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

Percentage Accurate: 60.7% → 87.9%

Time: 11.4s

Alternatives: 14

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+257}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+257))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+257)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+257)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+257):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+257))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+257)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+257]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000028e257 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.5%

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

   2. Taylor expanded in y around inf 76.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000028e257

   1. Initial program 99.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+257}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 2: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{y + x}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}} + \left(\frac{z \cdot x}{t_1} + \frac{z - b}{\frac{t_1}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= z -4.4e+192)
     (/ (+ y x) (/ t_1 z))
     (+ (/ a (/ t_1 (+ y t))) (+ (/ (* z x) t_1) (/ (- z b) (/ t_1 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -4.4e+192) {
		tmp = (y + x) / (t_1 / z);
	} else {
		tmp = (a / (t_1 / (y + t))) + (((z * x) / t_1) + ((z - b) / (t_1 / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (z <= (-4.4d+192)) then
        tmp = (y + x) / (t_1 / z)
    else
        tmp = (a / (t_1 / (y + t))) + (((z * x) / t_1) + ((z - b) / (t_1 / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -4.4e+192) {
		tmp = (y + x) / (t_1 / z);
	} else {
		tmp = (a / (t_1 / (y + t))) + (((z * x) / t_1) + ((z - b) / (t_1 / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if z <= -4.4e+192:
		tmp = (y + x) / (t_1 / z)
	else:
		tmp = (a / (t_1 / (y + t))) + (((z * x) / t_1) + ((z - b) / (t_1 / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (z <= -4.4e+192)
		tmp = Float64(Float64(y + x) / Float64(t_1 / z));
	else
		tmp = Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(Float64(z * x) / t_1) + Float64(Float64(z - b) / Float64(t_1 / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (z <= -4.4e+192)
		tmp = (y + x) / (t_1 / z);
	else
		tmp = (a / (t_1 / (y + t))) + (((z * x) / t_1) + ((z - b) / (t_1 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+192], N[(N[(y + x), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000001e192

   1. Initial program 17.1%

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

   2. Taylor expanded in z around inf 17.5%

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

      1. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

   if -4.4000000000000001e192 < z

   1. Initial program 67.3%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in a around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. +-commutative 67.3%

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

      3. associate-+l+ 67.3%

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

      4. associate-/l* 73.3%

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

      5. associate-/l* 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}} + \left(\frac{z \cdot x}{y + \left(x + t\right)} + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\right)\\ \end{array} \]

