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

Percentage Accurate: 61.0% → 87.4%

Time: 12.1s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% 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: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 4e+248) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 4e+248) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 4e+248) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 4e+248:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 4e+248)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 4e+248)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 4e+248], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.00000000000000018e248 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000018e248

   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
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+248}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{\left(x + y\right) + t}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.7e-39)
     t_1
     (if (<= y -3.3e-140)
       (* b (- (/ z b) (/ y (+ (+ x y) t))))
       (if (<= y 7.8e-91)
         (/ (+ (* (+ x y) z) (* (+ y t) a)) (+ y (+ x t)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.7e-39) {
		tmp = t_1;
	} else if (y <= -3.3e-140) {
		tmp = b * ((z / b) - (y / ((x + y) + t)));
	} else if (y <= 7.8e-91) {
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.7d-39)) then
        tmp = t_1
    else if (y <= (-3.3d-140)) then
        tmp = b * ((z / b) - (y / ((x + y) + t)))
    else if (y <= 7.8d-91) then
        tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.7e-39) {
		tmp = t_1;
	} else if (y <= -3.3e-140) {
		tmp = b * ((z / b) - (y / ((x + y) + t)));
	} else if (y <= 7.8e-91) {
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.7e-39:
		tmp = t_1
	elif y <= -3.3e-140:
		tmp = b * ((z / b) - (y / ((x + y) + t)))
	elif y <= 7.8e-91:
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.7e-39)
		tmp = t_1;
	elseif (y <= -3.3e-140)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(Float64(x + y) + t))));
	elseif (y <= 7.8e-91)
		tmp = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.7e-39)
		tmp = t_1;
	elseif (y <= -3.3e-140)
		tmp = b * ((z / b) - (y / ((x + y) + t)));
	elseif (y <= 7.8e-91)
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.7e-39], t$95$1, If[LessEqual[y, -3.3e-140], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-91], N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e-39 or 7.79999999999999987e-91 < y

   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 y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.4%

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

   if -1.7e-39 < y < -3.29999999999999987e-140

   1. Initial program 75.0%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 87.1%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in a around -inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(a \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(-1 \cdot \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}\right), \color{blue}{\left(\frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right)\right) \]

   8. Simplified 81.1%

      \[\leadsto 0 - z \cdot \color{blue}{\left(\left(-a\right) \cdot \left(-1 \cdot \left(\frac{\frac{\left(y + x\right) \cdot -1}{t + \left(y + x\right)} + \frac{y \cdot b}{\left(t + \left(y + x\right)\right) \cdot z}}{a} - \frac{t + y}{\left(t + \left(y + x\right)\right) \cdot z}\right)\right)\right)} \]

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{a \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{a \cdot \left(t + \left(x + y\right)\right)} - \left(\frac{t}{z \cdot \left(t + \left(x + y\right)\right)} + \frac{y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}{b} - \frac{y}{t + \left(x + y\right)}\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{a \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{a \cdot \left(t + \left(x + y\right)\right)} - \left(\frac{t}{z \cdot \left(t + \left(x + y\right)\right)} + \frac{y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}{b}\right), \color{blue}{\left(\frac{y}{t + \left(x + y\right)}\right)}\right)\right) \]

   11. Simplified 66.9%

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

   12. Taylor expanded in x around inf

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\color{blue}{\left(\frac{z}{b}\right)}, \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]
   13. Step-by-step derivation

       1. /-lowering-/.f64 65.4%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   14. Simplified 65.4%

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

   if -3.29999999999999987e-140 < y < 7.79999999999999987e-91

   1. Initial program 82.9%

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

   3. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right)}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(t + y\right)\right), \left(z \cdot \left(x + y\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{+.f64}\left(x, t\right)}, y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(t + y\right)\right), \left(z \cdot \left(x + y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \left(z \cdot \left(x + y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{t}\right), y\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \left(y + x\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      6. +-lowering-+.f64 68.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

