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

Percentage Accurate: 60.2% → 87.3%

Time: 16.4s

Alternatives: 14

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.2% 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: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+207}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+207))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+207)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+207)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+207):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+207))
		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 * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+207)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+207]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999999e207 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.0%

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

   3. Taylor expanded in y around inf 72.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e207

   1. Initial program 99.8%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+207}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{y + t}\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{y + t}{t\_2}\\ t_4 := z \cdot \frac{x + y}{t\_2}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-32}:\\ \;\;\;\;z - t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-107}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-194}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-242}:\\ \;\;\;\;b \cdot \frac{y}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-257}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;a - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b (+ y t))))
        (t_2 (+ y (+ x t)))
        (t_3 (* a (/ (+ y t) t_2)))
        (t_4 (* z (/ (+ x y) t_2))))
   (if (<= z -7.5e+80)
     t_4
     (if (<= z -3.3e+19)
       (+ z a)
       (if (<= z -2.8e-32)
         (- z t_1)
         (if (<= z -1.6e-107)
           (- (+ z a) b)
           (if (<= z -1.9e-194)
             t_3
             (if (<= z -4.5e-242)
               (* b (/ y (- (- y) (+ x t))))
               (if (<= z 2.85e-257)
                 t_3
                 (if (<= z 1.32e+95) (- a t_1) t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (y + t));
	double t_2 = y + (x + t);
	double t_3 = a * ((y + t) / t_2);
	double t_4 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -7.5e+80) {
		tmp = t_4;
	} else if (z <= -3.3e+19) {
		tmp = z + a;
	} else if (z <= -2.8e-32) {
		tmp = z - t_1;
	} else if (z <= -1.6e-107) {
		tmp = (z + a) - b;
	} else if (z <= -1.9e-194) {
		tmp = t_3;
	} else if (z <= -4.5e-242) {
		tmp = b * (y / (-y - (x + t)));
	} else if (z <= 2.85e-257) {
		tmp = t_3;
	} else if (z <= 1.32e+95) {
		tmp = a - t_1;
	} 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 = y * (b / (y + t))
    t_2 = y + (x + t)
    t_3 = a * ((y + t) / t_2)
    t_4 = z * ((x + y) / t_2)
    if (z <= (-7.5d+80)) then
        tmp = t_4
    else if (z <= (-3.3d+19)) then
        tmp = z + a
    else if (z <= (-2.8d-32)) then
        tmp = z - t_1
    else if (z <= (-1.6d-107)) then
        tmp = (z + a) - b
    else if (z <= (-1.9d-194)) then
        tmp = t_3
    else if (z <= (-4.5d-242)) then
        tmp = b * (y / (-y - (x + t)))
    else if (z <= 2.85d-257) then
        tmp = t_3
    else if (z <= 1.32d+95) then
        tmp = a - t_1
    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 = y * (b / (y + t));
	double t_2 = y + (x + t);
	double t_3 = a * ((y + t) / t_2);
	double t_4 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -7.5e+80) {
		tmp = t_4;
	} else if (z <= -3.3e+19) {
		tmp = z + a;
	} else if (z <= -2.8e-32) {
		tmp = z - t_1;
	} else if (z <= -1.6e-107) {
		tmp = (z + a) - b;
	} else if (z <= -1.9e-194) {
		tmp = t_3;
	} else if (z <= -4.5e-242) {
		tmp = b * (y / (-y - (x + t)));
	} else if (z <= 2.85e-257) {
		tmp = t_3;
	} else if (z <= 1.32e+95) {
		tmp = a - t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / (y + t))
	t_2 = y + (x + t)
	t_3 = a * ((y + t) / t_2)
	t_4 = z * ((x + y) / t_2)
	tmp = 0
	if z <= -7.5e+80:
		tmp = t_4
	elif z <= -3.3e+19:
		tmp = z + a
	elif z <= -2.8e-32:
		tmp = z - t_1
	elif z <= -1.6e-107:
		tmp = (z + a) - b
	elif z <= -1.9e-194:
		tmp = t_3
	elif z <= -4.5e-242:
		tmp = b * (y / (-y - (x + t)))
	elif z <= 2.85e-257:
		tmp = t_3
	elif z <= 1.32e+95:
		tmp = a - t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / Float64(y + t)))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * Float64(Float64(y + t) / t_2))
	t_4 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (z <= -7.5e+80)
		tmp = t_4;
	elseif (z <= -3.3e+19)
		tmp = Float64(z + a);
	elseif (z <= -2.8e-32)
		tmp = Float64(z - t_1);
	elseif (z <= -1.6e-107)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= -1.9e-194)
		tmp = t_3;
	elseif (z <= -4.5e-242)
		tmp = Float64(b * Float64(y / Float64(Float64(-y) - Float64(x + t))));
	elseif (z <= 2.85e-257)
		tmp = t_3;
	elseif (z <= 1.32e+95)
		tmp = Float64(a - t_1);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / (y + t));
	t_2 = y + (x + t);
	t_3 = a * ((y + t) / t_2);
	t_4 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (z <= -7.5e+80)
		tmp = t_4;
	elseif (z <= -3.3e+19)
		tmp = z + a;
	elseif (z <= -2.8e-32)
		tmp = z - t_1;
	elseif (z <= -1.6e-107)
		tmp = (z + a) - b;
	elseif (z <= -1.9e-194)
		tmp = t_3;
	elseif (z <= -4.5e-242)
		tmp = b * (y / (-y - (x + t)));
	elseif (z <= 2.85e-257)
		tmp = t_3;
	elseif (z <= 1.32e+95)
		tmp = a - t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+80], t$95$4, If[LessEqual[z, -3.3e+19], N[(z + a), $MachinePrecision], If[LessEqual[z, -2.8e-32], N[(z - t$95$1), $MachinePrecision], If[LessEqual[z, -1.6e-107], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, -1.9e-194], t$95$3, If[LessEqual[z, -4.5e-242], N[(b * N[(y / N[((-y) - N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e-257], t$95$3, If[LessEqual[z, 1.32e+95], N[(a - t$95$1), $MachinePrecision], t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -7.49999999999999994e80 or 1.32e95 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 28.5%

