t$95$4 + N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+130], t$95$2, N[(t$95$3 + N[(a + t$95$4), $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 5.7%

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

   3. Simplified 5.7%

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

   4. Taylor expanded in a around inf 5.7%

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

      1. associate-/l* 32.8%

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

      2. +-commutative 32.8%

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

      3. associate-/l* 70.7%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in t around inf 98.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e130

   1. Initial program 99.1%

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

   if 4.9999999999999996e130 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 29.3%

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

   3. Simplified 30.5%

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

   4. Taylor expanded in a around inf 29.6%

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

      1. associate-/l* 47.3%

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

      2. +-commutative 47.3%

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

      3. associate-/l* 76.8%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 96.3%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{z}{\frac{y + \left(t + x\right)}{x}} + \frac{a}{1 + \frac{x}{t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(a + \frac{z}{\frac{y + \left(t + x\right)}{x}}\right)\\ \end{array} \]

Alternative 5: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(z + a\right)\\ \mathbf{elif}\;t_2 \leq 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* b y)) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ (/ (- z b) (/ t_1 y)) (+ z a))
     (if (<= t_2 1e+237) t_2 (- (+ z a) b)))))

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 * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((z - b) / (t_1 / y)) + (z + a);
	} else if (t_2 <= 1e+237) {
		tmp = t_2;
	} 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 = y + (t + x);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z - b) / (t_1 / y)) + (z + a);
	} else if (t_2 <= 1e+237) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((z - b) / (t_1 / y)) + (z + a)
	elif t_2 <= 1e+237:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(b * y)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(z + a));
	elseif (t_2 <= 1e+237)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((z - b) / (t_1 / y)) + (z + a);
	elseif (t_2 <= 1e+237)
		tmp = t_2;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+237], t$95$2, 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 5.7%

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

   3. Simplified 5.7%

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

   4. Taylor expanded in a around inf 5.7%

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

      1. associate-/l* 32.8%

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

      2. +-commutative 32.8%

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

      3. associate-/l* 70.7%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 89.6%

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

   8. Taylor expanded in x around inf 63.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999994e236

   1. Initial program 99.2%

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

   if 9.9999999999999994e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 13.6%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. +-commutative 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + a\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 10^{+237}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ \frac{z - b}{\frac{t_1}{y}} + \left(\frac{a}{\frac{t_1}{y + t}} + \frac{z}{\frac{t_1}{x}}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))))
   (+ (/ (- z b) (/ t_1 y)) (+ (/ a (/ t_1 (+ y t))) (/ z (/ t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	return ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + (z / (t_1 / x)));
}

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
    t_1 = y + (t + x)
    code = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + (z / (t_1 / x)))
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);
	return ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + (z / (t_1 / x)));
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	return ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + (z / (t_1 / x)))

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	return Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(z / Float64(t_1 / x))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	tmp = ((z - b) / (t_1 / y)) + ((a / (t_1 / (y + t))) + (z / (t_1 / x)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 62.8%

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

3. Simplified 63.1%

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

4. Taylor expanded in a around inf 62.9%

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

   1. associate-/l* 71.6%

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

   2. +-commutative 71.6%

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

   3. associate-/l* 86.3%

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

   4. associate-/l* 98.4%

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

6. Simplified 98.4%

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

7. Final simplification 98.4%

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

Alternative 7: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{z - b}{\frac{t_1}{y}} + \left(z + a\right)\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-166}:\\ \;\;\;\;z \cdot \frac{y + x}{t_1}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (+ (/ (- z b) (/ t_1 y)) (+ z a)))
        (t_3 (- (+ z a) b)))
   (if (<= y -5e+58)
     t_3
     (if (<= y -2e-92)
       t_2
       (if (<= y -2.1e-166)
         (* z (/ (+ y x) t_1))
         (if (<= y -5.8e-213)
           (/ a (/ t_1 (+ y t)))
           (if (<= y 9.5e-50)
             (/ (+ (* z x) (* t a)) (+ t x))
             (if (<= y 3.5e+152) t_2 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 = ((z - b) / (t_1 / y)) + (z + a);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -5e+58) {
		tmp = t_3;
	} else if (y <= -2e-92) {
		tmp = t_2;
	} else if (y <= -2.1e-166) {
		tmp = z * ((y + x) / t_1);
	} else if (y <= -5.8e-213) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 9.5e-50) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 3.5e+152) {
		tmp = t_2;
	} 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 = ((z - b) / (t_1 / y)) + (z + a)
    t_3 = (z + a) - b
    if (y <= (-5d+58)) then
        tmp = t_3
    else if (y <= (-2d-92)) then
        tmp = t_2
    else if (y <= (-2.1d-166)) then
        tmp = z * ((y + x) / t_1)
    else if (y <= (-5.8d-213)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 9.5d-50) then
        tmp = ((z * x) + (t * a)) / (t + x)
    else if (y <= 3.5d+152) then
        tmp = t_2
    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 = ((z - b) / (t_1 / y)) + (z + a);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -5e+58) {
		tmp = t_3;
	} else if (y <= -2e-92) {
		tmp = t_2;
	} else if (y <= -2.1e-166) {
		tmp = z * ((y + x) / t_1);
	} else if (y <= -5.8e-213) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 9.5e-50) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (y <= 3.5e+152) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = ((z - b) / (t_1 / y)) + (z + a)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -5e+58:
		tmp = t_3
	elif y <= -2e-92:
		tmp = t_2
	elif y <= -2.1e-166:
		tmp = z * ((y + x) / t_1)
	elif y <= -5.8e-213:
		tmp = a / (t_1 / (y + t))
	elif y <= 9.5e-50:
		tmp = ((z * x) + (t * a)) / (t + x)
	elif y <= 3.5e+152:
		tmp = t_2
	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(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(z + a))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5e+58)
		tmp = t_3;
	elseif (y <= -2e-92)
		tmp = t_2;
	elseif (y <= -2.1e-166)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif (y <= -5.8e-213)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 9.5e-50)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x));
	elseif (y <= 3.5e+152)
		tmp = t_2;
	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 = ((z - b) / (t_1 / y)) + (z + a);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5e+58)
		tmp = t_3;
	elseif (y <= -2e-92)
		tmp = t_2;
	elseif (y <= -2.1e-166)
		tmp = z * ((y + x) / t_1);
	elseif (y <= -5.8e-213)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 9.5e-50)
		tmp = ((z * x) + (t * a)) / (t + x);
	elseif (y <= 3.5e+152)
		tmp = t_2;
	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[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5e+58], t$95$3, If[LessEqual[y, -2e-92], t$95$2, If[LessEqual[y, -2.1e-166], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-213], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-50], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+152], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.99999999999999986e58 or 3.49999999999999981e152 < y