   5. Simplified 68.5%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{\left(x + y\right) + t}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(\frac{a}{z} + \frac{x + y}{\left(x + y\right) + t}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ (/ a z) (/ (+ x y) (+ (+ x y) t))))))
   (if (<= z -2.3e-79)
     t_1
     (if (<= z 1.65e+23)
       (/ (- (+ (* t a) (* x z)) (* y b)) (+ y (+ x t)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((a / z) + ((x + y) / ((x + y) + t)));
	double tmp;
	if (z <= -2.3e-79) {
		tmp = t_1;
	} else if (z <= 1.65e+23) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((a / z) + ((x + y) / ((x + y) + t)))
    if (z <= (-2.3d-79)) then
        tmp = t_1
    else if (z <= 1.65d+23) then
        tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((a / z) + ((x + y) / ((x + y) + t)));
	double tmp;
	if (z <= -2.3e-79) {
		tmp = t_1;
	} else if (z <= 1.65e+23) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((a / z) + ((x + y) / ((x + y) + t)))
	tmp = 0
	if z <= -2.3e-79:
		tmp = t_1
	elif z <= 1.65e+23:
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(a / z) + Float64(Float64(x + y) / Float64(Float64(x + y) + t))))
	tmp = 0.0
	if (z <= -2.3e-79)
		tmp = t_1;
	elseif (z <= 1.65e+23)
		tmp = Float64(Float64(Float64(Float64(t * a) + Float64(x * z)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((a / z) + ((x + y) / ((x + y) + t)));
	tmp = 0.0;
	if (z <= -2.3e-79)
		tmp = t_1;
	elseif (z <= 1.65e+23)
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(N[(a / z), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e-79], t$95$1, If[LessEqual[z, 1.65e+23], N[(N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000012e-79 or 1.65000000000000015e23 < z

   1. Initial program 48.9%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 75.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{neg.f64}\left(x\right), y\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, x\right)\right)\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 75.4%

      \[\leadsto 0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \color{blue}{\frac{a}{z}}\right) \]

   if -2.30000000000000012e-79 < z < 1.65000000000000015e23

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(a \cdot t + x \cdot z\right)}, \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. *-lowering-*.f64 66.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

   5. Simplified 66.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \frac{x + y}{\left(x + y\right) + t}\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \frac{x + y}{\left(x + y\right) + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-93}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -8.2e-37)
     t_1
     (if (<= y 3.55e-93)
       (/ (- (+ (* t a) (* x z)) (* y b)) (+ y (+ x t)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -8.2e-37) {
		tmp = t_1;
	} else if (y <= 3.55e-93) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-8.2d-37)) then
        tmp = t_1
    else if (y <= 3.55d-93) then
        tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -8.2e-37) {
		tmp = t_1;
	} else if (y <= 3.55e-93) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -8.2e-37:
		tmp = t_1
	elif y <= 3.55e-93:
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -8.2e-37)
		tmp = t_1;
	elseif (y <= 3.55e-93)
		tmp = Float64(Float64(Float64(Float64(t * a) + Float64(x * z)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -8.2e-37)
		tmp = t_1;
	elseif (y <= 3.55e-93)
		tmp = (((t * a) + (x * z)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.2e-37], t$95$1, If[LessEqual[y, 3.55e-93], N[(N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999996e-37 or 3.55e-93 < y

   1. Initial program 44.7%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.9%

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

   if -8.1999999999999996e-37 < y < 3.55e-93

   1. Initial program 80.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(a \cdot t + x \cdot z\right)}, \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      4. *-lowering-*.f64 71.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

   5. Simplified 71.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-93}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{\left(x + y\right) + t}\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.45e-40)
     t_1
     (if (<= y -2.8e-140)
       (* b (- (/ z b) (/ y (+ (+ x y) t))))
       (if (<= y 4.7e-93) (/ (+ (* t a) (* x z)) (+ x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.45e-40) {
		tmp = t_1;
	} else if (y <= -2.8e-140) {
		tmp = b * ((z / b) - (y / ((x + y) + t)));
	} else if (y <= 4.7e-93) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.45d-40)) then
        tmp = t_1
    else if (y <= (-2.8d-140)) then
        tmp = b * ((z / b) - (y / ((x + y) + t)))
    else if (y <= 4.7d-93) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.45e-40) {
		tmp = t_1;
	} else if (y <= -2.8e-140) {
		tmp = b * ((z / b) - (y / ((x + y) + t)));
	} else if (y <= 4.7e-93) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.45e-40:
		tmp = t_1
	elif y <= -2.8e-140:
		tmp = b * ((z / b) - (y / ((x + y) + t)))
	elif y <= 4.7e-93:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.45e-40)
		tmp = t_1;
	elseif (y <= -2.8e-140)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(Float64(x + y) + t))));
	elseif (y <= 4.7e-93)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.45e-40)
		tmp = t_1;
	elseif (y <= -2.8e-140)
		tmp = b * ((z / b) - (y / ((x + y) + t)));
	elseif (y <= 4.7e-93)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.45e-40], t$95$1, If[LessEqual[y, -2.8e-140], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-93], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4499999999999999e-40 or 4.6999999999999999e-93 < y

