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

Percentage Accurate: 60.9% → 88.9%

Time: 12.8s

Alternatives: 13

Speedup: 0.7×

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: 60.9% 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: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot t\_2\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+52} \lor \neg \left(z \leq 1820\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{a \cdot \frac{t + y}{z}}{t\_1}\right) - \frac{b \cdot \frac{y}{z}}{t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_2} + \left(\mathsf{fma}\left(z, \frac{x + y}{t\_3}, \frac{y}{t\_2}\right) - b \cdot \frac{y}{t\_3}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ y (+ x t))) (t_3 (* a t_2)))
   (if (or (<= z -4.1e+52) (not (<= z 1820.0)))
     (*
      z
      (+
       (/ x t_1)
       (- (+ (/ y t_1) (/ (* a (/ (+ t y) z)) t_1)) (/ (* b (/ y z)) t_1))))
     (*
      a
      (+ (/ t t_2) (- (fma z (/ (+ x y) t_3) (/ y t_2)) (* b (/ y t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = a * t_2;
	double tmp;
	if ((z <= -4.1e+52) || !(z <= 1820.0)) {
		tmp = z * ((x / t_1) + (((y / t_1) + ((a * ((t + y) / z)) / t_1)) - ((b * (y / z)) / t_1)));
	} else {
		tmp = a * ((t / t_2) + (fma(z, ((x + y) / t_3), (y / t_2)) - (b * (y / t_3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(a * t_2)
	tmp = 0.0
	if ((z <= -4.1e+52) || !(z <= 1820.0))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(Float64(y / t_1) + Float64(Float64(a * Float64(Float64(t + y) / z)) / t_1)) - Float64(Float64(b * Float64(y / z)) / t_1))));
	else
		tmp = Float64(a * Float64(Float64(t / t_2) + Float64(fma(z, Float64(Float64(x + y) / t_3), Float64(y / t_2)) - Float64(b * Float64(y / t_3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * t$95$2), $MachinePrecision]}, If[Or[LessEqual[z, -4.1e+52], N[Not[LessEqual[z, 1820.0]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(y / z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e52 or 1820 < z

   1. Initial program 43.3%

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

   3. Taylor expanded in z around inf 61.5%

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

      1. associate--l+ 61.5%

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

      2. +-commutative 61.5%

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

      3. +-commutative 61.5%

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

      4. associate-/r* 63.3%

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

      5. associate-/l* 77.3%

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

      6. +-commutative 77.3%

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

      7. associate-/r* 78.7%

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

      8. associate-/l* 91.0%

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

      9. +-commutative 91.0%

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

   5. Simplified 91.0%

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

   if -4.1e52 < z < 1820

   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 a around inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. associate-+r+ 73.8%

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

      3. +-commutative 73.8%

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

      4. associate-/l* 74.6%

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

      5. fma-define 74.6%

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

      6. +-commutative 74.6%

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

      7. associate-+r+ 74.6%

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

      8. associate-+r+ 74.6%

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

   5. Simplified 86.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+52} \lor \neg \left(z \leq 1820\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{a \cdot \frac{t + y}{z}}{t + \left(x + y\right)}\right) - \frac{b \cdot \frac{y}{z}}{t + \left(x + y\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(z, \frac{x + y}{a \cdot \left(y + \left(x + t\right)\right)}, \frac{y}{y + \left(x + t\right)}\right) - b \cdot \frac{y}{a \cdot \left(y + \left(x + t\right)\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := a \cdot \left(t + y\right)\\ t_3 := \frac{\left(t\_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \frac{y}{t\_1}\right) + \frac{t\_2 - y \cdot b}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (* a (+ t y)))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+231)))
     (- (+ z a) b)
     (+ (* z (+ (/ x t_1) (/ y t_1))) (/ (- t_2 (* y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = a * (t + y);
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = a * (t + y);
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = a * (t + y)
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 2e+231):
		tmp = (z + a) - b
	else:
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(a * Float64(t + y))
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+231))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))) + Float64(Float64(t_2 - Float64(y * b)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = a * (t + y);
	t_3 = ((t_2 + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 2e+231)))
		tmp = (z + a) - b;
	else
		tmp = (z * ((x / t_1) + (y / t_1))) + ((t_2 - (y * b)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+231]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e231