   1. Initial program 43.4%

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

   2. Taylor expanded in y around inf 73.9%

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

      1. +-commutative 73.9%

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

   4. Simplified 73.9%

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

   if -4.99999999999999986e58 < y < -1.99999999999999998e-92 or 9.4999999999999993e-50 < y < 3.49999999999999981e152

   1. Initial program 61.1%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in a around inf 61.3%

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

      1. associate-/l* 67.7%

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

      2. +-commutative 67.7%

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

      3. associate-/l* 88.4%

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

      4. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 95.3%

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

   8. Taylor expanded in x around inf 72.4%

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

   if -1.99999999999999998e-92 < y < -2.0999999999999999e-166

   1. Initial program 83.3%

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

   2. Taylor expanded in z around inf 55.0%

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

      1. associate-/l* 57.3%

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

   4. Simplified 57.3%

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

      1. associate-/r/ 71.6%

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

   6. Applied egg-rr 71.6%

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

   if -2.0999999999999999e-166 < y < -5.7999999999999999e-213

   1. Initial program 47.8%

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

   2. Taylor expanded in a around inf 47.5%

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

      1. associate-/l* 88.9%

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

   4. Simplified 88.9%

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

   if -5.7999999999999999e-213 < y < 9.4999999999999993e-50

   1. Initial program 83.2%

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

   2. Taylor expanded in y around 0 67.6%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+58}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-92}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + a\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-166}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-213}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{z - b}{\frac{t_1}{y}}\\ t_3 := t_2 + \left(z + a\right)\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{+168}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+68}:\\ \;\;\;\;t_2 + \left(a + \frac{z \cdot x}{y}\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+145}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+197}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \frac{a - b}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (/ (- z b) (/ t_1 y))) (t_3 (+ t_2 (+ z a))))
   (if (<= x -7.4e+168)
     (+ z (/ y (/ x (- a b))))
     (if (<= x -3.8e+39)
       t_3
       (if (<= x -1.4e-23)
         (/ (+ (* z x) (* t a)) (+ t x))
         (if (<= x 3.9e+68)
           (+ t_2 (+ a (/ (* z x) y)))
           (if (<= x 9.4e+145)
             (/ a (/ t_1 (+ y t)))
             (if (<= x 8.2e+197) t_3 (+ z (* y (/ (- a b) x)))))))))))

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 t_3 = t_2 + (z + a);
	double tmp;
	if (x <= -7.4e+168) {
		tmp = z + (y / (x / (a - b)));
	} else if (x <= -3.8e+39) {
		tmp = t_3;
	} else if (x <= -1.4e-23) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (x <= 3.9e+68) {
		tmp = t_2 + (a + ((z * x) / y));
	} else if (x <= 9.4e+145) {
		tmp = a / (t_1 / (y + t));
	} else if (x <= 8.2e+197) {
		tmp = t_3;
	} else {
		tmp = z + (y * ((a - b) / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = (z - b) / (t_1 / y)
    t_3 = t_2 + (z + a)
    if (x <= (-7.4d+168)) then
        tmp = z + (y / (x / (a - b)))
    else if (x <= (-3.8d+39)) then
        tmp = t_3
    else if (x <= (-1.4d-23)) then
        tmp = ((z * x) + (t * a)) / (t + x)
    else if (x <= 3.9d+68) then
        tmp = t_2 + (a + ((z * x) / y))
    else if (x <= 9.4d+145) then
        tmp = a / (t_1 / (y + t))
    else if (x <= 8.2d+197) then
        tmp = t_3
    else
        tmp = z + (y * ((a - b) / 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 t_1 = y + (t + x);
	double t_2 = (z - b) / (t_1 / y);
	double t_3 = t_2 + (z + a);
	double tmp;
	if (x <= -7.4e+168) {
		tmp = z + (y / (x / (a - b)));
	} else if (x <= -3.8e+39) {
		tmp = t_3;
	} else if (x <= -1.4e-23) {
		tmp = ((z * x) + (t * a)) / (t + x);
	} else if (x <= 3.9e+68) {
		tmp = t_2 + (a + ((z * x) / y));
	} else if (x <= 9.4e+145) {
		tmp = a / (t_1 / (y + t));
	} else if (x <= 8.2e+197) {
		tmp = t_3;
	} else {
		tmp = z + (y * ((a - b) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (z - b) / (t_1 / y)
	t_3 = t_2 + (z + a)
	tmp = 0
	if x <= -7.4e+168:
		tmp = z + (y / (x / (a - b)))
	elif x <= -3.8e+39:
		tmp = t_3
	elif x <= -1.4e-23:
		tmp = ((z * x) + (t * a)) / (t + x)
	elif x <= 3.9e+68:
		tmp = t_2 + (a + ((z * x) / y))
	elif x <= 9.4e+145:
		tmp = a / (t_1 / (y + t))
	elif x <= 8.2e+197:
		tmp = t_3
	else:
		tmp = z + (y * ((a - b) / x))
	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))
	t_3 = Float64(t_2 + Float64(z + a))
	tmp = 0.0
	if (x <= -7.4e+168)
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	elseif (x <= -3.8e+39)
		tmp = t_3;
	elseif (x <= -1.4e-23)
		tmp = Float64(Float64(Float64(z * x) + Float64(t * a)) / Float64(t + x));
	elseif (x <= 3.9e+68)
		tmp = Float64(t_2 + Float64(a + Float64(Float64(z * x) / y)));
	elseif (x <= 9.4e+145)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (x <= 8.2e+197)
		tmp = t_3;
	else
		tmp = Float64(z + Float64(y * Float64(Float64(a - b) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = (z - b) / (t_1 / y);
	t_3 = t_2 + (z + a);
	tmp = 0.0;
	if (x <= -7.4e+168)
		tmp = z + (y / (x / (a - b)));
	elseif (x <= -3.8e+39)
		tmp = t_3;
	elseif (x <= -1.4e-23)
		tmp = ((z * x) + (t * a)) / (t + x);
	elseif (x <= 3.9e+68)
		tmp = t_2 + (a + ((z * x) / y));
	elseif (x <= 9.4e+145)
		tmp = a / (t_1 / (y + t));
	elseif (x <= 8.2e+197)
		tmp = t_3;
	else
		tmp = z + (y * ((a - b) / x));
	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 - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(z + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.4e+168], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e+39], t$95$3, If[LessEqual[x, -1.4e-23], N[(N[(N[(z * x), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+68], N[(t$95$2 + N[(a + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.4e+145], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+197], t$95$3, N[(z + N[(y * N[(N[(a - b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.40000000000000018e168