   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 y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.4%

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

   if -2.4499999999999999e-40 < y < -2.8000000000000002e-140

   1. Initial program 75.0%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 87.1%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in a around -inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(a \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(-1 \cdot \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}\right), \color{blue}{\left(\frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right)\right) \]

   8. Simplified 81.1%

      \[\leadsto 0 - z \cdot \color{blue}{\left(\left(-a\right) \cdot \left(-1 \cdot \left(\frac{\frac{\left(y + x\right) \cdot -1}{t + \left(y + x\right)} + \frac{y \cdot b}{\left(t + \left(y + x\right)\right) \cdot z}}{a} - \frac{t + y}{\left(t + \left(y + x\right)\right) \cdot z}\right)\right)\right)} \]

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{a \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{a \cdot \left(t + \left(x + y\right)\right)} - \left(\frac{t}{z \cdot \left(t + \left(x + y\right)\right)} + \frac{y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}{b} - \frac{y}{t + \left(x + y\right)}\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{a \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{a \cdot \left(t + \left(x + y\right)\right)} - \left(\frac{t}{z \cdot \left(t + \left(x + y\right)\right)} + \frac{y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}{b}\right), \color{blue}{\left(\frac{y}{t + \left(x + y\right)}\right)}\right)\right) \]

   11. Simplified 66.9%

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

   12. Taylor expanded in x around inf

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\color{blue}{\left(\frac{z}{b}\right)}, \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]
   13. Step-by-step derivation

       1. /-lowering-/.f64 65.4%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(z, b\right), \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   14. Simplified 65.4%

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

   if -2.8000000000000002e-140 < y < 4.6999999999999999e-93

   1. Initial program 82.9%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 62.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 62.0%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-40}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{\left(x + y\right) + t}\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-93}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t)) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -7.2e+87)
     t_2
     (if (<= z 1.35e+104) (* b (- (/ a b) (/ y t_1))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -7.2e+87) {
		tmp = t_2;
	} else if (z <= 1.35e+104) {
		tmp = b * ((a / b) - (y / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) + t
    t_2 = z * ((x + y) / t_1)
    if (z <= (-7.2d+87)) then
        tmp = t_2
    else if (z <= 1.35d+104) then
        tmp = b * ((a / b) - (y / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -7.2e+87) {
		tmp = t_2;
	} else if (z <= 1.35e+104) {
		tmp = b * ((a / b) - (y / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -7.2e+87:
		tmp = t_2
	elif z <= 1.35e+104:
		tmp = b * ((a / b) - (y / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -7.2e+87)
		tmp = t_2;
	elseif (z <= 1.35e+104)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -7.2e+87)
		tmp = t_2;
	elseif (z <= 1.35e+104)
		tmp = b * ((a / b) - (y / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+87], t$95$2, If[LessEqual[z, 1.35e+104], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999988e87 or 1.34999999999999992e104 < z

   1. Initial program 41.7%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 60.9%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in a around -inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(a \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(-1 \cdot \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}\right), \color{blue}{\left(\frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right)\right) \]

   8. Simplified 70.5%

      \[\leadsto 0 - z \cdot \color{blue}{\left(\left(-a\right) \cdot \left(-1 \cdot \left(\frac{\frac{\left(y + x\right) \cdot -1}{t + \left(y + x\right)} + \frac{y \cdot b}{\left(t + \left(y + x\right)\right) \cdot z}}{a} - \frac{t + y}{\left(t + \left(y + x\right)\right) \cdot z}\right)\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)}\right)}\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\frac{-1 \cdot \left(x + y\right)}{\color{blue}{t + \left(x + y\right)}}\right)\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(-1 \cdot \left(x + y\right)\right), \color{blue}{\left(t + \left(x + y\right)\right)}\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + y\right)\right)\right), \left(\color{blue}{t} + \left(x + y\right)\right)\right)\right)\right) \]

