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

Percentage Accurate: 60.6% → 87.9%

Time: 15.5s

Alternatives: 13

Speedup: 1.1×

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: 60.6% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+275}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z + a \cdot \frac{y + t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 -2e+275)
     t_3
     (if (<= t_2 5e+299)
       t_2
       (if (<= t_2 INFINITY) (+ z (* a (/ (+ y t) t_1))) 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 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -2e+275) {
		tmp = t_3;
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -2e+275) {
		tmp = t_3;
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if t_2 <= -2e+275:
		tmp = t_3
	elif t_2 <= 5e+299:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z + (a * ((y + t) / t_1))
	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(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= -2e+275)
		tmp = t_3;
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / t_1)));
	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 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (t_2 <= -2e+275)
		tmp = t_3;
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z + (a * ((y + t) / t_1));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+275], t$95$3, If[LessEqual[t$95$2, 5e+299], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

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)) < -1.99999999999999992e275 or +inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.9%

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

   3. Taylor expanded in y around inf 81.6%

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

   if -1.99999999999999992e275 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000003e299

   1. Initial program 99.6%

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

   if 5.0000000000000003e299 < (/.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 5.8%

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

   3. Taylor expanded in b around 0 5.8%

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

      1. mul-1-neg 5.8%

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

      2. +-commutative 5.8%

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

      3. associate-+l+ 5.8%

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

      4. associate-/l* 39.6%

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

      5. +-commutative 39.6%

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

      6. associate-+r+ 39.6%

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

      7. +-commutative 39.6%

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

      8. associate-+l+ 39.6%

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

      9. sub-neg 39.6%

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

      10. div-sub 39.6%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in x around inf 71.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+275}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq \infty:\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1} + x \cdot \frac{z}{x + t}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+191}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot z}{t\_1} + y \cdot \frac{z - b}{t\_1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ (* a (/ (+ y t) t_1)) (* x (/ z (+ x t)))))
        (t_3 (- (+ z a) b)))
   (if (<= y -3.4e+191)
     t_3
     (if (<= y -1.2e+109)
       t_2
       (if (<= y -6.4e+76)
         (+ (/ (* x z) t_1) (* y (/ (- z b) t_1)))
         (if (<= y 1.15e+31) 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 * ((y + t) / t_1)) + (x * (z / (x + t)));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.4e+191) {
		tmp = t_3;
	} else if (y <= -1.2e+109) {
		tmp = t_2;
	} else if (y <= -6.4e+76) {
		tmp = ((x * z) / t_1) + (y * ((z - b) / t_1));
	} else if (y <= 1.15e+31) {
		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 * ((y + t) / t_1)) + (x * (z / (x + t)))
    t_3 = (z + a) - b
    if (y <= (-3.4d+191)) then
        tmp = t_3
    else if (y <= (-1.2d+109)) then
        tmp = t_2
    else if (y <= (-6.4d+76)) then
        tmp = ((x * z) / t_1) + (y * ((z - b) / t_1))
    else if (y <= 1.15d+31) 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 * ((y + t) / t_1)) + (x * (z / (x + t)));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.4e+191) {
		tmp = t_3;
	} else if (y <= -1.2e+109) {
		tmp = t_2;
	} else if (y <= -6.4e+76) {
		tmp = ((x * z) / t_1) + (y * ((z - b) / t_1));
	} else if (y <= 1.15e+31) {
		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 * ((y + t) / t_1)) + (x * (z / (x + t)))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -3.4e+191:
		tmp = t_3
	elif y <= -1.2e+109:
		tmp = t_2
	elif y <= -6.4e+76:
		tmp = ((x * z) / t_1) + (y * ((z - b) / t_1))
	elif y <= 1.15e+31:
		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(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(x * Float64(z / Float64(x + t))))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.4e+191)
		tmp = t_3;
	elseif (y <= -1.2e+109)
		tmp = t_2;
	elseif (y <= -6.4e+76)
		tmp = Float64(Float64(Float64(x * z) / t_1) + Float64(y * Float64(Float64(z - b) / t_1)));
	elseif (y <= 1.15e+31)
		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 * ((y + t) / t_1)) + (x * (z / (x + t)));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.4e+191)
		tmp = t_3;
	elseif (y <= -1.2e+109)
		tmp = t_2;
	elseif (y <= -6.4e+76)
		tmp = ((x * z) / t_1) + (y * ((z - b) / t_1));
	elseif (y <= 1.15e+31)
		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[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.4e+191], t$95$3, If[LessEqual[y, -1.2e+109], t$95$2, If[LessEqual[y, -6.4e+76], N[(N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y * N[(N[(z - b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+31], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000009e191 or 1.15e31 < y