Alternative 3: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \left(z + \frac{z - b}{\frac{t_1}{y}}\right)\\ t_3 := \frac{y + x}{\frac{t_1}{z}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+189}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+75}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-251}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ a (+ z (/ (- z b) (/ t_1 y)))))
        (t_3 (/ (+ y x) (/ t_1 z))))
   (if (<= z -2.1e+189)
     t_3
     (if (<= z -1.55e+91)
       (- (+ z a) b)
       (if (<= z -2.3e+75)
         (+ a (* x (/ z (+ x t))))
         (if (<= z -2.7e-235)
           t_2
           (if (<= z 3.05e-251)
             (/ (- (* a (+ y t)) (* y b)) t_1)
             (if (<= z 3.2e+48) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z + ((z - b) / (t_1 / y)));
	double t_3 = (y + x) / (t_1 / z);
	double tmp;
	if (z <= -2.1e+189) {
		tmp = t_3;
	} else if (z <= -1.55e+91) {
		tmp = (z + a) - b;
	} else if (z <= -2.3e+75) {
		tmp = a + (x * (z / (x + t)));
	} else if (z <= -2.7e-235) {
		tmp = t_2;
	} else if (z <= 3.05e-251) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (z <= 3.2e+48) {
		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 + (x + t)
    t_2 = a + (z + ((z - b) / (t_1 / y)))
    t_3 = (y + x) / (t_1 / z)
    if (z <= (-2.1d+189)) then
        tmp = t_3
    else if (z <= (-1.55d+91)) then
        tmp = (z + a) - b
    else if (z <= (-2.3d+75)) then
        tmp = a + (x * (z / (x + t)))
    else if (z <= (-2.7d-235)) then
        tmp = t_2
    else if (z <= 3.05d-251) then
        tmp = ((a * (y + t)) - (y * b)) / t_1
    else if (z <= 3.2d+48) 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 + (x + t);
	double t_2 = a + (z + ((z - b) / (t_1 / y)));
	double t_3 = (y + x) / (t_1 / z);
	double tmp;
	if (z <= -2.1e+189) {
		tmp = t_3;
	} else if (z <= -1.55e+91) {
		tmp = (z + a) - b;
	} else if (z <= -2.3e+75) {
		tmp = a + (x * (z / (x + t)));
	} else if (z <= -2.7e-235) {
		tmp = t_2;
	} else if (z <= 3.05e-251) {
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	} else if (z <= 3.2e+48) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + (z + ((z - b) / (t_1 / y)))
	t_3 = (y + x) / (t_1 / z)
	tmp = 0
	if z <= -2.1e+189:
		tmp = t_3
	elif z <= -1.55e+91:
		tmp = (z + a) - b
	elif z <= -2.3e+75:
		tmp = a + (x * (z / (x + t)))
	elif z <= -2.7e-235:
		tmp = t_2
	elif z <= 3.05e-251:
		tmp = ((a * (y + t)) - (y * b)) / t_1
	elif z <= 3.2e+48:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a + Float64(z + Float64(Float64(z - b) / Float64(t_1 / y))))
	t_3 = Float64(Float64(y + x) / Float64(t_1 / z))
	tmp = 0.0
	if (z <= -2.1e+189)
		tmp = t_3;
	elseif (z <= -1.55e+91)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= -2.3e+75)
		tmp = Float64(a + Float64(x * Float64(z / Float64(x + t))));
	elseif (z <= -2.7e-235)
		tmp = t_2;
	elseif (z <= 3.05e-251)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_1);
	elseif (z <= 3.2e+48)
		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 + (x + t);
	t_2 = a + (z + ((z - b) / (t_1 / y)));
	t_3 = (y + x) / (t_1 / z);
	tmp = 0.0;
	if (z <= -2.1e+189)
		tmp = t_3;
	elseif (z <= -1.55e+91)
		tmp = (z + a) - b;
	elseif (z <= -2.3e+75)
		tmp = a + (x * (z / (x + t)));
	elseif (z <= -2.7e-235)
		tmp = t_2;
	elseif (z <= 3.05e-251)
		tmp = ((a * (y + t)) - (y * b)) / t_1;
	elseif (z <= 3.2e+48)
		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[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+189], t$95$3, If[LessEqual[z, -1.55e+91], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, -2.3e+75], N[(a + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-235], t$95$2, If[LessEqual[z, 3.05e-251], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 3.2e+48], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.09999999999999992e189 or 3.2000000000000001e48 < z

   1. Initial program 39.3%

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

   2. Taylor expanded in z around inf 36.0%

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

      1. associate-/l* 72.6%

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

   4. Simplified 72.6%

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

   if -2.09999999999999992e189 < z < -1.54999999999999999e91

   1. Initial program 53.8%

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

   2. Taylor expanded in y around inf 74.1%

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

   if -1.54999999999999999e91 < z < -2.2999999999999999e75

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in a around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. +-commutative 98.8%

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

      3. associate-+l+ 98.8%

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

      4. associate-/l* 99.2%

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

      5. associate-/l* 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around inf 99.2%

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

   8. Taylor expanded in y around 0 99.2%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 99.6%

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

   10. Simplified 99.6%

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

   if -2.2999999999999999e75 < z < -2.7000000000000002e-235 or 3.0500000000000001e-251 < z < 3.2000000000000001e48

   1. Initial program 72.7%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. +-commutative 72.7%

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

      3. associate-+l+ 72.7%

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

      4. associate-/l* 82.4%

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

      5. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 85.3%

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

   8. Taylor expanded in x around inf 77.4%

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

   if -2.7000000000000002e-235 < z < 3.0500000000000001e-251

   1. Initial program 87.7%

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

   2. Taylor expanded in z around 0 87.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+189}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+75}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-235}:\\ \;\;\;\;a + \left(z + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-251}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;a + \left(z + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \end{array} \]