   1. Initial program 55.6%

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

      1. associate--l+ 55.6%

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

      2. fma-def 55.6%

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

      3. *-commutative 55.6%

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

      4. distribute-rgt-in 55.6%

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

      5. associate--l+ 55.6%

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

      6. fma-def 55.6%

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

      7. distribute-lft-out-- 55.6%

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

      8. +-commutative 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in t around 0 49.5%

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

   5. Taylor expanded in x around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

   if -7.40000000000000018e168 < x < -3.7999999999999998e39 or 9.4000000000000004e145 < x < 8.2000000000000006e197

   1. Initial program 53.0%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in a around inf 52.8%

      \[\leadsto \color{blue}{\frac{\left(z - b\right) \cdot y}{y + \left(t + x\right)} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right)} \]
   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* 72.8%

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

      4. associate-/l* 97.2%

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

   6. Simplified 97.2%

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

   7. Taylor expanded in y around inf 89.2%

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

   8. Taylor expanded in x around inf 72.0%

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

   if -3.7999999999999998e39 < x < -1.3999999999999999e-23

   1. Initial program 65.0%

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

   2. Taylor expanded in y around 0 66.1%

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

   if -1.3999999999999999e-23 < x < 3.90000000000000019e68

   1. Initial program 68.4%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in a around inf 68.6%

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

      1. associate-/l* 80.8%

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

      2. +-commutative 80.8%

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

      3. associate-/l* 98.7%

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

      4. associate-/l* 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around inf 95.8%

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

   8. Taylor expanded in y around inf 77.0%

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

   if 3.90000000000000019e68 < x < 9.4000000000000004e145

   1. Initial program 56.5%

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

   2. Taylor expanded in a around inf 39.3%

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

      1. associate-/l* 73.7%

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

   4. Simplified 73.7%

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

   if 8.2000000000000006e197 < x

   1. Initial program 55.7%

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

      1. associate--l+ 55.7%

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

      2. fma-def 55.7%

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

      3. *-commutative 55.7%

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

      4. distribute-rgt-in 55.5%

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

      5. associate--l+ 55.5%

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

      6. fma-def 55.5%

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

      7. distribute-lft-out-- 55.7%

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

      8. +-commutative 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in t around 0 54.1%

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

   5. Taylor expanded in z around 0 73.7%

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

   6. Taylor expanded in y around 0 73.0%

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

      1. associate-*r/ 84.4%

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

   8. Simplified 84.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+168}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + a\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{z \cdot x + t \cdot a}{t + x}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+68}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(a + \frac{z \cdot x}{y}\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+145}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+197}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \frac{a - b}{x}\\ \end{array} \]

Alternative 9: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := z \cdot \frac{y + x}{t_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{y + x}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{-y}{\frac{t_1}{b}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+213}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (* z (/ (+ y x) t_1))) (t_3 (- (+ z a) b)))
   (if (<= t -3.5e+109)
     a
     (if (<= t -3.4e-137)
       t_3
       (if (<= t 1.05e+48)
         (+ z (/ (* y (- a b)) (+ y x)))
         (if (<= t 1.95e+80)
           t_3
           (if (<= t 1.4e+109)
             t_2
             (if (<= t 7.5e+123)
               (/ (- y) (/ t_1 b))
               (if (<= t 6.5e+213) t_2 a)))))))))