   1. Initial program 40.0%

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

   3. Taylor expanded in y around inf 81.7%

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

   if -3.40000000000000009e191 < y < -1.19999999999999994e109 or -6.39999999999999953e76 < y < 1.15e31

   1. Initial program 73.2%

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

   3. Taylor expanded in b around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. associate-+l+ 73.2%

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

      4. associate-/l* 84.7%

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

      5. +-commutative 84.7%

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

      6. associate-+r+ 84.7%

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

      7. +-commutative 84.7%

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

      8. associate-+l+ 84.7%

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

      9. sub-neg 84.7%

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

      10. div-sub 84.7%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in y around 0 72.5%

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

      1. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

   if -1.19999999999999994e109 < y < -6.39999999999999953e76

   1. Initial program 52.3%

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

   3. Taylor expanded in a around -inf 42.7%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in a around 0 44.3%

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

      1. associate-+r+ 44.3%

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

      2. +-commutative 44.3%

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

      3. associate-/l* 89.8%

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

      4. associate-+r+ 89.8%

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

      5. +-commutative 89.8%

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

   8. Simplified 89.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+191}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)} + y \cdot \frac{z - b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + x \cdot \frac{z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+43} \lor \neg \left(b \leq 2.2 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{x \cdot z}{t\_1} + \frac{y}{t\_1} \cdot \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y + t}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= b -2.4e+43) (not (<= b 2.2e+174)))
     (+ (/ (* x z) t_1) (* (/ y t_1) (- z b)))
     (+ z (* a (/ (+ y t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((b <= -2.4e+43) || !(b <= 2.2e+174)) {
		tmp = ((x * z) / t_1) + ((y / t_1) * (z - b));
	} else {
		tmp = z + (a * ((y + t) / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((b <= (-2.4d+43)) .or. (.not. (b <= 2.2d+174))) then
        tmp = ((x * z) / t_1) + ((y / t_1) * (z - b))
    else
        tmp = z + (a * ((y + t) / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((b <= -2.4e+43) || !(b <= 2.2e+174)) {
		tmp = ((x * z) / t_1) + ((y / t_1) * (z - b));
	} else {
		tmp = z + (a * ((y + t) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (b <= -2.4e+43) or not (b <= 2.2e+174):
		tmp = ((x * z) / t_1) + ((y / t_1) * (z - b))
	else:
		tmp = z + (a * ((y + t) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((b <= -2.4e+43) || !(b <= 2.2e+174))
		tmp = Float64(Float64(Float64(x * z) / t_1) + Float64(Float64(y / t_1) * Float64(z - b)));
	else
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((b <= -2.4e+43) || ~((b <= 2.2e+174)))
		tmp = ((x * z) / t_1) + ((y / t_1) * (z - b));
	else
		tmp = z + (a * ((y + t) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.4e+43], N[Not[LessEqual[b, 2.2e+174]], $MachinePrecision]], N[(N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y / t$95$1), $MachinePrecision] * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.40000000000000023e43 or 2.2000000000000002e174 < b