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

      1. associate-/l* 77.4%

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

      2. +-commutative 77.4%

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

      3. +-commutative 77.4%

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

      4. +-commutative 77.4%

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

      5. associate-+l+ 77.4%

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

      6. +-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -7.49999999999999994e80 < z < -3.3e19

   1. Initial program 51.9%

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

   3. Taylor expanded in y around inf 69.5%

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

   4. Taylor expanded in b around 0 88.1%

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

      1. +-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -3.3e19 < z < -2.7999999999999999e-32

   1. Initial program 68.1%

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

      1. div-sub 68.0%

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

      2. fma-define 68.0%

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

      3. +-commutative 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-+l+ 68.0%

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

      6. +-commutative 68.0%

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

      7. associate-+l+ 68.0%

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

      8. +-commutative 68.0%

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

      9. associate-/l* 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in x around inf 76.2%

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

   6. Taylor expanded in x around 0 44.5%

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

      1. *-commutative 20.5%

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

      2. +-commutative 20.5%

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

      3. associate-/l* 39.9%

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

      4. +-commutative 39.9%

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

   8. Simplified 63.9%

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

   if -2.7999999999999999e-32 < z < -1.60000000000000006e-107

   1. Initial program 43.4%

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

   3. Taylor expanded in y around inf 93.8%

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

   if -1.60000000000000006e-107 < z < -1.9000000000000001e-194 or -4.4999999999999999e-242 < z < 2.8499999999999999e-257

   1. Initial program 73.7%

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

   3. Taylor expanded in a around inf 52.1%

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

      1. associate-/l* 73.3%

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

      2. +-commutative 73.3%

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

      3. +-commutative 73.3%

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

      4. associate-+l+ 73.3%

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

      5. +-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.9000000000000001e-194 < z < -4.4999999999999999e-242

   1. Initial program 90.7%

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

   3. Taylor expanded in b around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. associate-/l* 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