       4. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{neg.f64}\left(\left(x + y\right)\right), \left(\color{blue}{t} + \left(x + y\right)\right)\right)\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{neg.f64}\left(\mathsf{+.f64}\left(x, y\right)\right), \left(t + \left(x + y\right)\right)\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{neg.f64}\left(\mathsf{+.f64}\left(x, y\right)\right), \mathsf{+.f64}\left(t, \color{blue}{\left(x + y\right)}\right)\right)\right)\right) \]

       7. +-lowering-+.f64 75.4%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{neg.f64}\left(\mathsf{+.f64}\left(x, y\right)\right), \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right)\right)\right)\right) \]

   11. Simplified 75.4%

       \[\leadsto 0 - z \cdot \color{blue}{\frac{-\left(x + y\right)}{t + \left(x + y\right)}} \]

   if -7.19999999999999988e87 < z < 1.34999999999999992e104

   1. Initial program 72.9%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + -1 \cdot \frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \left(\mathsf{neg}\left(\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}\right)\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(-1 \cdot \frac{x + y}{t + \left(x + y\right)} - \color{blue}{\frac{\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} - \frac{b \cdot y}{t + \left(x + y\right)}}{z}}\right)\right)\right) \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{0 - z \cdot \left(\frac{\left(-x\right) - y}{t + \left(y + x\right)} - \frac{a \cdot \left(t + y\right) - y \cdot b}{z \cdot \left(t + \left(y + x\right)\right)}\right)} \]

   6. Taylor expanded in a around -inf

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(a \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a\right)\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}} - -1 \cdot \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)\right) \]

      5. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \left(-1 \cdot \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a} - \frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(a\right), \mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{-1 \cdot \frac{x + y}{t + \left(x + y\right)} + \frac{b \cdot y}{z \cdot \left(t + \left(x + y\right)\right)}}{a}\right), \color{blue}{\left(\frac{t + y}{z \cdot \left(t + \left(x + y\right)\right)}\right)}\right)\right)\right)\right)\right) \]

   8. Simplified 67.7%

      \[\leadsto 0 - z \cdot \color{blue}{\left(\left(-a\right) \cdot \left(-1 \cdot \left(\frac{\frac{\left(y + x\right) \cdot -1}{t + \left(y + x\right)} + \frac{y \cdot b}{\left(t + \left(y + x\right)\right) \cdot z}}{a} - \frac{t + y}{\left(t + \left(y + x\right)\right) \cdot z}\right)\right)\right)} \]

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \frac{a \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{a \cdot \left(t + \left(x + y\right)\right)} - \left(\frac{t}{z \cdot \left(t + \left(x + y\right)\right)} + \frac{y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}{b} - \frac{y}{t + \left(x + y\right)}\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{a \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{a \cdot \left(t + \left(x + y\right)\right)} - \left(\frac{t}{z \cdot \left(t + \left(x + y\right)\right)} + \frac{y}{z \cdot \left(t + \left(x + y\right)\right)}\right)\right)\right)}{b}\right), \color{blue}{\left(\frac{y}{t + \left(x + y\right)}\right)}\right)\right) \]

   11. Simplified 75.0%

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

   12. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\color{blue}{\left(\frac{a}{b}\right)}, \mathsf{/.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]
   13. Step-by-step derivation

       1. /-lowering-/.f64 58.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, b\right), \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   14. Simplified 58.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{\left(x + y\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{\left(x + y\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-91}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.45e-80)
     t_1
     (if (<= y 1.22e-91) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.45e-80) {
		tmp = t_1;
	} else if (y <= 1.22e-91) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.45d-80)) then
        tmp = t_1
    else if (y <= 1.22d-91) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.45e-80) {
		tmp = t_1;
	} else if (y <= 1.22e-91) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.45e-80:
		tmp = t_1
	elif y <= 1.22e-91:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.45e-80)
		tmp = t_1;
	elseif (y <= 1.22e-91)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.45e-80)
		tmp = t_1;
	elseif (y <= 1.22e-91)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.45e-80], t$95$1, If[LessEqual[y, 1.22e-91], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.44999999999999995e-80 or 1.21999999999999998e-91 < y