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 * ((y + x) / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (t <= -3.5e+109) {
		tmp = a;
	} else if (t <= -3.4e-137) {
		tmp = t_3;
	} else if (t <= 1.05e+48) {
		tmp = z + ((y * (a - b)) / (y + x));
	} else if (t <= 1.95e+80) {
		tmp = t_3;
	} else if (t <= 1.4e+109) {
		tmp = t_2;
	} else if (t <= 7.5e+123) {
		tmp = -y / (t_1 / b);
	} else if (t <= 6.5e+213) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = z * ((y + x) / t_1)
    t_3 = (z + a) - b
    if (t <= (-3.5d+109)) then
        tmp = a
    else if (t <= (-3.4d-137)) then
        tmp = t_3
    else if (t <= 1.05d+48) then
        tmp = z + ((y * (a - b)) / (y + x))
    else if (t <= 1.95d+80) then
        tmp = t_3
    else if (t <= 1.4d+109) then
        tmp = t_2
    else if (t <= 7.5d+123) then
        tmp = -y / (t_1 / b)
    else if (t <= 6.5d+213) then
        tmp = t_2
    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 t_1 = y + (t + x);
	double t_2 = z * ((y + x) / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (t <= -3.5e+109) {
		tmp = a;
	} else if (t <= -3.4e-137) {
		tmp = t_3;
	} else if (t <= 1.05e+48) {
		tmp = z + ((y * (a - b)) / (y + x));
	} else if (t <= 1.95e+80) {
		tmp = t_3;
	} else if (t <= 1.4e+109) {
		tmp = t_2;
	} else if (t <= 7.5e+123) {
		tmp = -y / (t_1 / b);
	} else if (t <= 6.5e+213) {
		tmp = t_2;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = z * ((y + x) / t_1)
	t_3 = (z + a) - b
	tmp = 0
	if t <= -3.5e+109:
		tmp = a
	elif t <= -3.4e-137:
		tmp = t_3
	elif t <= 1.05e+48:
		tmp = z + ((y * (a - b)) / (y + x))
	elif t <= 1.95e+80:
		tmp = t_3
	elif t <= 1.4e+109:
		tmp = t_2
	elif t <= 7.5e+123:
		tmp = -y / (t_1 / b)
	elif t <= 6.5e+213:
		tmp = t_2
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(z * Float64(Float64(y + x) / t_1))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -3.5e+109)
		tmp = a;
	elseif (t <= -3.4e-137)
		tmp = t_3;
	elseif (t <= 1.05e+48)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(y + x)));
	elseif (t <= 1.95e+80)
		tmp = t_3;
	elseif (t <= 1.4e+109)
		tmp = t_2;
	elseif (t <= 7.5e+123)
		tmp = Float64(Float64(-y) / Float64(t_1 / b));
	elseif (t <= 6.5e+213)
		tmp = t_2;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = z * ((y + x) / t_1);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (t <= -3.5e+109)
		tmp = a;
	elseif (t <= -3.4e-137)
		tmp = t_3;
	elseif (t <= 1.05e+48)
		tmp = z + ((y * (a - b)) / (y + x));
	elseif (t <= 1.95e+80)
		tmp = t_3;
	elseif (t <= 1.4e+109)
		tmp = t_2;
	elseif (t <= 7.5e+123)
		tmp = -y / (t_1 / b);
	elseif (t <= 6.5e+213)
		tmp = t_2;
	else
		tmp = a;
	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[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -3.5e+109], a, If[LessEqual[t, -3.4e-137], t$95$3, If[LessEqual[t, 1.05e+48], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+80], t$95$3, If[LessEqual[t, 1.4e+109], t$95$2, If[LessEqual[t, 7.5e+123], N[((-y) / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+213], t$95$2, a]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.49999999999999983e109 or 6.49999999999999982e213 < t

   1. Initial program 48.9%

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

   2. Taylor expanded in t around inf 63.9%

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

   if -3.49999999999999983e109 < t < -3.40000000000000014e-137 or 1.0499999999999999e48 < t < 1.94999999999999999e80

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 67.4%

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

      1. +-commutative 67.4%

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

   4. Simplified 67.4%

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

   if -3.40000000000000014e-137 < t < 1.0499999999999999e48

   1. Initial program 75.5%

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

      1. associate--l+ 75.5%

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

      2. fma-def 75.6%

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

      3. *-commutative 75.6%

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

      4. distribute-rgt-in 75.6%

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

      5. associate--l+ 75.6%

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

      6. fma-def 75.6%

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

      7. distribute-lft-out-- 75.8%

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

      8. +-commutative 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around 0 68.7%

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

   5. Taylor expanded in z around 0 77.0%

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

   if 1.94999999999999999e80 < t < 1.4000000000000001e109 or 7.4999999999999999e123 < t < 6.49999999999999982e213