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. div-sub 99.8%

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

      5. *-commutative 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(x + y\right)} + \frac{y}{t + \left(x + y\right)}\right) + \frac{a \cdot \left(t + y\right) - y \cdot b}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(z \cdot x + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* a (+ t y)) (* z (+ x y))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+231)))
     t_3
     (/ (+ (* t a) (+ (* z x) (* y t_3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+231)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+231)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+231):
		tmp = t_3
	else:
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+231))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(z * x) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((a * (t + y)) + (z * (x + y))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+231)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((z * x) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+231]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e231

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(z \cdot x + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.75 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-117}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{z \cdot x}{a \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.75e+143)
     t_1
     (if (<= y -9.4e-117)
       (+ z a)
       (if (<= y 5e-163)
         (* a (+ (/ t (+ x t)) (/ (* z x) (* a (+ x t)))))
         (if (<= y 2e-37) (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.75e+143) {
		tmp = t_1;
	} else if (y <= -9.4e-117) {
		tmp = z + a;
	} else if (y <= 5e-163) {
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (x + t))));
	} else if (y <= 2e-37) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-3.75d+143)) then
        tmp = t_1
    else if (y <= (-9.4d-117)) then
        tmp = z + a
    else if (y <= 5d-163) then
        tmp = a * ((t / (x + t)) + ((z * x) / (a * (x + t))))
    else if (y <= 2d-37) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.75e+143) {
		tmp = t_1;
	} else if (y <= -9.4e-117) {
		tmp = z + a;
	} else if (y <= 5e-163) {
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (x + t))));
	} else if (y <= 2e-37) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.75e+143:
		tmp = t_1
	elif y <= -9.4e-117:
		tmp = z + a
	elif y <= 5e-163:
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (x + t))))
	elif y <= 2e-37:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.75e+143)
		tmp = t_1;
	elseif (y <= -9.4e-117)
		tmp = Float64(z + a);
	elseif (y <= 5e-163)
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(Float64(z * x) / Float64(a * Float64(x + t)))));
	elseif (y <= 2e-37)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.75e+143)
		tmp = t_1;
	elseif (y <= -9.4e-117)
		tmp = z + a;
	elseif (y <= 5e-163)
		tmp = a * ((t / (x + t)) + ((z * x) / (a * (x + t))));
	elseif (y <= 2e-37)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.75e+143], t$95$1, If[LessEqual[y, -9.4e-117], N[(z + a), $MachinePrecision], If[LessEqual[y, 5e-163], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(a * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-37], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.74999999999999987e143 or 2.00000000000000013e-37 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -3.74999999999999987e143 < y < -9.40000000000000017e-117

   1. Initial program 47.8%

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

   3. Taylor expanded in y around inf 48.2%

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

   4. Taylor expanded in b around 0 68.5%

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

      1. +-commutative 68.5%

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

   6. Simplified 68.5%

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

   if -9.40000000000000017e-117 < y < 4.99999999999999977e-163

   1. Initial program 71.5%

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

   3. Taylor expanded in a around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. associate-+r+ 75.9%

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

      3. +-commutative 75.9%

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

      4. associate-/l* 76.1%

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

      5. fma-define 76.1%

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

      6. +-commutative 76.1%

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

      7. associate-+r+ 76.1%

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

      8. associate-+r+ 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in y around 0 68.8%

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

   if 4.99999999999999977e-163 < y < 2.00000000000000013e-37

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. *-commutative 64.9%

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

   5. Simplified 64.9%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.75 \cdot 10^{+143}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-117}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + \frac{z \cdot x}{a \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.75 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-199}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-158}:\\ \;\;\;\;\frac{t \cdot a}{x + t} + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 10^{-34}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.75e+143)
     t_1
     (if (<= y -5.6e-199)
       (+ z a)
       (if (<= y 2.7e-158)
         (+ (/ (* t a) (+ x t)) (/ (* z x) (+ x t)))
         (if (<= y 1e-34) (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.75e+143) {
		tmp = t_1;
	} else if (y <= -5.6e-199) {
		tmp = z + a;
	} else if (y <= 2.7e-158) {
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t));
	} else if (y <= 1e-34) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-3.75d+143)) then
        tmp = t_1
    else if (y <= (-5.6d-199)) then
        tmp = z + a
    else if (y <= 2.7d-158) then
        tmp = ((t * a) / (x + t)) + ((z * x) / (x + t))
    else if (y <= 1d-34) then
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.75e+143) {
		tmp = t_1;
	} else if (y <= -5.6e-199) {
		tmp = z + a;
	} else if (y <= 2.7e-158) {
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t));
	} else if (y <= 1e-34) {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.75e+143:
		tmp = t_1
	elif y <= -5.6e-199:
		tmp = z + a
	elif y <= 2.7e-158:
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t))
	elif y <= 1e-34:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.75e+143)
		tmp = t_1;
	elseif (y <= -5.6e-199)
		tmp = Float64(z + a);
	elseif (y <= 2.7e-158)
		tmp = Float64(Float64(Float64(t * a) / Float64(x + t)) + Float64(Float64(z * x) / Float64(x + t)));
	elseif (y <= 1e-34)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.75e+143)
		tmp = t_1;
	elseif (y <= -5.6e-199)
		tmp = z + a;
	elseif (y <= 2.7e-158)
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t));
	elseif (y <= 1e-34)
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.75e+143], t$95$1, If[LessEqual[y, -5.6e-199], N[(z + a), $MachinePrecision], If[LessEqual[y, 2.7e-158], N[(N[(N[(t * a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-34], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.74999999999999987e143 or 9.99999999999999928e-35 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -3.74999999999999987e143 < y < -5.60000000000000036e-199