Alternative 4: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y + x}{\frac{t_1}{z}}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+74}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;a + \left(z + \frac{z - b}{\frac{t_1}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ (+ y x) (/ t_1 z))))
   (if (<= z -3.7e+192)
     t_2
     (if (<= z -1.3e+91)
       (- (+ z a) b)
       (if (<= z -2.6e+74)
         (+ a (* x (/ z (+ x t))))
         (if (<= z 4.8e+47) (+ a (+ z (/ (- z b) (/ t_1 y)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (y + x) / (t_1 / z);
	double tmp;
	if (z <= -3.7e+192) {
		tmp = t_2;
	} else if (z <= -1.3e+91) {
		tmp = (z + a) - b;
	} else if (z <= -2.6e+74) {
		tmp = a + (x * (z / (x + t)));
	} else if (z <= 4.8e+47) {
		tmp = a + (z + ((z - b) / (t_1 / y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (y + x) / (t_1 / z)
    if (z <= (-3.7d+192)) then
        tmp = t_2
    else if (z <= (-1.3d+91)) then
        tmp = (z + a) - b
    else if (z <= (-2.6d+74)) then
        tmp = a + (x * (z / (x + t)))
    else if (z <= 4.8d+47) then
        tmp = a + (z + ((z - b) / (t_1 / y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (y + x) / (t_1 / z);
	double tmp;
	if (z <= -3.7e+192) {
		tmp = t_2;
	} else if (z <= -1.3e+91) {
		tmp = (z + a) - b;
	} else if (z <= -2.6e+74) {
		tmp = a + (x * (z / (x + t)));
	} else if (z <= 4.8e+47) {
		tmp = a + (z + ((z - b) / (t_1 / y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (y + x) / (t_1 / z)
	tmp = 0
	if z <= -3.7e+192:
		tmp = t_2
	elif z <= -1.3e+91:
		tmp = (z + a) - b
	elif z <= -2.6e+74:
		tmp = a + (x * (z / (x + t)))
	elif z <= 4.8e+47:
		tmp = a + (z + ((z - b) / (t_1 / y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(y + x) / Float64(t_1 / z))
	tmp = 0.0
	if (z <= -3.7e+192)
		tmp = t_2;
	elseif (z <= -1.3e+91)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= -2.6e+74)
		tmp = Float64(a + Float64(x * Float64(z / Float64(x + t))));
	elseif (z <= 4.8e+47)
		tmp = Float64(a + Float64(z + Float64(Float64(z - b) / Float64(t_1 / y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (y + x) / (t_1 / z);
	tmp = 0.0;
	if (z <= -3.7e+192)
		tmp = t_2;
	elseif (z <= -1.3e+91)
		tmp = (z + a) - b;
	elseif (z <= -2.6e+74)
		tmp = a + (x * (z / (x + t)));
	elseif (z <= 4.8e+47)
		tmp = a + (z + ((z - b) / (t_1 / y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+192], t$95$2, If[LessEqual[z, -1.3e+91], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, -2.6e+74], N[(a + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+47], N[(a + N[(z + N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7000000000000001e192 or 4.80000000000000037e47 < z

   1. Initial program 39.3%

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

   2. Taylor expanded in z around inf 36.0%

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

      1. associate-/l* 72.6%

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

   4. Simplified 72.6%

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

   if -3.7000000000000001e192 < z < -1.3e91

   1. Initial program 53.8%

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

   2. Taylor expanded in y around inf 74.1%

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

   if -1.3e91 < z < -2.6000000000000001e74

   1. Initial program 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in a around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. +-commutative 98.8%

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

      3. associate-+l+ 98.8%

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

      4. associate-/l* 99.2%

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

      5. associate-/l* 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around inf 99.2%

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

   8. Taylor expanded in y around 0 99.2%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 99.6%

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

   10. Simplified 99.6%

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

   if -2.6000000000000001e74 < z < 4.80000000000000037e47

   1. Initial program 75.2%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. +-commutative 75.2%

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

      3. associate-+l+ 75.2%

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

      4. associate-/l* 82.0%

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

      5. associate-/l* 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in y around inf 81.0%

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

   8. Taylor expanded in x around inf 73.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+192}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+74}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;a + \left(z + \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \end{array} \]