   1. Initial program 54.8%

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

   2. Taylor expanded in z around inf 45.0%

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

      1. associate-/l* 79.4%

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

   4. Simplified 79.4%

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

      1. associate-/r/ 79.7%

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

   6. Applied egg-rr 79.7%

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

   if 1.4000000000000001e109 < t < 7.4999999999999999e123

   1. Initial program 60.3%

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

   2. Taylor expanded in b around inf 45.7%

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

      1. mul-1-neg 45.7%

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

      2. associate-/l* 66.9%

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

      3. distribute-neg-frac 66.9%

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

   4. Simplified 66.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-137}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{y + x}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(t + x\right)}{b}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 10: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(t + x\right)\\ t_3 := z \cdot \frac{y + x}{t_2}\\ t_4 := \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+105}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{y + x}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+123}:\\ \;\;\;\;\frac{-y}{\frac{t_2}{b}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+207}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ t x)))
        (t_3 (* z (/ (+ y x) t_2)))
        (t_4 (/ a (/ t_2 (+ y t)))))
   (if (<= t -7.4e+105)
     t_4
     (if (<= t -3.1e-137)
       t_1
       (if (<= t 1.15e+48)
         (+ z (/ (* y (- a b)) (+ y x)))
         (if (<= t 1.05e+86)
           t_1
           (if (<= t 1.42e+109)
             t_3
             (if (<= t 1.4e+123)
               (/ (- y) (/ t_2 b))
               (if (<= t 7e+207) t_3 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (t + x);
	double t_3 = z * ((y + x) / t_2);
	double t_4 = a / (t_2 / (y + t));
	double tmp;
	if (t <= -7.4e+105) {
		tmp = t_4;
	} else if (t <= -3.1e-137) {
		tmp = t_1;
	} else if (t <= 1.15e+48) {
		tmp = z + ((y * (a - b)) / (y + x));
	} else if (t <= 1.05e+86) {
		tmp = t_1;
	} else if (t <= 1.42e+109) {
		tmp = t_3;
	} else if (t <= 1.4e+123) {
		tmp = -y / (t_2 / b);
	} else if (t <= 7e+207) {
		tmp = t_3;
	} 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 = (z + a) - b
    t_2 = y + (t + x)
    t_3 = z * ((y + x) / t_2)
    t_4 = a / (t_2 / (y + t))
    if (t <= (-7.4d+105)) then
        tmp = t_4
    else if (t <= (-3.1d-137)) then
        tmp = t_1
    else if (t <= 1.15d+48) then
        tmp = z + ((y * (a - b)) / (y + x))
    else if (t <= 1.05d+86) then
        tmp = t_1
    else if (t <= 1.42d+109) then
        tmp = t_3
    else if (t <= 1.4d+123) then
        tmp = -y / (t_2 / b)
    else if (t <= 7d+207) then
        tmp = t_3
    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 = (z + a) - b;
	double t_2 = y + (t + x);
	double t_3 = z * ((y + x) / t_2);
	double t_4 = a / (t_2 / (y + t));
	double tmp;
	if (t <= -7.4e+105) {
		tmp = t_4;
	} else if (t <= -3.1e-137) {
		tmp = t_1;
	} else if (t <= 1.15e+48) {
		tmp = z + ((y * (a - b)) / (y + x));
	} else if (t <= 1.05e+86) {
		tmp = t_1;
	} else if (t <= 1.42e+109) {
		tmp = t_3;
	} else if (t <= 1.4e+123) {
		tmp = -y / (t_2 / b);
	} else if (t <= 7e+207) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (t + x)
	t_3 = z * ((y + x) / t_2)
	t_4 = a / (t_2 / (y + t))
	tmp = 0
	if t <= -7.4e+105:
		tmp = t_4
	elif t <= -3.1e-137:
		tmp = t_1
	elif t <= 1.15e+48:
		tmp = z + ((y * (a - b)) / (y + x))
	elif t <= 1.05e+86:
		tmp = t_1
	elif t <= 1.42e+109:
		tmp = t_3
	elif t <= 1.4e+123:
		tmp = -y / (t_2 / b)
	elif t <= 7e+207:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(z * Float64(Float64(y + x) / t_2))
	t_4 = Float64(a / Float64(t_2 / Float64(y + t)))
	tmp = 0.0
	if (t <= -7.4e+105)
		tmp = t_4;
	elseif (t <= -3.1e-137)
		tmp = t_1;
	elseif (t <= 1.15e+48)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(y + x)));
	elseif (t <= 1.05e+86)
		tmp = t_1;
	elseif (t <= 1.42e+109)
		tmp = t_3;
	elseif (t <= 1.4e+123)
		tmp = Float64(Float64(-y) / Float64(t_2 / b));
	elseif (t <= 7e+207)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (t + x);
	t_3 = z * ((y + x) / t_2);
	t_4 = a / (t_2 / (y + t));
	tmp = 0.0;
	if (t <= -7.4e+105)
		tmp = t_4;
	elseif (t <= -3.1e-137)
		tmp = t_1;
	elseif (t <= 1.15e+48)
		tmp = z + ((y * (a - b)) / (y + x));
	elseif (t <= 1.05e+86)
		tmp = t_1;
	elseif (t <= 1.42e+109)
		tmp = t_3;
	elseif (t <= 1.4e+123)
		tmp = -y / (t_2 / b);
	elseif (t <= 7e+207)
		tmp = t_3;
	else
		tmp = t_4;
	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[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+105], t$95$4, If[LessEqual[t, -3.1e-137], t$95$1, If[LessEqual[t, 1.15e+48], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+86], t$95$1, If[LessEqual[t, 1.42e+109], t$95$3, If[LessEqual[t, 1.4e+123], N[((-y) / N[(t$95$2 / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+207], t$95$3, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.3999999999999997e105 or 7.00000000000000056e207 < t

   1. Initial program 48.9%

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

   2. Taylor expanded in a around inf 34.5%

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

      1. associate-/l* 67.4%

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

   4. Simplified 67.4%

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

   if -7.3999999999999997e105 < t < -3.09999999999999978e-137 or 1.15e48 < t < 1.0499999999999999e86

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 67.4%

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

      1. +-commutative 67.4%

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

   4. Simplified 67.4%

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

   if -3.09999999999999978e-137 < t < 1.15e48

   1. Initial program 75.5%

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

      1. associate--l+ 75.5%

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

      2. fma-def 75.6%

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

      3. *-commutative 75.6%

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

      4. distribute-rgt-in 75.6%

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

      5. associate--l+ 75.6%

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

      6. fma-def 75.6%

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

      7. distribute-lft-out-- 75.8%

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

      8. +-commutative 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around 0 68.7%

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

   5. Taylor expanded in z around 0 77.0%

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

   if 1.0499999999999999e86 < t < 1.4200000000000001e109 or 1.40000000000000006e123 < t < 7.00000000000000056e207

   1. Initial program 54.8%

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

   2. Taylor expanded in z around inf 45.0%

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

      1. associate-/l* 79.4%

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

   4. Simplified 79.4%

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

      1. associate-/r/ 79.7%

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

   6. Applied egg-rr 79.7%

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

   if 1.4200000000000001e109 < t < 1.40000000000000006e123

   1. Initial program 60.3%

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

   2. Taylor expanded in b around inf 45.7%

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

      1. mul-1-neg 45.7%

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

      2. associate-/l* 66.9%

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

      3. distribute-neg-frac 66.9%

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

   4. Simplified 66.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+105}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-137}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{y + x}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+123}:\\ \;\;\;\;\frac{-y}{\frac{y + \left(t + x\right)}{b}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{y + t}}\\ \end{array} \]

Alternative 11: 61.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-292}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ z (/ y (/ x (- a b))))))
   (if (<= x -1.9e+66)
     t_2
     (if (<= x -3.5e-244)
       t_1
       (if (<= x 3.7e-292) a (if (<= x 2.8e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (y / (x / (a - b)));
	double tmp;
	if (x <= -1.9e+66) {
		tmp = t_2;
	} else if (x <= -3.5e-244) {
		tmp = t_1;
	} else if (x <= 3.7e-292) {
		tmp = a;
	} else if (x <= 2.8e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z + (y / (x / (a - b)))
    if (x <= (-1.9d+66)) then
        tmp = t_2
    else if (x <= (-3.5d-244)) then
        tmp = t_1
    else if (x <= 3.7d-292) then
        tmp = a
    else if (x <= 2.8d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (y / (x / (a - b)));
	double tmp;
	if (x <= -1.9e+66) {
		tmp = t_2;
	} else if (x <= -3.5e-244) {
		tmp = t_1;
	} else if (x <= 3.7e-292) {
		tmp = a;
	} else if (x <= 2.8e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z + (y / (x / (a - b)))
	tmp = 0
	if x <= -1.9e+66:
		tmp = t_2
	elif x <= -3.5e-244:
		tmp = t_1
	elif x <= 3.7e-292:
		tmp = a
	elif x <= 2.8e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z + Float64(y / Float64(x / Float64(a - b))))
	tmp = 0.0
	if (x <= -1.9e+66)
		tmp = t_2;
	elseif (x <= -3.5e-244)
		tmp = t_1;
	elseif (x <= 3.7e-292)
		tmp = a;
	elseif (x <= 2.8e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z + (y / (x / (a - b)));
	tmp = 0.0;
	if (x <= -1.9e+66)
		tmp = t_2;
	elseif (x <= -3.5e-244)
		tmp = t_1;
	elseif (x <= 3.7e-292)
		tmp = a;
	elseif (x <= 2.8e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+66], t$95$2, If[LessEqual[x, -3.5e-244], t$95$1, If[LessEqual[x, 3.7e-292], a, If[LessEqual[x, 2.8e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9000000000000001e66 or 2.7999999999999999e111 < x