      4. +-commutative 68.1%

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

      5. +-commutative 68.1%

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

      6. associate-+l+ 68.1%

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

      7. +-commutative 68.1%

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

   5. Simplified 68.1%

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

   if 2.8499999999999999e-257 < z < 1.32e95

   1. Initial program 70.2%

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

      1. div-sub 70.2%

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

      2. fma-define 70.2%

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

      3. +-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. associate-+l+ 70.2%

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

      6. +-commutative 70.2%

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

      7. associate-+l+ 70.2%

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

      8. +-commutative 70.2%

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

      9. associate-/l* 75.2%

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

   4. Applied egg-rr 75.2%

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

   5. Taylor expanded in t around inf 76.2%

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

   6. Taylor expanded in x around 0 66.3%

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

      1. *-commutative 66.3%

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

      2. +-commutative 66.3%

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

      3. associate-/l* 72.9%

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

      4. +-commutative 72.9%

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

   8. Simplified 72.9%

      \[\leadsto a - \color{blue}{y \cdot \frac{b}{t + y}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-32}:\\ \;\;\;\;z - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-107}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-242}:\\ \;\;\;\;b \cdot \frac{y}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;a - y \cdot \frac{b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{x + \left(y + t\right)}\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t\_2}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+80}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+20}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-32}:\\ \;\;\;\;z - t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-285}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{t\_2}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+95}:\\ \;\;\;\;a - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b (+ x (+ y t)))))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (/ (+ x y) t_2))))
   (if (<= z -7e+80)
     t_3
     (if (<= z -1.8e+20)
       (+ z a)
       (if (<= z -2.45e-32)
         (- z t_1)
         (if (<= z -1.9e-111)
           (- (+ z a) b)
           (if (<= z -3.3e-285)
             (/ (- (* (+ y t) a) (* y b)) t_2)
             (if (<= z 1.3e+95) (- a t_1) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (x + (y + t)));
	double t_2 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -7e+80) {
		tmp = t_3;
	} else if (z <= -1.8e+20) {
		tmp = z + a;
	} else if (z <= -2.45e-32) {
		tmp = z - t_1;
	} else if (z <= -1.9e-111) {
		tmp = (z + a) - b;
	} else if (z <= -3.3e-285) {
		tmp = (((y + t) * a) - (y * b)) / t_2;
	} else if (z <= 1.3e+95) {
		tmp = a - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (b / (x + (y + t)))
    t_2 = y + (x + t)
    t_3 = z * ((x + y) / t_2)
    if (z <= (-7d+80)) then
        tmp = t_3
    else if (z <= (-1.8d+20)) then
        tmp = z + a
    else if (z <= (-2.45d-32)) then
        tmp = z - t_1
    else if (z <= (-1.9d-111)) then
        tmp = (z + a) - b
    else if (z <= (-3.3d-285)) then
        tmp = (((y + t) * a) - (y * b)) / t_2
    else if (z <= 1.3d+95) then
        tmp = a - t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (x + (y + t)));
	double t_2 = y + (x + t);
	double t_3 = z * ((x + y) / t_2);
	double tmp;
	if (z <= -7e+80) {
		tmp = t_3;
	} else if (z <= -1.8e+20) {
		tmp = z + a;
	} else if (z <= -2.45e-32) {
		tmp = z - t_1;
	} else if (z <= -1.9e-111) {
		tmp = (z + a) - b;
	} else if (z <= -3.3e-285) {
		tmp = (((y + t) * a) - (y * b)) / t_2;
	} else if (z <= 1.3e+95) {
		tmp = a - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / (x + (y + t)))
	t_2 = y + (x + t)
	t_3 = z * ((x + y) / t_2)
	tmp = 0
	if z <= -7e+80:
		tmp = t_3
	elif z <= -1.8e+20:
		tmp = z + a
	elif z <= -2.45e-32:
		tmp = z - t_1
	elif z <= -1.9e-111:
		tmp = (z + a) - b
	elif z <= -3.3e-285:
		tmp = (((y + t) * a) - (y * b)) / t_2
	elif z <= 1.3e+95:
		tmp = a - t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / Float64(x + Float64(y + t))))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (z <= -7e+80)
		tmp = t_3;
	elseif (z <= -1.8e+20)
		tmp = Float64(z + a);
	elseif (z <= -2.45e-32)
		tmp = Float64(z - t_1);
	elseif (z <= -1.9e-111)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= -3.3e-285)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / t_2);
	elseif (z <= 1.3e+95)
		tmp = Float64(a - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / (x + (y + t)));
	t_2 = y + (x + t);
	t_3 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (z <= -7e+80)
		tmp = t_3;
	elseif (z <= -1.8e+20)
		tmp = z + a;
	elseif (z <= -2.45e-32)
		tmp = z - t_1;
	elseif (z <= -1.9e-111)
		tmp = (z + a) - b;
	elseif (z <= -3.3e-285)
		tmp = (((y + t) * a) - (y * b)) / t_2;
	elseif (z <= 1.3e+95)
		tmp = a - t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+80], t$95$3, If[LessEqual[z, -1.8e+20], N[(z + a), $MachinePrecision], If[LessEqual[z, -2.45e-32], N[(z - t$95$1), $MachinePrecision], If[LessEqual[z, -1.9e-111], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, -3.3e-285], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.3e+95], N[(a - t$95$1), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.99999999999999987e80 or 1.29999999999999995e95 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 28.5%

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

      1. associate-/l* 77.4%

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

      2. +-commutative 77.4%

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

      3. +-commutative 77.4%

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

      4. +-commutative 77.4%

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

      5. associate-+l+ 77.4%

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

      6. +-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -6.99999999999999987e80 < z < -1.8e20

   1. Initial program 51.9%

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

   3. Taylor expanded in y around inf 69.5%

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

   4. Taylor expanded in b around 0 88.1%

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

      1. +-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -1.8e20 < z < -2.4499999999999999e-32

   1. Initial program 68.1%

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

      1. div-sub 68.0%

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

      2. fma-define 68.0%

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

      3. +-commutative 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-+l+ 68.0%

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

      6. +-commutative 68.0%

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

      7. associate-+l+ 68.0%

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

      8. +-commutative 68.0%

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

      9. associate-/l* 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in x around inf 76.2%

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

   if -2.4499999999999999e-32 < z < -1.90000000000000011e-111

   1. Initial program 41.0%

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

   3. Taylor expanded in y around inf 94.2%

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

   if -1.90000000000000011e-111 < z < -3.29999999999999985e-285

   1. Initial program 82.3%

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

   3. Taylor expanded in z around 0 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -3.29999999999999985e-285 < z < 1.29999999999999995e95