Alternative 5: 65.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-58}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+46}:\\ \;\;\;\;a - b \cdot \frac{y}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ y x) (/ (+ y (+ x t)) z))))
   (if (<= z -1.46e+100)
     t_1
     (if (<= z -1.8e-58)
       (+ a (* x (/ z (+ x t))))
       (if (<= z 8e+46) (- a (* b (/ y (+ t (+ y x))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) / ((y + (x + t)) / z);
	double tmp;
	if (z <= -1.46e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-58) {
		tmp = a + (x * (z / (x + t)));
	} else if (z <= 8e+46) {
		tmp = a - (b * (y / (t + (y + x))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y + x) / ((y + (x + t)) / z)
    if (z <= (-1.46d+100)) then
        tmp = t_1
    else if (z <= (-1.8d-58)) then
        tmp = a + (x * (z / (x + t)))
    else if (z <= 8d+46) then
        tmp = a - (b * (y / (t + (y + x))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) / ((y + (x + t)) / z);
	double tmp;
	if (z <= -1.46e+100) {
		tmp = t_1;
	} else if (z <= -1.8e-58) {
		tmp = a + (x * (z / (x + t)));
	} else if (z <= 8e+46) {
		tmp = a - (b * (y / (t + (y + x))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + x) / ((y + (x + t)) / z)
	tmp = 0
	if z <= -1.46e+100:
		tmp = t_1
	elif z <= -1.8e-58:
		tmp = a + (x * (z / (x + t)))
	elif z <= 8e+46:
		tmp = a - (b * (y / (t + (y + x))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) / Float64(Float64(y + Float64(x + t)) / z))
	tmp = 0.0
	if (z <= -1.46e+100)
		tmp = t_1;
	elseif (z <= -1.8e-58)
		tmp = Float64(a + Float64(x * Float64(z / Float64(x + t))));
	elseif (z <= 8e+46)
		tmp = Float64(a - Float64(b * Float64(y / Float64(t + Float64(y + x)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + x) / ((y + (x + t)) / z);
	tmp = 0.0;
	if (z <= -1.46e+100)
		tmp = t_1;
	elseif (z <= -1.8e-58)
		tmp = a + (x * (z / (x + t)));
	elseif (z <= 8e+46)
		tmp = a - (b * (y / (t + (y + x))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.46e+100], t$95$1, If[LessEqual[z, -1.8e-58], N[(a + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+46], N[(a - N[(b * N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.46e100 or 7.9999999999999999e46 < z

   1. Initial program 42.2%

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

   2. Taylor expanded in z around inf 37.9%

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

      1. associate-/l* 70.5%

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

   4. Simplified 70.5%

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

   if -1.46e100 < z < -1.80000000000000005e-58

   1. Initial program 85.1%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in a around inf 85.0%

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

      1. +-commutative 85.0%

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

      2. +-commutative 85.0%

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

      3. associate-+l+ 85.0%

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

      4. associate-/l* 96.7%

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

      5. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around inf 81.5%

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

   8. Taylor expanded in y around 0 67.5%

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

      1. associate-/l* 67.6%

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

      2. associate-/r/ 65.5%

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

   10. Simplified 65.5%

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

   if -1.80000000000000005e-58 < z < 7.9999999999999999e46

   1. Initial program 73.0%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in a around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. +-commutative 73.0%

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

      3. associate-+l+ 73.0%

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

      4. associate-/l* 78.1%

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

      5. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in y around inf 81.9%

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

   8. Taylor expanded in z around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

      3. associate-/l* 66.0%

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

      4. associate-/r/ 68.9%

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

      5. +-commutative 68.9%

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

      6. associate-+l+ 68.9%

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

   10. Simplified 68.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+100}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-58}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+46}:\\ \;\;\;\;a - b \cdot \frac{y}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{\frac{y + \left(x + t\right)}{z}}\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+183} \lor \neg \left(t \leq 2.15 \cdot 10^{+152}\right):\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e+183) (not (<= t 2.15e+152)))
   (+ a (* y (- (/ z t) (/ b t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+183) || !(t <= 2.15e+152)) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3d+183)) .or. (.not. (t <= 2.15d+152))) then
        tmp = a + (y * ((z / t) - (b / t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+183) || !(t <= 2.15e+152)) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e+183) or not (t <= 2.15e+152):
		tmp = a + (y * ((z / t) - (b / t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e+183) || !(t <= 2.15e+152))
		tmp = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3e+183) || ~((t <= 2.15e+152)))
		tmp = a + (y * ((z / t) - (b / t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e+183], N[Not[LessEqual[t, 2.15e+152]], $MachinePrecision]], N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999996e183 or 2.14999999999999997e152 < t