   1. Initial program 54.5%

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

      1. associate--l+ 54.5%

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

      2. fma-def 54.5%

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

      3. *-commutative 54.5%

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

      4. distribute-rgt-in 54.4%

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

      5. associate--l+ 54.4%

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

      6. fma-def 54.4%

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

      7. distribute-lft-out-- 54.7%

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

      8. +-commutative 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in t around 0 48.3%

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

   5. Taylor expanded in x around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

   if -1.9000000000000001e66 < x < -3.49999999999999992e-244 or 3.69999999999999997e-292 < x < 2.7999999999999999e111

   1. Initial program 66.8%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

   4. Simplified 60.3%

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

   if -3.49999999999999992e-244 < x < 3.69999999999999997e-292

   1. Initial program 73.5%

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

   2. Taylor expanded in t around inf 58.1%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+66}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-244}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-292}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \end{array} \]

Alternative 12: 61.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + y \cdot \frac{a - b}{x}\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ z (* y (/ (- a b) x)))))
   (if (<= x -1.15e+66)
     t_2
     (if (<= x -4.6e-244)
       t_1
       (if (<= x 3.2e-292) a (if (<= x 6.8e+113) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (y * ((a - b) / x));
	double tmp;
	if (x <= -1.15e+66) {
		tmp = t_2;
	} else if (x <= -4.6e-244) {
		tmp = t_1;
	} else if (x <= 3.2e-292) {
		tmp = a;
	} else if (x <= 6.8e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z + (y * ((a - b) / x))
    if (x <= (-1.15d+66)) then
        tmp = t_2
    else if (x <= (-4.6d-244)) then
        tmp = t_1
    else if (x <= 3.2d-292) then
        tmp = a
    else if (x <= 6.8d+113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (y * ((a - b) / x));
	double tmp;
	if (x <= -1.15e+66) {
		tmp = t_2;
	} else if (x <= -4.6e-244) {
		tmp = t_1;
	} else if (x <= 3.2e-292) {
		tmp = a;
	} else if (x <= 6.8e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z + (y * ((a - b) / x))
	tmp = 0
	if x <= -1.15e+66:
		tmp = t_2
	elif x <= -4.6e-244:
		tmp = t_1
	elif x <= 3.2e-292:
		tmp = a
	elif x <= 6.8e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z + Float64(y * Float64(Float64(a - b) / x)))
	tmp = 0.0
	if (x <= -1.15e+66)
		tmp = t_2;
	elseif (x <= -4.6e-244)
		tmp = t_1;
	elseif (x <= 3.2e-292)
		tmp = a;
	elseif (x <= 6.8e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z + (y * ((a - b) / x));
	tmp = 0.0;
	if (x <= -1.15e+66)
		tmp = t_2;
	elseif (x <= -4.6e-244)
		tmp = t_1;
	elseif (x <= 3.2e-292)
		tmp = a;
	elseif (x <= 6.8e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(y * N[(N[(a - b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+66], t$95$2, If[LessEqual[x, -4.6e-244], t$95$1, If[LessEqual[x, 3.2e-292], a, If[LessEqual[x, 6.8e+113], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e66 or 6.80000000000000038e113 < x

   1. Initial program 54.5%

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

      1. associate--l+ 54.5%

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

      2. fma-def 54.5%

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

      3. *-commutative 54.5%

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

      4. distribute-rgt-in 54.4%

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

      5. associate--l+ 54.4%

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

      6. fma-def 54.4%

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

      7. distribute-lft-out-- 54.7%

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

      8. +-commutative 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in t around 0 48.3%

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

   5. Taylor expanded in z around 0 67.2%

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

   6. Taylor expanded in y around 0 64.8%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

   if -1.15e66 < x < -4.6e-244 or 3.2000000000000002e-292 < x < 6.80000000000000038e113

   1. Initial program 66.8%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

   4. Simplified 60.3%

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

   if -4.6e-244 < x < 3.2000000000000002e-292

   1. Initial program 73.5%

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

   2. Taylor expanded in t around inf 58.1%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+66}:\\ \;\;\;\;z + y \cdot \frac{a - b}{x}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-244}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+113}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \frac{a - b}{x}\\ \end{array} \]