   1. Initial program 45.9%

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

   3. Taylor expanded in a around -inf 49.0%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in a around 0 38.4%

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

      1. associate-+r+ 38.4%

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

      2. +-commutative 38.4%

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

      3. associate-/l* 64.6%

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

      4. associate-+r+ 64.6%

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

      5. +-commutative 64.6%

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

   8. Simplified 64.6%

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

      1. clear-num 64.4%

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

      2. un-div-inv 65.6%

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

      3. +-commutative 65.6%

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

      4. +-commutative 65.6%

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

      5. associate-+l+ 65.6%

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

   10. Applied egg-rr 65.6%

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

       1. associate-/r/ 69.2%

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

       2. associate-+r+ 69.2%

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

   12. Simplified 69.2%

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

   if -2.40000000000000023e43 < b < 2.2000000000000002e174

   1. Initial program 65.3%

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

   3. Taylor expanded in b around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. +-commutative 65.4%

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

      3. associate-+l+ 65.4%

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

      4. associate-/l* 77.7%

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

      5. +-commutative 77.7%

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

      6. associate-+r+ 77.7%

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

      7. +-commutative 77.7%

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

      8. associate-+l+ 77.7%

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

      9. sub-neg 77.7%

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

      10. div-sub 77.7%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in x around inf 79.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+43} \lor \neg \left(b \leq 2.2 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)} \cdot \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-61}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4e-36)
     t_1
     (if (<= y -4.8e-259)
       (+ z a)
       (if (<= y -7.2e-305)
         (* x (/ z (+ x t)))
         (if (<= y 9.2e-61) (+ z a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4e-36) {
		tmp = t_1;
	} else if (y <= -4.8e-259) {
		tmp = z + a;
	} else if (y <= -7.2e-305) {
		tmp = x * (z / (x + t));
	} else if (y <= 9.2e-61) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4d-36)) then
        tmp = t_1
    else if (y <= (-4.8d-259)) then
        tmp = z + a
    else if (y <= (-7.2d-305)) then
        tmp = x * (z / (x + t))
    else if (y <= 9.2d-61) then
        tmp = z + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4e-36) {
		tmp = t_1;
	} else if (y <= -4.8e-259) {
		tmp = z + a;
	} else if (y <= -7.2e-305) {
		tmp = x * (z / (x + t));
	} else if (y <= 9.2e-61) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4e-36:
		tmp = t_1
	elif y <= -4.8e-259:
		tmp = z + a
	elif y <= -7.2e-305:
		tmp = x * (z / (x + t))
	elif y <= 9.2e-61:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4e-36)
		tmp = t_1;
	elseif (y <= -4.8e-259)
		tmp = Float64(z + a);
	elseif (y <= -7.2e-305)
		tmp = Float64(x * Float64(z / Float64(x + t)));
	elseif (y <= 9.2e-61)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4e-36)
		tmp = t_1;
	elseif (y <= -4.8e-259)
		tmp = z + a;
	elseif (y <= -7.2e-305)
		tmp = x * (z / (x + t));
	elseif (y <= 9.2e-61)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4e-36], t$95$1, If[LessEqual[y, -4.8e-259], N[(z + a), $MachinePrecision], If[LessEqual[y, -7.2e-305], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-61], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999998e-36 or 9.19999999999999967e-61 < y

   1. Initial program 47.1%

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

   3. Taylor expanded in y around inf 76.0%

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

   if -3.9999999999999998e-36 < y < -4.8000000000000001e-259 or -7.20000000000000007e-305 < y < 9.19999999999999967e-61

   1. Initial program 77.5%

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

   3. Taylor expanded in b around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. +-commutative 77.5%

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

      3. associate-+l+ 77.5%

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

      4. associate-/l* 90.7%

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

      5. +-commutative 90.7%

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

      6. associate-+r+ 90.7%

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

      7. +-commutative 90.7%

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

      8. associate-+l+ 90.7%

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

      9. sub-neg 90.7%

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

      10. div-sub 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in x around inf 78.1%