   1. Initial program 46.9%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 67.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 67.2%

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

   if -2.44999999999999995e-80 < y < 1.21999999999999998e-91

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 55.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 55.9%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-91}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* t (- (/ a x) (/ z x))))))
   (if (<= x -6.5e+146) t_1 (if (<= x 1.25e+78) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (t * ((a / x) - (z / x)));
	double tmp;
	if (x <= -6.5e+146) {
		tmp = t_1;
	} else if (x <= 1.25e+78) {
		tmp = (z + a) - b;
	} 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 + (t * ((a / x) - (z / x)))
    if (x <= (-6.5d+146)) then
        tmp = t_1
    else if (x <= 1.25d+78) then
        tmp = (z + a) - b
    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 + (t * ((a / x) - (z / x)));
	double tmp;
	if (x <= -6.5e+146) {
		tmp = t_1;
	} else if (x <= 1.25e+78) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (t * ((a / x) - (z / x)))
	tmp = 0
	if x <= -6.5e+146:
		tmp = t_1
	elif x <= 1.25e+78:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))))
	tmp = 0.0
	if (x <= -6.5e+146)
		tmp = t_1;
	elseif (x <= 1.25e+78)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (t * ((a / x) - (z / x)));
	tmp = 0.0;
	if (x <= -6.5e+146)
		tmp = t_1;
	elseif (x <= 1.25e+78)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+146], t$95$1, If[LessEqual[x, 1.25e+78], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999997e146 or 1.24999999999999996e78 < x

   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 y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 34.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 34.6%

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

   6. Taylor expanded in t around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{a}{x} - \frac{z}{x}\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \color{blue}{\left(\frac{z}{x}\right)}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{\color{blue}{z}}{x}\right)\right)\right)\right) \]

      5. /-lowering-/.f64 64.7%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 64.7%

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

   if -6.4999999999999997e146 < x < 1.24999999999999996e78

   1. Initial program 68.6%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 58.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 58.4%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+146}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.15e+78) (- (+ z a) b) (* x (/ z (+ x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.15e+78) {
		tmp = (z + a) - b;
	} else {
		tmp = x * (z / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.15d+78) then
        tmp = (z + a) - b
    else
        tmp = x * (z / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.15e+78) {
		tmp = (z + a) - b;
	} else {
		tmp = x * (z / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.15e+78:
		tmp = (z + a) - b
	else:
		tmp = x * (z / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.15e+78)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(x * Float64(z / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.15e+78)
		tmp = (z + a) - b;
	else
		tmp = x * (z / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.15e+78], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.1500000000000001e78

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 54.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 54.8%

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

   if 1.1500000000000001e78 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 41.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 41.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{z}{t + x}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{\left(t + x\right)}\right)\right) \]

      4. +-lowering-+.f64 57.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   8. Simplified 57.7%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+98}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 6200000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.4e+98) z (if (<= z 6200000000000.0) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.4e+98) {
		tmp = z;
	} else if (z <= 6200000000000.0) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7.4d+98)) then
        tmp = z
    else if (z <= 6200000000000.0d0) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.4e+98) {
		tmp = z;
	} else if (z <= 6200000000000.0) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.4e+98:
		tmp = z
	elif z <= 6200000000000.0:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.4e+98)
		tmp = z;
	elseif (z <= 6200000000000.0)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.4e+98)
		tmp = z;
	elseif (z <= 6200000000000.0)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.4e+98], z, If[LessEqual[z, 6200000000000.0], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -7.3999999999999997e98 or 6.2e12 < z

   1. Initial program 44.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 53.8%

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

   if -7.3999999999999997e98 < z < 6.2e12

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a} \]
   4. Step-by-step derivation

   5. Simplified 36.4%

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

Alternative 11: 55.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 2.8e+78) (- (+ z a) b) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.8e+78) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 2.8d+78) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.8e+78) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.8e+78:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.8e+78)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 2.8e+78)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.8e+78], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 2.8000000000000001e78

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 54.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 54.8%

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

   if 2.8000000000000001e78 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{z} \]
   4. Step-by-step derivation

   5. Simplified 54.2%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.1%

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

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{a} \]
4. Step-by-step derivation

5. Simplified 27.3%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Developer Target 1: 81.5% 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 2024144 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ 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)))