Alternative 13: 59.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + y \cdot \frac{a}{x}\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-292}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ z (* y (/ a x)))))
   (if (<= x -5.6e+179)
     t_2
     (if (<= x -3.2e-244)
       t_1
       (if (<= x 3e-292) a (if (<= x 2.4e+109) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (y * (a / x));
	double tmp;
	if (x <= -5.6e+179) {
		tmp = t_2;
	} else if (x <= -3.2e-244) {
		tmp = t_1;
	} else if (x <= 3e-292) {
		tmp = a;
	} else if (x <= 2.4e+109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = z + (y * (a / x))
    if (x <= (-5.6d+179)) then
        tmp = t_2
    else if (x <= (-3.2d-244)) then
        tmp = t_1
    else if (x <= 3d-292) then
        tmp = a
    else if (x <= 2.4d+109) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = z + (y * (a / x));
	double tmp;
	if (x <= -5.6e+179) {
		tmp = t_2;
	} else if (x <= -3.2e-244) {
		tmp = t_1;
	} else if (x <= 3e-292) {
		tmp = a;
	} else if (x <= 2.4e+109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = z + (y * (a / x))
	tmp = 0
	if x <= -5.6e+179:
		tmp = t_2
	elif x <= -3.2e-244:
		tmp = t_1
	elif x <= 3e-292:
		tmp = a
	elif x <= 2.4e+109:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(z + Float64(y * Float64(a / x)))
	tmp = 0.0
	if (x <= -5.6e+179)
		tmp = t_2;
	elseif (x <= -3.2e-244)
		tmp = t_1;
	elseif (x <= 3e-292)
		tmp = a;
	elseif (x <= 2.4e+109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = z + (y * (a / x));
	tmp = 0.0;
	if (x <= -5.6e+179)
		tmp = t_2;
	elseif (x <= -3.2e-244)
		tmp = t_1;
	elseif (x <= 3e-292)
		tmp = a;
	elseif (x <= 2.4e+109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+179], t$95$2, If[LessEqual[x, -3.2e-244], t$95$1, If[LessEqual[x, 3e-292], a, If[LessEqual[x, 2.4e+109], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.60000000000000001e179 or 2.39999999999999987e109 < x

   1. Initial program 55.6%

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

      1. associate--l+ 55.6%

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

      2. fma-def 55.6%

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

      3. *-commutative 55.6%

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

      4. distribute-rgt-in 55.5%

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

      5. associate--l+ 55.5%

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

      6. fma-def 55.5%

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

      7. distribute-lft-out-- 55.7%

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

      8. +-commutative 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in t around 0 48.8%

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

   5. Taylor expanded in x around inf 66.6%

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

   6. Taylor expanded in a around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 64.9%

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

      3. associate-/r/ 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in y around 0 60.9%

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

       1. *-commutative 60.9%

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

       2. associate-*l/ 64.9%

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

       3. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -5.60000000000000001e179 < x < -3.1999999999999998e-244 or 3.00000000000000015e-292 < x < 2.39999999999999987e109

   1. Initial program 64.8%

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

   2. Taylor expanded in y around inf 60.7%

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

      1. +-commutative 60.7%

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

   4. Simplified 60.7%

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

   if -3.1999999999999998e-244 < x < 3.00000000000000015e-292

   1. Initial program 73.5%

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

   2. Taylor expanded in t around inf 58.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+179}:\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-244}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-292}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+109}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \frac{a}{x}\\ \end{array} \]

Alternative 14: 54.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -1.25e+109)
     a
     (if (<= t 9.8e-206)
       t_1
       (if (<= t 5.5e+15) z (if (<= t 2.2e+209) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.25e+109) {
		tmp = a;
	} else if (t <= 9.8e-206) {
		tmp = t_1;
	} else if (t <= 5.5e+15) {
		tmp = z;
	} else if (t <= 2.2e+209) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-1.25d+109)) then
        tmp = a
    else if (t <= 9.8d-206) then
        tmp = t_1
    else if (t <= 5.5d+15) then
        tmp = z
    else if (t <= 2.2d+209) then
        tmp = t_1
    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 t_1 = (z + a) - b;
	double tmp;
	if (t <= -1.25e+109) {
		tmp = a;
	} else if (t <= 9.8e-206) {
		tmp = t_1;
	} else if (t <= 5.5e+15) {
		tmp = z;
	} else if (t <= 2.2e+209) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -1.25e+109:
		tmp = a
	elif t <= 9.8e-206:
		tmp = t_1
	elif t <= 5.5e+15:
		tmp = z
	elif t <= 2.2e+209:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -1.25e+109)
		tmp = a;
	elseif (t <= 9.8e-206)
		tmp = t_1;
	elseif (t <= 5.5e+15)
		tmp = z;
	elseif (t <= 2.2e+209)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -1.25e+109)
		tmp = a;
	elseif (t <= 9.8e-206)
		tmp = t_1;
	elseif (t <= 5.5e+15)
		tmp = z;
	elseif (t <= 2.2e+209)
		tmp = t_1;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -1.25e+109], a, If[LessEqual[t, 9.8e-206], t$95$1, If[LessEqual[t, 5.5e+15], z, If[LessEqual[t, 2.2e+209], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e109 or 2.1999999999999999e209 < t

   1. Initial program 48.9%

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

   2. Taylor expanded in t around inf 63.9%

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

   if -1.25e109 < t < 9.7999999999999999e-206 or 5.5e15 < t < 2.1999999999999999e209

   1. Initial program 65.5%

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

   2. Taylor expanded in y around inf 60.5%

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

      1. +-commutative 60.5%

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

   4. Simplified 60.5%

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

   if 9.7999999999999999e-206 < t < 5.5e15

   1. Initial program 75.0%

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

   2. Taylor expanded in x around inf 59.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-206}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+209}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 53.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;z + a \cdot \frac{y}{x}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -3.5e+109)
     a
     (if (<= t 3e-205)
       t_1
       (if (<= t 7.5e+32) (+ z (* a (/ y x))) (if (<= t 1.65e+208) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -3.5e+109) {
		tmp = a;
	} else if (t <= 3e-205) {
		tmp = t_1;
	} else if (t <= 7.5e+32) {
		tmp = z + (a * (y / x));
	} else if (t <= 1.65e+208) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-3.5d+109)) then
        tmp = a
    else if (t <= 3d-205) then
        tmp = t_1
    else if (t <= 7.5d+32) then
        tmp = z + (a * (y / x))
    else if (t <= 1.65d+208) then
        tmp = t_1
    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 t_1 = (z + a) - b;
	double tmp;
	if (t <= -3.5e+109) {
		tmp = a;
	} else if (t <= 3e-205) {
		tmp = t_1;
	} else if (t <= 7.5e+32) {
		tmp = z + (a * (y / x));
	} else if (t <= 1.65e+208) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -3.5e+109:
		tmp = a
	elif t <= 3e-205:
		tmp = t_1
	elif t <= 7.5e+32:
		tmp = z + (a * (y / x))
	elif t <= 1.65e+208:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -3.5e+109)
		tmp = a;
	elseif (t <= 3e-205)
		tmp = t_1;
	elseif (t <= 7.5e+32)
		tmp = Float64(z + Float64(a * Float64(y / x)));
	elseif (t <= 1.65e+208)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -3.5e+109)
		tmp = a;
	elseif (t <= 3e-205)
		tmp = t_1;
	elseif (t <= 7.5e+32)
		tmp = z + (a * (y / x));
	elseif (t <= 1.65e+208)
		tmp = t_1;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t, -3.5e+109], a, If[LessEqual[t, 3e-205], t$95$1, If[LessEqual[t, 7.5e+32], N[(z + N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+208], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.49999999999999983e109 or 1.65e208 < t