   1. Initial program 70.6%

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

      1. div-sub 70.6%

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

      2. fma-define 70.6%

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

      3. +-commutative 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-+l+ 70.6%

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

      6. +-commutative 70.6%

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

      7. associate-+l+ 70.6%

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

      8. +-commutative 70.6%

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

      9. associate-/l* 74.7%

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in t around inf 75.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+20}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-32}:\\ \;\;\;\;z - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-111}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-285}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+95}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+19}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-32}:\\ \;\;\;\;z - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ y (+ x t))))))
   (if (<= z -5e+78)
     t_1
     (if (<= z -3.9e+19)
       (+ z a)
       (if (<= z -2.8e-32)
         (- z (* y (/ b (+ y t))))
         (if (<= z 1.32e+95) (- a (* y (/ b (+ x (+ y t))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (y + (x + t)));
	double tmp;
	if (z <= -5e+78) {
		tmp = t_1;
	} else if (z <= -3.9e+19) {
		tmp = z + a;
	} else if (z <= -2.8e-32) {
		tmp = z - (y * (b / (y + t)));
	} else if (z <= 1.32e+95) {
		tmp = a - (y * (b / (x + (y + 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 * ((x + y) / (y + (x + t)))
    if (z <= (-5d+78)) then
        tmp = t_1
    else if (z <= (-3.9d+19)) then
        tmp = z + a
    else if (z <= (-2.8d-32)) then
        tmp = z - (y * (b / (y + t)))
    else if (z <= 1.32d+95) then
        tmp = a - (y * (b / (x + (y + 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 * ((x + y) / (y + (x + t)));
	double tmp;
	if (z <= -5e+78) {
		tmp = t_1;
	} else if (z <= -3.9e+19) {
		tmp = z + a;
	} else if (z <= -2.8e-32) {
		tmp = z - (y * (b / (y + t)));
	} else if (z <= 1.32e+95) {
		tmp = a - (y * (b / (x + (y + t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / (y + (x + t)))
	tmp = 0
	if z <= -5e+78:
		tmp = t_1
	elif z <= -3.9e+19:
		tmp = z + a
	elif z <= -2.8e-32:
		tmp = z - (y * (b / (y + t)))
	elif z <= 1.32e+95:
		tmp = a - (y * (b / (x + (y + t))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (z <= -5e+78)
		tmp = t_1;
	elseif (z <= -3.9e+19)
		tmp = Float64(z + a);
	elseif (z <= -2.8e-32)
		tmp = Float64(z - Float64(y * Float64(b / Float64(y + t))));
	elseif (z <= 1.32e+95)
		tmp = Float64(a - Float64(y * Float64(b / Float64(x + Float64(y + t)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((x + y) / (y + (x + t)));
	tmp = 0.0;
	if (z <= -5e+78)
		tmp = t_1;
	elseif (z <= -3.9e+19)
		tmp = z + a;
	elseif (z <= -2.8e-32)
		tmp = z - (y * (b / (y + t)));
	elseif (z <= 1.32e+95)
		tmp = a - (y * (b / (x + (y + 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[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+78], t$95$1, If[LessEqual[z, -3.9e+19], N[(z + a), $MachinePrecision], If[LessEqual[z, -2.8e-32], N[(z - N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+95], N[(a - N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999984e78 or 1.32e95 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 28.5%

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

      1. associate-/l* 77.4%

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

      2. +-commutative 77.4%

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

      3. +-commutative 77.4%

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

      4. +-commutative 77.4%

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

      5. associate-+l+ 77.4%

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

      6. +-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -4.99999999999999984e78 < z < -3.9e19

   1. Initial program 51.9%

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

   3. Taylor expanded in y around inf 69.5%

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

   4. Taylor expanded in b around 0 88.1%

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

      1. +-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -3.9e19 < z < -2.7999999999999999e-32

   1. Initial program 68.1%

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

      1. div-sub 68.0%

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

      2. fma-define 68.0%

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

      3. +-commutative 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-+l+ 68.0%

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

      6. +-commutative 68.0%

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

      7. associate-+l+ 68.0%

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

      8. +-commutative 68.0%

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

      9. associate-/l* 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in x around inf 76.2%