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

   7. Taylor expanded in t around inf 54.8%

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

   if -4.8000000000000001e-259 < y < -7.20000000000000007e-305

   1. Initial program 82.0%

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

   3. Taylor expanded in y around 0 75.9%

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

   4. Taylor expanded in a around 0 57.9%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

   6. Simplified 70.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-36}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-61}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+62} \lor \neg \left(x \leq 2.85 \cdot 10^{-41}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + y \cdot \frac{z - b}{\left(y + t\right) \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -9.5e+62) (not (<= x 2.85e-41)))
   (+ z (* a (/ (+ y t) (+ y (+ x t)))))
   (* a (+ 1.0 (* y (/ (- z b) (* (+ y t) a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9.5e+62) || !(x <= 2.85e-41)) {
		tmp = z + (a * ((y + t) / (y + (x + t))));
	} else {
		tmp = a * (1.0 + (y * ((z - b) / ((y + t) * a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-9.5d+62)) .or. (.not. (x <= 2.85d-41))) then
        tmp = z + (a * ((y + t) / (y + (x + t))))
    else
        tmp = a * (1.0d0 + (y * ((z - b) / ((y + t) * a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9.5e+62) || !(x <= 2.85e-41)) {
		tmp = z + (a * ((y + t) / (y + (x + t))));
	} else {
		tmp = a * (1.0 + (y * ((z - b) / ((y + t) * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -9.5e+62) or not (x <= 2.85e-41):
		tmp = z + (a * ((y + t) / (y + (x + t))))
	else:
		tmp = a * (1.0 + (y * ((z - b) / ((y + t) * a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -9.5e+62) || !(x <= 2.85e-41))
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t)))));
	else
		tmp = Float64(a * Float64(1.0 + Float64(y * Float64(Float64(z - b) / Float64(Float64(y + t) * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -9.5e+62) || ~((x <= 2.85e-41)))
		tmp = z + (a * ((y + t) / (y + (x + t))));
	else
		tmp = a * (1.0 + (y * ((z - b) / ((y + t) * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -9.5e+62], N[Not[LessEqual[x, 2.85e-41]], $MachinePrecision]], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 + N[(y * N[(N[(z - b), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000003e62 or 2.85000000000000023e-41 < x

   1. Initial program 52.6%

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

   3. Taylor expanded in b around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. +-commutative 52.6%

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

      3. associate-+l+ 52.6%

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

      4. associate-/l* 61.9%

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

      5. +-commutative 61.9%

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

      6. associate-+r+ 61.9%

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

      7. +-commutative 61.9%

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

      8. associate-+l+ 61.9%

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

      9. sub-neg 61.9%

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

      10. div-sub 61.9%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in x around inf 76.8%

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

   if -9.5000000000000003e62 < x < 2.85000000000000023e-41

   1. Initial program 67.5%

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

   3. Taylor expanded in a around -inf 75.4%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in x around 0 65.3%

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

      1. associate-/l* 71.3%

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

      2. *-commutative 71.3%

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

      3. +-commutative 71.3%

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

   8. Simplified 71.3%

      \[\leadsto \color{blue}{a \cdot \left(1 + y \cdot \frac{z - b}{\left(y + t\right) \cdot a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+62} \lor \neg \left(x \leq 2.85 \cdot 10^{-41}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + y \cdot \frac{z - b}{\left(y + t\right) \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+63} \lor \neg \left(x \leq 4.5 \cdot 10^{-149}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5.3e+63) (not (<= x 4.5e-149)))
   (+ z (* a (/ (+ y t) (+ y (+ x t)))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.3e+63) || !(x <= 4.5e-149)) {
		tmp = z + (a * ((y + t) / (y + (x + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-5.3d+63)) .or. (.not. (x <= 4.5d-149))) then
        tmp = z + (a * ((y + t) / (y + (x + t))))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.3e+63) || !(x <= 4.5e-149)) {
		tmp = z + (a * ((y + t) / (y + (x + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5.3e+63) or not (x <= 4.5e-149):
		tmp = z + (a * ((y + t) / (y + (x + t))))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5.3e+63) || !(x <= 4.5e-149))
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t)))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5.3e+63) || ~((x <= 4.5e-149)))
		tmp = z + (a * ((y + t) / (y + (x + t))));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5.3e+63], N[Not[LessEqual[x, 4.5e-149]], $MachinePrecision]], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2999999999999999e63 or 4.4999999999999998e-149 < x

   1. Initial program 56.3%

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

   3. Taylor expanded in b around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-+l+ 56.3%

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

      4. associate-/l* 66.7%

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

      5. +-commutative 66.7%

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

      6. associate-+r+ 66.7%

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

      7. +-commutative 66.7%

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

      8. associate-+l+ 66.7%

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

      9. sub-neg 66.7%

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

      10. div-sub 66.7%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in x around inf 75.6%