   1. Initial program 48.9%

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

   2. Taylor expanded in t around inf 63.9%

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

   if -3.49999999999999983e109 < t < 3e-205 or 7.49999999999999959e32 < t < 1.65e208

   1. Initial program 65.7%

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

   2. Taylor expanded in y around inf 61.3%

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

      1. +-commutative 61.3%

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

   4. Simplified 61.3%

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

   if 3e-205 < t < 7.49999999999999959e32

   1. Initial program 74.1%

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

      1. associate--l+ 74.1%

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

      2. fma-def 74.3%

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

      3. *-commutative 74.3%

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

      4. distribute-rgt-in 74.3%

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

      5. associate--l+ 74.3%

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

      6. fma-def 74.3%

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

      7. distribute-lft-out-- 74.3%

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

      8. +-commutative 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in t around 0 58.9%

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

   5. Taylor expanded in x around inf 62.5%

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

   6. Taylor expanded in a around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 59.7%

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

      3. associate-/r/ 60.0%

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

   8. Simplified 60.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-205}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;z + a \cdot \frac{y}{x}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+208}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 57.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-78} \lor \neg \left(y \leq 1.8 \cdot 10^{-107}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y + x}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.2e-78) (not (<= y 1.8e-107)))
   (- (+ z a) b)
   (* z (/ (+ y x) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e-78) || !(y <= 1.8e-107)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((y + x) / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.2d-78)) .or. (.not. (y <= 1.8d-107))) then
        tmp = (z + a) - b
    else
        tmp = z * ((y + x) / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e-78) || !(y <= 1.8e-107)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((y + x) / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.2e-78) or not (y <= 1.8e-107):
		tmp = (z + a) - b
	else:
		tmp = z * ((y + x) / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.2e-78) || !(y <= 1.8e-107))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(y + x) / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.2e-78) || ~((y <= 1.8e-107)))
		tmp = (z + a) - b;
	else
		tmp = z * ((y + x) / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.2e-78], N[Not[LessEqual[y, 1.8e-107]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(y + x), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2000000000000005e-78 or 1.79999999999999988e-107 < y

   1. Initial program 55.6%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

   4. Simplified 63.1%

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

   if -7.2000000000000005e-78 < y < 1.79999999999999988e-107

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 43.8%

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

      1. associate-/l* 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in y around 0 38.3%

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

      1. associate-/r/ 53.0%

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

   7. Applied egg-rr 53.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-78} \lor \neg \left(y \leq 1.8 \cdot 10^{-107}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y + x}{t + x}\\ \end{array} \]

Alternative 17: 57.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-80} \lor \neg \left(y \leq 2.25 \cdot 10^{-107}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t + x}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e-80) (not (<= y 2.25e-107)))
   (- (+ z a) b)
   (/ z (/ (+ t x) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e-80) || !(y <= 2.25e-107)) {
		tmp = (z + a) - b;
	} else {
		tmp = z / ((t + x) / 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 <= (-8.2d-80)) .or. (.not. (y <= 2.25d-107))) then
        tmp = (z + a) - b
    else
        tmp = z / ((t + x) / 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 <= -8.2e-80) || !(y <= 2.25e-107)) {
		tmp = (z + a) - b;
	} else {
		tmp = z / ((t + x) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e-80) or not (y <= 2.25e-107):
		tmp = (z + a) - b
	else:
		tmp = z / ((t + x) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e-80) || !(y <= 2.25e-107))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z / Float64(Float64(t + x) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e-80) || ~((y <= 2.25e-107)))
		tmp = (z + a) - b;
	else
		tmp = z / ((t + x) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e-80], N[Not[LessEqual[y, 2.25e-107]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z / N[(N[(t + x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999999e-80 or 2.25000000000000008e-107 < y

   1. Initial program 55.6%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

   4. Simplified 63.1%

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

   if -8.1999999999999999e-80 < y < 2.25000000000000008e-107

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 43.8%

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

      1. associate-/l* 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in y around 0 38.3%

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

   6. Taylor expanded in y around 0 40.4%

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

      1. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-80} \lor \neg \left(y \leq 2.25 \cdot 10^{-107}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t + x}{x}}\\ \end{array} \]

Alternative 18: 41.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -880000000:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+212}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -880000000.0) a (if (<= t 4.2e+212) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -880000000.0) {
		tmp = a;
	} else if (t <= 4.2e+212) {
		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 <= (-880000000.0d0)) then
        tmp = a
    else if (t <= 4.2d+212) 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 <= -880000000.0) {
		tmp = a;
	} else if (t <= 4.2e+212) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -880000000.0:
		tmp = a
	elif t <= 4.2e+212:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -880000000.0)
		tmp = a;
	elseif (t <= 4.2e+212)
		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 <= -880000000.0)
		tmp = a;
	elseif (t <= 4.2e+212)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -880000000.0], a, If[LessEqual[t, 4.2e+212], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8e8 or 4.2e212 < t

   1. Initial program 54.1%

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

   2. Taylor expanded in t around inf 60.4%

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

   if -8.8e8 < t < 4.2e212

   1. Initial program 67.1%

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

   2. Taylor expanded in x around inf 46.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -880000000:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+212}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19: 32.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.8%

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

2. Taylor expanded in t around inf 31.1%

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

3. Final simplification 31.1%

   \[\leadsto a \]

Developer target: 82.0% 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 2023240 
(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)))