   1. Initial program 54.2%

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

   3. Taylor expanded in y around inf 45.7%

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

   4. Taylor expanded in b around 0 62.6%

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

      1. +-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -5.60000000000000036e-199 < y < 2.6999999999999998e-158

   1. Initial program 71.3%

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

   3. Taylor expanded in z around 0 82.4%

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

      1. associate--l+ 82.4%

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

      2. fma-define 82.4%

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

      3. associate-+r+ 82.4%

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

      4. associate-+r+ 82.4%

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

      5. div-sub 82.4%

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

      6. *-commutative 82.4%

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

      7. associate-+r+ 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around 0 61.5%

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

      1. *-commutative 61.5%

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

   8. Simplified 61.5%

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

   if 2.6999999999999998e-158 < y < 9.99999999999999928e-35

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. *-commutative 64.9%

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

   5. Simplified 64.9%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.75 \cdot 10^{+143}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-199}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-158}:\\ \;\;\;\;\frac{t \cdot a}{x + t} + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 10^{-34}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;\frac{t \cdot a}{x + t} + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.6e+148)
     t_1
     (if (<= y -3.05e-198)
       (+ z a)
       (if (<= y 1.35e-101)
         (+ (/ (* t a) (+ x t)) (/ (* z x) (+ x t)))
         (if (<= y 1.3e-38) (* z (/ (+ x y) (+ t (+ x y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.6e+148) {
		tmp = t_1;
	} else if (y <= -3.05e-198) {
		tmp = z + a;
	} else if (y <= 1.35e-101) {
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t));
	} else if (y <= 1.3e-38) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.6d+148)) then
        tmp = t_1
    else if (y <= (-3.05d-198)) then
        tmp = z + a
    else if (y <= 1.35d-101) then
        tmp = ((t * a) / (x + t)) + ((z * x) / (x + t))
    else if (y <= 1.3d-38) then
        tmp = z * ((x + y) / (t + (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.6e+148) {
		tmp = t_1;
	} else if (y <= -3.05e-198) {
		tmp = z + a;
	} else if (y <= 1.35e-101) {
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t));
	} else if (y <= 1.3e-38) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.6e+148:
		tmp = t_1
	elif y <= -3.05e-198:
		tmp = z + a
	elif y <= 1.35e-101:
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t))
	elif y <= 1.3e-38:
		tmp = z * ((x + y) / (t + (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.6e+148)
		tmp = t_1;
	elseif (y <= -3.05e-198)
		tmp = Float64(z + a);
	elseif (y <= 1.35e-101)
		tmp = Float64(Float64(Float64(t * a) / Float64(x + t)) + Float64(Float64(z * x) / Float64(x + t)));
	elseif (y <= 1.3e-38)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.6e+148)
		tmp = t_1;
	elseif (y <= -3.05e-198)
		tmp = z + a;
	elseif (y <= 1.35e-101)
		tmp = ((t * a) / (x + t)) + ((z * x) / (x + t));
	elseif (y <= 1.3e-38)
		tmp = z * ((x + y) / (t + (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.6e+148], t$95$1, If[LessEqual[y, -3.05e-198], N[(z + a), $MachinePrecision], If[LessEqual[y, 1.35e-101], N[(N[(N[(t * a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-38], N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000001e148 or 1.30000000000000005e-38 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -4.6000000000000001e148 < y < -3.05e-198

   1. Initial program 54.2%

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

   3. Taylor expanded in y around inf 45.7%

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

   4. Taylor expanded in b around 0 62.6%

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

      1. +-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -3.05e-198 < y < 1.3500000000000001e-101