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

   if -5.2999999999999999e63 < x < 4.4999999999999998e-149

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 71.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+63} \lor \neg \left(x \leq 4.5 \cdot 10^{-149}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+120}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+199}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.22e+120)
   (+ z (* a (/ (+ y t) x)))
   (if (<= x 7e+199) (- (+ z a) b) (+ z (* y (- (/ a x) (/ b x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.22e+120) {
		tmp = z + (a * ((y + t) / x));
	} else if (x <= 7e+199) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (y * ((a / x) - (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) :: tmp
    if (x <= (-1.22d+120)) then
        tmp = z + (a * ((y + t) / x))
    else if (x <= 7d+199) then
        tmp = (z + a) - b
    else
        tmp = z + (y * ((a / x) - (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 tmp;
	if (x <= -1.22e+120) {
		tmp = z + (a * ((y + t) / x));
	} else if (x <= 7e+199) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (y * ((a / x) - (b / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.22e+120:
		tmp = z + (a * ((y + t) / x))
	elif x <= 7e+199:
		tmp = (z + a) - b
	else:
		tmp = z + (y * ((a / x) - (b / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.22e+120)
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / x)));
	elseif (x <= 7e+199)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(y * Float64(Float64(a / x) - Float64(b / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.22e+120)
		tmp = z + (a * ((y + t) / x));
	elseif (x <= 7e+199)
		tmp = (z + a) - b;
	else
		tmp = z + (y * ((a / x) - (b / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.22e+120], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+199], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(y * N[(N[(a / x), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.22e120

   1. Initial program 45.8%

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

   3. Taylor expanded in b around 0 45.7%

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

      1. mul-1-neg 45.7%

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

      2. +-commutative 45.7%

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

      3. associate-+l+ 45.7%

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

      4. associate-/l* 49.7%

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

      5. +-commutative 49.7%

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

      6. associate-+r+ 49.7%

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

      7. +-commutative 49.7%

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

      8. associate-+l+ 49.7%

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

      9. sub-neg 49.7%

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

      10. div-sub 49.7%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in x around inf 77.8%

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

   7. Taylor expanded in x around inf 66.3%

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

      1. associate-/l* 72.9%

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

      2. +-commutative 72.9%

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

   9. Simplified 72.9%

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

   if -1.22e120 < x < 6.99999999999999962e199

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 66.2%

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

   if 6.99999999999999962e199 < x

   1. Initial program 45.7%

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

   3. Taylor expanded in t around 0 40.2%

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

   4. Taylor expanded in y around 0 83.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+120}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+199}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+119} \lor \neg \left(x \leq 1.6 \cdot 10^{+195}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -9.2e+119) (not (<= x 1.6e+195)))
   (+ z (* a (/ (+ y t) x)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9.2e+119) || !(x <= 1.6e+195)) {
		tmp = z + (a * ((y + t) / x));
	} 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 ((x <= (-9.2d+119)) .or. (.not. (x <= 1.6d+195))) then
        tmp = z + (a * ((y + t) / x))
    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 ((x <= -9.2e+119) || !(x <= 1.6e+195)) {
		tmp = z + (a * ((y + t) / x));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -9.2e+119) or not (x <= 1.6e+195):
		tmp = z + (a * ((y + t) / x))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -9.2e+119) || !(x <= 1.6e+195))
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / x)));
	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 ((x <= -9.2e+119) || ~((x <= 1.6e+195)))
		tmp = z + (a * ((y + t) / x));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -9.2e+119], N[Not[LessEqual[x, 1.6e+195]], $MachinePrecision]], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2000000000000003e119 or 1.59999999999999991e195 < x

   1. Initial program 45.1%

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

   3. Taylor expanded in b around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. +-commutative 45.1%

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

      3. associate-+l+ 45.1%

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

      4. associate-/l* 48.3%

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

      5. +-commutative 48.3%

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

      6. associate-+r+ 48.3%

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

      7. +-commutative 48.3%

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

      8. associate-+l+ 48.3%

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

      9. sub-neg 48.3%

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

      10. div-sub 48.3%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in x around inf 78.4%

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

   7. Taylor expanded in x around inf 66.8%

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

      1. associate-/l* 75.6%

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

      2. +-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -9.2000000000000003e119 < x < 1.59999999999999991e195

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 66.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+119} \lor \neg \left(x \leq 1.6 \cdot 10^{+195}\right):\\ \;\;\;\;z + a \cdot \frac{y + t}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-36} \lor \neg \left(y \leq 1.04 \cdot 10^{-54}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e-36) (not (<= y 1.04e-54))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e-36) || !(y <= 1.04e-54)) {
		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 <= (-1.75d-36)) .or. (.not. (y <= 1.04d-54))) 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 <= -1.75e-36) || !(y <= 1.04e-54)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e-36) or not (y <= 1.04e-54):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e-36) || !(y <= 1.04e-54))
		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 <= -1.75e-36) || ~((y <= 1.04e-54)))
		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, -1.75e-36], N[Not[LessEqual[y, 1.04e-54]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e-36 or 1.04e-54 < y