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

   6. Taylor expanded in x around 0 44.5%

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

      1. *-commutative 20.5%

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

      2. +-commutative 20.5%

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

      3. associate-/l* 39.9%

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

      4. +-commutative 39.9%

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

   8. Simplified 63.9%

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

   if -2.7999999999999999e-32 < z < 1.32e95

   1. Initial program 70.0%

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

      1. div-sub 70.0%

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

      2. fma-define 70.0%

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

      3. +-commutative 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-+l+ 69.9%

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

      6. +-commutative 69.9%

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

      7. associate-+l+ 69.9%

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

      8. +-commutative 69.9%

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

      9. associate-/l* 71.4%

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

   4. Applied egg-rr 71.4%

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

   5. Taylor expanded in t around inf 73.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+19}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-32}:\\ \;\;\;\;z - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ t_2 := y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+20}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;z - t\_2\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;a - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ y (+ x t))))) (t_2 (* y (/ b (+ x (+ y t))))))
   (if (<= z -1.5e+80)
     t_1
     (if (<= z -1.02e+20)
       (+ z a)
       (if (<= z -2.15e-32) (- z t_2) (if (<= z 1.32e+95) (- a t_2) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (y + (x + t)));
	double t_2 = y * (b / (x + (y + t)));
	double tmp;
	if (z <= -1.5e+80) {
		tmp = t_1;
	} else if (z <= -1.02e+20) {
		tmp = z + a;
	} else if (z <= -2.15e-32) {
		tmp = z - t_2;
	} else if (z <= 1.32e+95) {
		tmp = a - t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x + y) / (y + (x + t)))
    t_2 = y * (b / (x + (y + t)))
    if (z <= (-1.5d+80)) then
        tmp = t_1
    else if (z <= (-1.02d+20)) then
        tmp = z + a
    else if (z <= (-2.15d-32)) then
        tmp = z - t_2
    else if (z <= 1.32d+95) then
        tmp = a - t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (y + (x + t)));
	double t_2 = y * (b / (x + (y + t)));
	double tmp;
	if (z <= -1.5e+80) {
		tmp = t_1;
	} else if (z <= -1.02e+20) {
		tmp = z + a;
	} else if (z <= -2.15e-32) {
		tmp = z - t_2;
	} else if (z <= 1.32e+95) {
		tmp = a - t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / (y + (x + t)))
	t_2 = y * (b / (x + (y + t)))
	tmp = 0
	if z <= -1.5e+80:
		tmp = t_1
	elif z <= -1.02e+20:
		tmp = z + a
	elif z <= -2.15e-32:
		tmp = z - t_2
	elif z <= 1.32e+95:
		tmp = a - t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))))
	t_2 = Float64(y * Float64(b / Float64(x + Float64(y + t))))
	tmp = 0.0
	if (z <= -1.5e+80)
		tmp = t_1;
	elseif (z <= -1.02e+20)
		tmp = Float64(z + a);
	elseif (z <= -2.15e-32)
		tmp = Float64(z - t_2);
	elseif (z <= 1.32e+95)
		tmp = Float64(a - t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((x + y) / (y + (x + t)));
	t_2 = y * (b / (x + (y + t)));
	tmp = 0.0;
	if (z <= -1.5e+80)
		tmp = t_1;
	elseif (z <= -1.02e+20)
		tmp = z + a;
	elseif (z <= -2.15e-32)
		tmp = z - t_2;
	elseif (z <= 1.32e+95)
		tmp = a - t_2;
	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[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+80], t$95$1, If[LessEqual[z, -1.02e+20], N[(z + a), $MachinePrecision], If[LessEqual[z, -2.15e-32], N[(z - t$95$2), $MachinePrecision], If[LessEqual[z, 1.32e+95], N[(a - t$95$2), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.49999999999999993e80 or 1.32e95 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 28.5%

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

      1. associate-/l* 77.4%

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

      2. +-commutative 77.4%

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

      3. +-commutative 77.4%

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

      4. +-commutative 77.4%

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

      5. associate-+l+ 77.4%

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

      6. +-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -1.49999999999999993e80 < z < -1.02e20

   1. Initial program 51.9%

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

   3. Taylor expanded in y around inf 69.5%

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

   4. Taylor expanded in b around 0 88.1%

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

      1. +-commutative 88.1%

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

   6. Simplified 88.1%

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

   if -1.02e20 < z < -2.14999999999999995e-32

   1. Initial program 68.1%

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

      1. div-sub 68.0%

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

      2. fma-define 68.0%

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

      3. +-commutative 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-+l+ 68.0%

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

      6. +-commutative 68.0%

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

      7. associate-+l+ 68.0%

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

      8. +-commutative 68.0%

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

      9. associate-/l* 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in x around inf 76.2%

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

   if -2.14999999999999995e-32 < z < 1.32e95

   1. Initial program 70.0%

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

      1. div-sub 70.0%

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

      2. fma-define 70.0%

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

      3. +-commutative 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-+l+ 69.9%

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

      6. +-commutative 69.9%

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

      7. associate-+l+ 69.9%

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

      8. +-commutative 69.9%

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

      9. associate-/l* 71.4%

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

   4. Applied egg-rr 71.4%

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

   5. Taylor expanded in t around inf 73.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+20}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;z - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;a - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a - y \cdot \frac{b}{y + t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-180}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (- a (* y (/ b (+ y t))))))
   (if (<= t -2.8e+139)
     t_2
     (if (<= t -2.2e-48)
       t_1
       (if (<= t -1.62e-180) (+ z a) (if (<= t 9e+115) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (y * (b / (y + t)));
	double tmp;
	if (t <= -2.8e+139) {
		tmp = t_2;
	} else if (t <= -2.2e-48) {
		tmp = t_1;
	} else if (t <= -1.62e-180) {
		tmp = z + a;
	} else if (t <= 9e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a - (y * (b / (y + t)))
    if (t <= (-2.8d+139)) then
        tmp = t_2
    else if (t <= (-2.2d-48)) then
        tmp = t_1
    else if (t <= (-1.62d-180)) then
        tmp = z + a
    else if (t <= 9d+115) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (y * (b / (y + t)));
	double tmp;
	if (t <= -2.8e+139) {
		tmp = t_2;
	} else if (t <= -2.2e-48) {
		tmp = t_1;
	} else if (t <= -1.62e-180) {
		tmp = z + a;
	} else if (t <= 9e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a - (y * (b / (y + t)))
	tmp = 0
	if t <= -2.8e+139:
		tmp = t_2
	elif t <= -2.2e-48:
		tmp = t_1
	elif t <= -1.62e-180:
		tmp = z + a
	elif t <= 9e+115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a - Float64(y * Float64(b / Float64(y + t))))
	tmp = 0.0
	if (t <= -2.8e+139)
		tmp = t_2;
	elseif (t <= -2.2e-48)
		tmp = t_1;
	elseif (t <= -1.62e-180)
		tmp = Float64(z + a);
	elseif (t <= 9e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a - (y * (b / (y + t)));
	tmp = 0.0;
	if (t <= -2.8e+139)
		tmp = t_2;
	elseif (t <= -2.2e-48)
		tmp = t_1;
	elseif (t <= -1.62e-180)
		tmp = z + a;
	elseif (t <= 9e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+139], t$95$2, If[LessEqual[t, -2.2e-48], t$95$1, If[LessEqual[t, -1.62e-180], N[(z + a), $MachinePrecision], If[LessEqual[t, 9e+115], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999998e139 or 8.99999999999999927e115 < t