   1. Initial program 53.2%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in x around 0 45.1%

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

   5. Taylor expanded in y around 0 76.4%

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

   if -2.99999999999999996e183 < t < 2.14999999999999997e152

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 63.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+183} \lor \neg \left(t \leq 2.15 \cdot 10^{+152}\right):\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 7: 61.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+183}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e+183)
   (+ a (/ y (/ t z)))
   (if (<= t 6.4e+105) (- (+ z a) b) (+ a (* x (/ z (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+183) {
		tmp = a + (y / (t / z));
	} else if (t <= 6.4e+105) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (x * (z / (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.15d+183)) then
        tmp = a + (y / (t / z))
    else if (t <= 6.4d+105) then
        tmp = (z + a) - b
    else
        tmp = a + (x * (z / (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+183) {
		tmp = a + (y / (t / z));
	} else if (t <= 6.4e+105) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (x * (z / (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e+183:
		tmp = a + (y / (t / z))
	elif t <= 6.4e+105:
		tmp = (z + a) - b
	else:
		tmp = a + (x * (z / (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e+183)
		tmp = Float64(a + Float64(y / Float64(t / z)));
	elseif (t <= 6.4e+105)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(x * Float64(z / Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e+183)
		tmp = a + (y / (t / z));
	elseif (t <= 6.4e+105)
		tmp = (z + a) - b;
	else
		tmp = a + (x * (z / (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.15e+183], N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e+105], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1500000000000002e183

   1. Initial program 48.4%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in x around 0 35.7%

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

   5. Taylor expanded in y around 0 76.4%

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

   6. Taylor expanded in b around 0 38.7%

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

      1. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   if -2.1500000000000002e183 < t < 6.4e105

   1. Initial program 63.3%

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

   2. Taylor expanded in y around inf 64.0%

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

   if 6.4e105 < t

   1. Initial program 62.5%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in a around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. +-commutative 62.8%

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

      3. associate-+l+ 62.8%

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

      4. associate-/l* 77.2%

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

      5. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in y around inf 82.7%

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

   8. Taylor expanded in y around 0 57.6%

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

      1. associate-/l* 66.0%

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

      2. associate-/r/ 63.7%

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

   10. Simplified 63.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+183}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{x + t}\\ \end{array} \]

Alternative 8: 60.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+185}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e+185)
   (+ a (/ y (/ t z)))
   (if (<= t 1.5e+152) (- (+ z a) b) (- a (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+185) {
		tmp = a + (y / (t / z));
	} else if (t <= 1.5e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (b * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.35d+185)) then
        tmp = a + (y / (t / z))
    else if (t <= 1.5d+152) then
        tmp = (z + a) - b
    else
        tmp = a - (b * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+185) {
		tmp = a + (y / (t / z));
	} else if (t <= 1.5e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (b * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e+185:
		tmp = a + (y / (t / z))
	elif t <= 1.5e+152:
		tmp = (z + a) - b
	else:
		tmp = a - (b * (y / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e+185)
		tmp = Float64(a + Float64(y / Float64(t / z)));
	elseif (t <= 1.5e+152)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a - Float64(b * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.35e+185)
		tmp = a + (y / (t / z));
	elseif (t <= 1.5e+152)
		tmp = (z + a) - b;
	else
		tmp = a - (b * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e+185], N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+152], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000003e185

   1. Initial program 48.4%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in x around 0 35.7%

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

   5. Taylor expanded in y around 0 76.4%

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

   6. Taylor expanded in b around 0 38.7%

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

      1. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   if -1.35000000000000003e185 < t < 1.49999999999999995e152

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 63.1%

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

   if 1.49999999999999995e152 < t

   1. Initial program 57.8%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in x around 0 54.1%

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

   5. Taylor expanded in y around 0 76.3%

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

   6. Taylor expanded in z around 0 57.9%

      \[\leadsto \color{blue}{a + -1 \cdot \frac{y \cdot b}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

      3. associate-/l* 69.0%

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

      4. associate-/r/ 65.5%

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

   8. Simplified 65.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+185}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \end{array} \]

Alternative 9: 60.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+183}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e+183)
   (+ a (/ y (/ t z)))
   (if (<= t 3.75e+152) (- (+ z a) b) (- a (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+183) {
		tmp = a + (y / (t / z));
	} else if (t <= 3.75e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (y * (b / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.15d+183)) then
        tmp = a + (y / (t / z))
    else if (t <= 3.75d+152) then
        tmp = (z + a) - b
    else
        tmp = a - (y * (b / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+183) {
		tmp = a + (y / (t / z));
	} else if (t <= 3.75e+152) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (y * (b / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e+183:
		tmp = a + (y / (t / z))
	elif t <= 3.75e+152:
		tmp = (z + a) - b
	else:
		tmp = a - (y * (b / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e+183)
		tmp = Float64(a + Float64(y / Float64(t / z)));
	elseif (t <= 3.75e+152)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a - Float64(y * Float64(b / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e+183)
		tmp = a + (y / (t / z));
	elseif (t <= 3.75e+152)
		tmp = (z + a) - b;
	else
		tmp = a - (y * (b / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.15e+183], N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.75e+152], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1500000000000002e183