   1. Initial program 47.1%

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

   3. Taylor expanded in y around inf 76.0%

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

   if -1.75e-36 < y < 1.04e-54

   1. Initial program 78.1%

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

   3. Taylor expanded in b around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. +-commutative 78.2%

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

      3. associate-+l+ 78.2%

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

      4. associate-/l* 89.1%

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

      5. +-commutative 89.1%

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

      6. associate-+r+ 89.1%

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

      7. +-commutative 89.1%

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

      8. associate-+l+ 89.1%

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

      9. sub-neg 89.1%

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

      10. div-sub 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in x around inf 76.6%

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

   7. Taylor expanded in t around inf 52.8%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-36} \lor \neg \left(y \leq 1.04 \cdot 10^{-54}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-26} \lor \neg \left(z \leq 8.8 \cdot 10^{-113}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.5e-26) (not (<= z 8.8e-113))) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-26) || !(z <= 8.8e-113)) {
		tmp = z + a;
	} else {
		tmp = 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 ((z <= (-7.5d-26)) .or. (.not. (z <= 8.8d-113))) then
        tmp = z + a
    else
        tmp = 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 ((z <= -7.5e-26) || !(z <= 8.8e-113)) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.5e-26) or not (z <= 8.8e-113):
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.5e-26) || !(z <= 8.8e-113))
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.5e-26) || ~((z <= 8.8e-113)))
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.5e-26], N[Not[LessEqual[z, 8.8e-113]], $MachinePrecision]], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999994e-26 or 8.80000000000000016e-113 < z

   1. Initial program 50.6%

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

   3. Taylor expanded in b around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. +-commutative 50.6%

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

      3. associate-+l+ 50.6%

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

      4. associate-/l* 60.2%

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

      5. +-commutative 60.2%

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

      6. associate-+r+ 60.2%

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

      7. +-commutative 60.2%

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

      8. associate-+l+ 60.2%

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

      9. sub-neg 60.2%

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

      10. div-sub 60.2%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in x around inf 73.1%

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

   7. Taylor expanded in t around inf 59.6%

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

   if -7.4999999999999994e-26 < z < 8.80000000000000016e-113

   1. Initial program 72.5%

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

   3. Taylor expanded in z around 0 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around inf 56.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-26} \lor \neg \left(z \leq 8.8 \cdot 10^{-113}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.65e+41) a (if (<= t 2.55e-21) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.65e+41) {
		tmp = a;
	} else if (t <= 2.55e-21) {
		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 <= (-2.65d+41)) then
        tmp = a
    else if (t <= 2.55d-21) 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 <= -2.65e+41) {
		tmp = a;
	} else if (t <= 2.55e-21) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.65e+41:
		tmp = a
	elif t <= 2.55e-21:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.65e+41)
		tmp = a;
	elseif (t <= 2.55e-21)
		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 <= -2.65e+41)
		tmp = a;
	elseif (t <= 2.55e-21)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.65e+41], a, If[LessEqual[t, 2.55e-21], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6499999999999998e41 or 2.55000000000000002e-21 < t

   1. Initial program 48.1%

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

   3. Taylor expanded in t around inf 52.6%

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

   if -2.6499999999999998e41 < t < 2.55000000000000002e-21

   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. Add Preprocessing

   3. Taylor expanded in x around inf 47.2%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% 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 59.8%

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

3. Taylor expanded in b around 0 59.8%

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

   1. mul-1-neg 59.8%

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

   2. +-commutative 59.8%

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

   3. associate-+l+ 59.8%

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

   4. associate-/l* 70.7%

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

   5. +-commutative 70.7%

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

   6. associate-+r+ 70.7%

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

   7. +-commutative 70.7%

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

   8. associate-+l+ 70.7%

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

   9. sub-neg 70.7%

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

   10. div-sub 70.6%

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

5. Simplified 70.5%

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

6. Taylor expanded in x around inf 67.7%

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

7. Taylor expanded in t around inf 53.1%

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

8. Final simplification 53.1%

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

Alternative 13: 32.7% 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 59.8%

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

3. Taylor expanded in t around inf 31.4%

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

4. Final simplification 31.4%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 81.8% 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 2024059 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (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)))