   1. Initial program 46.4%

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

      1. div-sub 46.3%

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

      2. fma-define 46.4%

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

      3. +-commutative 46.4%

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

      4. *-commutative 46.4%

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

      5. associate-+l+ 46.4%

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

      6. +-commutative 46.4%

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

      7. associate-+l+ 46.4%

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

      8. +-commutative 46.4%

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

      9. associate-/l* 49.6%

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

   4. Applied egg-rr 49.6%

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

   5. Taylor expanded in t around inf 68.5%

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

   6. Taylor expanded in x around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. +-commutative 62.9%

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

      3. associate-/l* 68.3%

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

      4. +-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -2.7999999999999998e139 < t < -2.20000000000000013e-48 or -1.61999999999999996e-180 < t < 8.99999999999999927e115

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 66.3%

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

   if -2.20000000000000013e-48 < t < -1.61999999999999996e-180

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 50.2%

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

   4. Taylor expanded in b around 0 66.5%

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

      1. +-commutative 66.5%

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

   6. Simplified 66.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+139}:\\ \;\;\;\;a - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-180}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+115}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - y \cdot \frac{b}{y + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a - b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-179}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (- a (* b (/ y t)))))
   (if (<= t -1.65e+139)
     t_2
     (if (<= t -1.2e-48)
       t_1
       (if (<= t -4.9e-179) (+ z a) (if (<= t 6.8e+116) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (b * (y / t));
	double tmp;
	if (t <= -1.65e+139) {
		tmp = t_2;
	} else if (t <= -1.2e-48) {
		tmp = t_1;
	} else if (t <= -4.9e-179) {
		tmp = z + a;
	} else if (t <= 6.8e+116) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a - (b * (y / t))
    if (t <= (-1.65d+139)) then
        tmp = t_2
    else if (t <= (-1.2d-48)) then
        tmp = t_1
    else if (t <= (-4.9d-179)) then
        tmp = z + a
    else if (t <= 6.8d+116) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a - (b * (y / t));
	double tmp;
	if (t <= -1.65e+139) {
		tmp = t_2;
	} else if (t <= -1.2e-48) {
		tmp = t_1;
	} else if (t <= -4.9e-179) {
		tmp = z + a;
	} else if (t <= 6.8e+116) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a - (b * (y / t))
	tmp = 0
	if t <= -1.65e+139:
		tmp = t_2
	elif t <= -1.2e-48:
		tmp = t_1
	elif t <= -4.9e-179:
		tmp = z + a
	elif t <= 6.8e+116:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a - Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.65e+139)
		tmp = t_2;
	elseif (t <= -1.2e-48)
		tmp = t_1;
	elseif (t <= -4.9e-179)
		tmp = Float64(z + a);
	elseif (t <= 6.8e+116)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a - (b * (y / t));
	tmp = 0.0;
	if (t <= -1.65e+139)
		tmp = t_2;
	elseif (t <= -1.2e-48)
		tmp = t_1;
	elseif (t <= -4.9e-179)
		tmp = z + a;
	elseif (t <= 6.8e+116)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+139], t$95$2, If[LessEqual[t, -1.2e-48], t$95$1, If[LessEqual[t, -4.9e-179], N[(z + a), $MachinePrecision], If[LessEqual[t, 6.8e+116], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6500000000000001e139 or 6.80000000000000046e116 < t

   1. Initial program 46.4%

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

      1. div-sub 46.3%

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

      2. fma-define 46.4%

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

      3. +-commutative 46.4%

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

      4. *-commutative 46.4%

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

      5. associate-+l+ 46.4%

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

      6. +-commutative 46.4%

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

      7. associate-+l+ 46.4%

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

      8. +-commutative 46.4%

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

      9. associate-/l* 49.6%

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

   4. Applied egg-rr 49.6%

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

   5. Taylor expanded in t around inf 68.5%

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

   6. Taylor expanded in t around inf 60.0%

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

      1. associate-/l* 65.3%

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

   8. Simplified 65.3%

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

   if -1.6500000000000001e139 < t < -1.2e-48 or -4.8999999999999999e-179 < t < 6.80000000000000046e116