   1. Initial program 48.4%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in x around 0 35.7%

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

   5. Taylor expanded in y around 0 76.4%

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

   6. Taylor expanded in b around 0 38.7%

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

      1. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   if -2.1500000000000002e183 < t < 3.75000000000000023e152

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 63.1%

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

   if 3.75000000000000023e152 < t

   1. Initial program 57.8%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in x around 0 54.1%

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

   5. Taylor expanded in y around 0 76.3%

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

   6. Taylor expanded in z around 0 69.1%

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

      1. neg-mul-1 69.1%

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

      2. distribute-neg-frac 69.1%

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

   8. Simplified 69.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+183}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \end{array} \]

Alternative 10: 59.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-128} \lor \neg \left(y \leq 1.05 \cdot 10^{-120}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.8e-128) (not (<= y 1.05e-120))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.8e-128) || !(y <= 1.05e-120)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.8d-128)) .or. (.not. (y <= 1.05d-120))) then
        tmp = (z + a) - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.8e-128) || !(y <= 1.05e-120)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.8e-128) or not (y <= 1.05e-120):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.8e-128) || !(y <= 1.05e-120))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.8e-128) || ~((y <= 1.05e-120)))
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.8e-128], N[Not[LessEqual[y, 1.05e-120]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000037e-128 or 1.05e-120 < y

   1. Initial program 54.6%

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

   2. Taylor expanded in y around inf 65.5%

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

   if -8.80000000000000037e-128 < y < 1.05e-120

   1. Initial program 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in a around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. +-commutative 82.6%

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

      3. associate-+l+ 82.6%

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

      4. associate-/l* 88.4%

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

      5. associate-/l* 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around inf 68.4%

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

   8. Taylor expanded in x around inf 52.2%

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

      1. +-commutative 52.2%

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

   10. Simplified 52.2%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-128} \lor \neg \left(y \leq 1.05 \cdot 10^{-120}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 11: 57.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+183}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.3e+183) (+ a (/ y (/ t z))) (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e+183) {
		tmp = a + (y / (t / z));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.3d+183)) then
        tmp = a + (y / (t / z))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e+183) {
		tmp = a + (y / (t / z));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.3e+183:
		tmp = a + (y / (t / z))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.3e+183)
		tmp = Float64(a + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.3e+183)
		tmp = a + (y / (t / z));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.3e+183], N[(a + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e183

   1. Initial program 48.4%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in x around 0 35.7%

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

   5. Taylor expanded in y around 0 76.4%

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

   6. Taylor expanded in b around 0 38.7%

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

      1. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   if -1.3e183 < t

   1. Initial program 63.2%

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

   2. Taylor expanded in y around inf 61.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+183}:\\ \;\;\;\;a + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 44.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -68000000:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -68000000.0) a (if (<= a 1.8e-6) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -68000000.0) {
		tmp = a;
	} else if (a <= 1.8e-6) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-68000000.0d0)) then
        tmp = a
    else if (a <= 1.8d-6) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -68000000.0) {
		tmp = a;
	} else if (a <= 1.8e-6) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -68000000.0:
		tmp = a
	elif a <= 1.8e-6:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -68000000.0)
		tmp = a;
	elseif (a <= 1.8e-6)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -68000000.0)
		tmp = a;
	elseif (a <= 1.8e-6)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -68000000.0], a, If[LessEqual[a, 1.8e-6], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.8e7 or 1.79999999999999992e-6 < a

   1. Initial program 54.3%

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

   2. Taylor expanded in t around inf 44.4%

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

   if -6.8e7 < a < 1.79999999999999992e-6

   1. Initial program 68.8%

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

   2. Taylor expanded in x around inf 46.5%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -68000000:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 51.7% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.8%

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

3. Simplified 62.4%

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

4. Taylor expanded in a around inf 61.8%

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

   1. +-commutative 61.8%

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

   2. +-commutative 61.8%

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

   3. associate-+l+ 61.8%

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

   4. associate-/l* 67.9%

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

   5. associate-/l* 87.4%

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

6. Simplified 87.4%

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

7. Taylor expanded in y around inf 76.0%

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

8. Taylor expanded in x around inf 51.1%

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

   1. +-commutative 51.1%

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

10. Simplified 51.1%

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

11. Final simplification 51.1%

    \[\leadsto z + a \]

Alternative 14: 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 61.8%

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

2. Taylor expanded in t around inf 25.6%

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

3. Final simplification 25.6%

   \[\leadsto a \]

Developer target: 81.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t_2}{t_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t_1}{t_2}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2023200 
(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)))