   1. Initial program 74.7%

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

   3. Taylor expanded in z around 0 85.3%

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

      1. associate--l+ 85.3%

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

      2. fma-define 85.3%

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

      3. associate-+r+ 85.3%

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

      4. associate-+r+ 85.3%

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

      5. div-sub 85.3%

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

      6. *-commutative 85.3%

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

      7. associate-+r+ 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in y around 0 59.4%

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

      1. *-commutative 59.4%

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

   8. Simplified 59.4%

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

   if 1.3500000000000001e-101 < y < 1.30000000000000005e-38

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 38.3%

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

      1. associate-/l* 60.5%

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

      2. +-commutative 60.5%

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

      3. +-commutative 60.5%

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

   5. Simplified 60.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+148}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;\frac{t \cdot a}{x + t} + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-100}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6.4e+154)
     t_1
     (if (<= y -1.36e-198)
       (+ z a)
       (if (<= y 6e-100)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= y 3e-38) (* z (/ (+ x y) (+ t (+ x y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.4e+154) {
		tmp = t_1;
	} else if (y <= -1.36e-198) {
		tmp = z + a;
	} else if (y <= 6e-100) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (y <= 3e-38) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-6.4d+154)) then
        tmp = t_1
    else if (y <= (-1.36d-198)) then
        tmp = z + a
    else if (y <= 6d-100) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (y <= 3d-38) then
        tmp = z * ((x + y) / (t + (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.4e+154) {
		tmp = t_1;
	} else if (y <= -1.36e-198) {
		tmp = z + a;
	} else if (y <= 6e-100) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (y <= 3e-38) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6.4e+154:
		tmp = t_1
	elif y <= -1.36e-198:
		tmp = z + a
	elif y <= 6e-100:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif y <= 3e-38:
		tmp = z * ((x + y) / (t + (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.4e+154)
		tmp = t_1;
	elseif (y <= -1.36e-198)
		tmp = Float64(z + a);
	elseif (y <= 6e-100)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (y <= 3e-38)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.4e+154)
		tmp = t_1;
	elseif (y <= -1.36e-198)
		tmp = z + a;
	elseif (y <= 6e-100)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (y <= 3e-38)
		tmp = z * ((x + y) / (t + (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.4e+154], t$95$1, If[LessEqual[y, -1.36e-198], N[(z + a), $MachinePrecision], If[LessEqual[y, 6e-100], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-38], N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4e154 or 2.99999999999999989e-38 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -6.4e154 < y < -1.36000000000000002e-198

   1. Initial program 54.2%

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

   3. Taylor expanded in y around inf 45.7%

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

   4. Taylor expanded in b around 0 62.6%

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

      1. +-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -1.36000000000000002e-198 < y < 6.0000000000000001e-100

   1. Initial program 74.7%

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

   3. Taylor expanded in y around 0 59.4%

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

   if 6.0000000000000001e-100 < y < 2.99999999999999989e-38

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 38.3%

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

      1. associate-/l* 60.5%

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

      2. +-commutative 60.5%

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

      3. +-commutative 60.5%

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

   5. Simplified 60.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-198}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-100}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-117}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -7.5e+142)
     t_1
     (if (<= y -8.4e-117)
       (+ z a)
       (if (<= y 9.5e-268)
         (* a (/ (+ t y) (+ y (+ x t))))
         (if (<= y 2.9e-38) (* z (/ (+ x y) (+ t (+ x y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= -8.4e-117) {
		tmp = z + a;
	} else if (y <= 9.5e-268) {
		tmp = a * ((t + y) / (y + (x + t)));
	} else if (y <= 2.9e-38) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-7.5d+142)) then
        tmp = t_1
    else if (y <= (-8.4d-117)) then
        tmp = z + a
    else if (y <= 9.5d-268) then
        tmp = a * ((t + y) / (y + (x + t)))
    else if (y <= 2.9d-38) then
        tmp = z * ((x + y) / (t + (x + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -7.5e+142) {
		tmp = t_1;
	} else if (y <= -8.4e-117) {
		tmp = z + a;
	} else if (y <= 9.5e-268) {
		tmp = a * ((t + y) / (y + (x + t)));
	} else if (y <= 2.9e-38) {
		tmp = z * ((x + y) / (t + (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -7.5e+142:
		tmp = t_1
	elif y <= -8.4e-117:
		tmp = z + a
	elif y <= 9.5e-268:
		tmp = a * ((t + y) / (y + (x + t)))
	elif y <= 2.9e-38:
		tmp = z * ((x + y) / (t + (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= -8.4e-117)
		tmp = Float64(z + a);
	elseif (y <= 9.5e-268)
		tmp = Float64(a * Float64(Float64(t + y) / Float64(y + Float64(x + t))));
	elseif (y <= 2.9e-38)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -7.5e+142)
		tmp = t_1;
	elseif (y <= -8.4e-117)
		tmp = z + a;
	elseif (y <= 9.5e-268)
		tmp = a * ((t + y) / (y + (x + t)));
	elseif (y <= 2.9e-38)
		tmp = z * ((x + y) / (t + (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -7.5e+142], t$95$1, If[LessEqual[y, -8.4e-117], N[(z + a), $MachinePrecision], If[LessEqual[y, 9.5e-268], N[(a * N[(N[(t + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-38], N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5000000000000002e142 or 2.89999999999999994e-38 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 87.1%