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 66.3%

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

   if -1.2e-48 < t < -4.8999999999999999e-179

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 50.2%

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

   4. Taylor expanded in b around 0 66.5%

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

      1. +-commutative 66.5%

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

   6. Simplified 66.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+139}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-48}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-179}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+116}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - y \cdot \frac{b}{x + y}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* y (/ b (+ x y))))))
   (if (<= x -3.6e+188)
     t_1
     (if (<= x -1.45e-28)
       (- (+ z a) b)
       (if (<= x 1.6e+49) (+ a (/ (* y (- z b)) (+ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (y * (b / (x + y)));
	double tmp;
	if (x <= -3.6e+188) {
		tmp = t_1;
	} else if (x <= -1.45e-28) {
		tmp = (z + a) - b;
	} else if (x <= 1.6e+49) {
		tmp = a + ((y * (z - b)) / (y + 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 - (y * (b / (x + y)))
    if (x <= (-3.6d+188)) then
        tmp = t_1
    else if (x <= (-1.45d-28)) then
        tmp = (z + a) - b
    else if (x <= 1.6d+49) then
        tmp = a + ((y * (z - b)) / (y + 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 - (y * (b / (x + y)));
	double tmp;
	if (x <= -3.6e+188) {
		tmp = t_1;
	} else if (x <= -1.45e-28) {
		tmp = (z + a) - b;
	} else if (x <= 1.6e+49) {
		tmp = a + ((y * (z - b)) / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (y * (b / (x + y)))
	tmp = 0
	if x <= -3.6e+188:
		tmp = t_1
	elif x <= -1.45e-28:
		tmp = (z + a) - b
	elif x <= 1.6e+49:
		tmp = a + ((y * (z - b)) / (y + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(y * Float64(b / Float64(x + y))))
	tmp = 0.0
	if (x <= -3.6e+188)
		tmp = t_1;
	elseif (x <= -1.45e-28)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 1.6e+49)
		tmp = Float64(a + Float64(Float64(y * Float64(z - b)) / Float64(y + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (y * (b / (x + y)));
	tmp = 0.0;
	if (x <= -3.6e+188)
		tmp = t_1;
	elseif (x <= -1.45e-28)
		tmp = (z + a) - b;
	elseif (x <= 1.6e+49)
		tmp = a + ((y * (z - b)) / (y + 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[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+188], t$95$1, If[LessEqual[x, -1.45e-28], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 1.6e+49], N[(a + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.60000000000000021e188 or 1.60000000000000007e49 < x

   1. Initial program 46.8%

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

      1. div-sub 46.8%

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

      2. fma-define 46.9%

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

      3. +-commutative 46.9%

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

      4. *-commutative 46.9%

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

      5. associate-+l+ 46.9%

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

      6. +-commutative 46.9%

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

      7. associate-+l+ 46.9%

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

      8. +-commutative 46.9%

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

      9. associate-/l* 49.8%

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

   4. Applied egg-rr 49.8%

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

   5. Taylor expanded in x around inf 70.1%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. +-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -3.60000000000000021e188 < x < -1.45000000000000006e-28

   1. Initial program 49.5%

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

   3. Taylor expanded in y around inf 67.0%

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

   if -1.45000000000000006e-28 < x < 1.60000000000000007e49

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0 57.9%

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

   4. Taylor expanded in a around 0 71.5%

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

      1. associate--l+ 71.5%

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

      2. +-commutative 71.5%

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

      3. *-commutative 71.5%

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

      4. +-commutative 71.5%

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

      5. div-sub 71.5%

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

      6. distribute-lft-out-- 71.5%

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

      7. +-commutative 71.5%

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

   6. Simplified 71.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+188}:\\ \;\;\;\;z - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - y \cdot \frac{b}{x + y}\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-71}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;a - y \cdot \frac{b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* y (/ b (+ x y))))))
   (if (<= x -3.4e+181)
     t_1
     (if (<= x -3.55e-71)
       (- (+ z a) b)
       (if (<= x 1.6e+50) (- a (* y (/ b (+ y t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (y * (b / (x + y)));
	double tmp;
	if (x <= -3.4e+181) {
		tmp = t_1;
	} else if (x <= -3.55e-71) {
		tmp = (z + a) - b;
	} else if (x <= 1.6e+50) {
		tmp = a - (y * (b / (y + 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 - (y * (b / (x + y)))
    if (x <= (-3.4d+181)) then
        tmp = t_1
    else if (x <= (-3.55d-71)) then
        tmp = (z + a) - b
    else if (x <= 1.6d+50) then
        tmp = a - (y * (b / (y + 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 - (y * (b / (x + y)));
	double tmp;
	if (x <= -3.4e+181) {
		tmp = t_1;
	} else if (x <= -3.55e-71) {
		tmp = (z + a) - b;
	} else if (x <= 1.6e+50) {
		tmp = a - (y * (b / (y + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (y * (b / (x + y)))
	tmp = 0
	if x <= -3.4e+181:
		tmp = t_1
	elif x <= -3.55e-71:
		tmp = (z + a) - b
	elif x <= 1.6e+50:
		tmp = a - (y * (b / (y + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(y * Float64(b / Float64(x + y))))
	tmp = 0.0
	if (x <= -3.4e+181)
		tmp = t_1;
	elseif (x <= -3.55e-71)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 1.6e+50)
		tmp = Float64(a - Float64(y * Float64(b / Float64(y + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (y * (b / (x + y)));
	tmp = 0.0;
	if (x <= -3.4e+181)
		tmp = t_1;
	elseif (x <= -3.55e-71)
		tmp = (z + a) - b;
	elseif (x <= 1.6e+50)
		tmp = a - (y * (b / (y + 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[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+181], t$95$1, If[LessEqual[x, -3.55e-71], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 1.6e+50], N[(a - N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000031e181 or 1.59999999999999991e50 < x

   1. Initial program 46.8%

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

      1. div-sub 46.8%

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

      2. fma-define 46.9%

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

      3. +-commutative 46.9%

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

      4. *-commutative 46.9%

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

      5. associate-+l+ 46.9%

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

      6. +-commutative 46.9%

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

      7. associate-+l+ 46.9%

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

      8. +-commutative 46.9%

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

      9. associate-/l* 49.8%

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

   4. Applied egg-rr 49.8%

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

   5. Taylor expanded in x around inf 70.1%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. +-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -3.40000000000000031e181 < x < -3.55000000000000004e-71

   1. Initial program 55.5%

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

   3. Taylor expanded in y around inf 70.2%

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

   if -3.55000000000000004e-71 < x < 1.59999999999999991e50

   1. Initial program 65.4%

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

      1. div-sub 65.4%

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

      2. fma-define 65.4%

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

      3. +-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-+l+ 65.4%

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

      6. +-commutative 65.4%

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

      7. associate-+l+ 65.4%

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

      8. +-commutative 65.4%

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

      9. associate-/l* 64.7%

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

   4. Applied egg-rr 64.7%

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

   5. Taylor expanded in t around inf 68.0%

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

   6. Taylor expanded in x around 0 60.6%

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

      1. *-commutative 60.6%

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

      2. +-commutative 60.6%

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

      3. associate-/l* 66.4%

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

      4. +-commutative 66.4%

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

   8. Simplified 66.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+181}:\\ \;\;\;\;z - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-71}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;a - y \cdot \frac{b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-5} \lor \neg \left(z \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e-5) (not (<= z 9.5e+38))) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-5) || !(z <= 9.5e+38)) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d-5)) .or. (.not. (z <= 9.5d+38))) then
        tmp = z + a
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-5) || !(z <= 9.5e+38)) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e-5) or not (z <= 9.5e+38):
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e-5) || !(z <= 9.5e+38))
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e-5) || ~((z <= 9.5e+38)))
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e-5], N[Not[LessEqual[z, 9.5e+38]], $MachinePrecision]], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000005e-5 or 9.4999999999999995e38 < z

   1. Initial program 43.2%

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

   3. Taylor expanded in y around inf 56.2%

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

   4. Taylor expanded in b around 0 60.9%

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

      1. +-commutative 60.9%

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

   6. Simplified 60.9%

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

   if -9.5000000000000005e-5 < z < 9.4999999999999995e38

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 60.3%

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

   4. Taylor expanded in z around 0 59.1%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-5} \lor \neg \left(z \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+95}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.8e-34) z (if (<= z 1.6e+95) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e-34) {
		tmp = z;
	} else if (z <= 1.6e+95) {
		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 <= (-3.8d-34)) then
        tmp = z
    else if (z <= 1.6d+95) 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 <= -3.8e-34) {
		tmp = z;
	} else if (z <= 1.6e+95) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.8e-34:
		tmp = z
	elif z <= 1.6e+95:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.8e-34)
		tmp = z;
	elseif (z <= 1.6e+95)
		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 <= -3.8e-34)
		tmp = z;
	elseif (z <= 1.6e+95)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.8e-34], z, If[LessEqual[z, 1.6e+95], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000001e-34 or 1.6e95 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in x around inf 57.7%

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

   if -3.8000000000000001e-34 < z < 1.6e95

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 48.9%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+95}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{+197}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2.25e+197) (- (+ z a) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.25e+197) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 2.25d+197) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.25e+197) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 2.25e+197:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2.25e+197)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 2.25e+197)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2.25e+197], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < 2.2500000000000001e197

   1. Initial program 59.1%

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

   3. Taylor expanded in y around inf 60.3%

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

   if 2.2500000000000001e197 < t

   1. Initial program 44.5%

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

   3. Taylor expanded in t around inf 74.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{+197}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{+256}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 8e+256) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8e+256) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8d+256) then
        tmp = z + a
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8e+256) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8e+256:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8e+256)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8e+256)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8e+256], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 8.0000000000000002e256

   1. Initial program 59.5%

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

   3. Taylor expanded in y around inf 58.1%

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

   4. Taylor expanded in b around 0 55.4%

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

      1. +-commutative 55.4%

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

   6. Simplified 55.4%

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

   if 8.0000000000000002e256 < b

   1. Initial program 20.9%

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

   3. Taylor expanded in b around inf 22.9%

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

      1. mul-1-neg 22.9%

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

      2. associate-/l* 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. +-commutative 67.4%

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

      5. +-commutative 67.4%

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

      6. associate-+l+ 67.4%

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

      7. +-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in y around inf 55.5%

      \[\leadsto \color{blue}{-1 \cdot b} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.5%

         \[\leadsto \color{blue}{-b} \]

   8. Simplified 55.5%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8 \cdot 10^{+256}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.5% 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 57.7%

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

3. Taylor expanded in t around inf 34.3%

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

4. Final simplification 34.3%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))