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

   if -7.5000000000000002e142 < y < -8.3999999999999996e-117

   1. Initial program 47.8%

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

   3. Taylor expanded in y around inf 48.2%

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

   4. Taylor expanded in b around 0 68.5%

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

      1. +-commutative 68.5%

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

   6. Simplified 68.5%

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

   if -8.3999999999999996e-117 < y < 9.50000000000000007e-268

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 63.5%

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

      2. associate-+r+ 63.5%

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

   5. Simplified 63.5%

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

   if 9.50000000000000007e-268 < y < 2.89999999999999994e-38

   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. Taylor expanded in z around inf 33.7%

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

      1. associate-/l* 50.1%

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

      2. +-commutative 50.1%

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

      3. +-commutative 50.1%

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

   5. Simplified 50.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+142}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-117}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+144} \lor \neg \left(y \leq 1.3 \cdot 10^{-64}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.8e+144) (not (<= y 1.3e-64))) (- (+ z a) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e+144) || !(y <= 1.3e-64)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.8d+144)) .or. (.not. (y <= 1.3d-64))) then
        tmp = (z + a) - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e+144) || !(y <= 1.3e-64)) {
		tmp = (z + a) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.8e+144) or not (y <= 1.3e-64):
		tmp = (z + a) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.8e+144) || !(y <= 1.3e-64))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.8e+144) || ~((y <= 1.3e-64)))
		tmp = (z + a) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.8e+144], N[Not[LessEqual[y, 1.3e-64]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000007e144 or 1.3e-64 < y

   1. Initial program 34.5%

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

   3. Taylor expanded in y around inf 85.1%

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

   if -2.80000000000000007e144 < y < 1.3e-64

   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. Taylor expanded in y around inf 33.3%

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

   4. Taylor expanded in b around 0 52.5%

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

      1. +-commutative 52.5%

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

   6. Simplified 52.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+144} \lor \neg \left(y \leq 1.3 \cdot 10^{-64}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-51}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.8e-51) z (if (<= z 1.1e-23) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e-51) {
		tmp = z;
	} else if (z <= 1.1e-23) {
		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 <= (-4.8d-51)) then
        tmp = z
    else if (z <= 1.1d-23) 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 <= -4.8e-51) {
		tmp = z;
	} else if (z <= 1.1e-23) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.8e-51:
		tmp = z
	elif z <= 1.1e-23:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.8e-51)
		tmp = z;
	elseif (z <= 1.1e-23)
		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 <= -4.8e-51)
		tmp = z;
	elseif (z <= 1.1e-23)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.8e-51], z, If[LessEqual[z, 1.1e-23], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-51 or 1.1e-23 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in x around inf 52.1%

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

   if -4.8e-51 < z < 1.1e-23

   1. Initial program 58.7%

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

   3. Taylor expanded in t around inf 50.0%

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

Alternative 11: 50.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+214}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.02e+214) (- a b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.02e+214) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.02d+214)) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.02e+214) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.02e+214:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.02e+214)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.02e+214)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.02e+214], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.02e214

   1. Initial program 30.2%

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

   3. Taylor expanded in z around 0 30.6%

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

      1. *-commutative 30.6%

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

   5. Simplified 30.6%

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

   6. Taylor expanded in y around inf 52.2%

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

   if -1.02e214 < b

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 57.7%

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

   4. Taylor expanded in b around 0 62.3%

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

      1. +-commutative 62.3%

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

   6. Simplified 62.3%

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

Alternative 12: 51.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+168}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= t -7.4e+168) a (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.4e+168) {
		tmp = a;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.4d+168)) then
        tmp = a
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.4e+168) {
		tmp = a;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.4e+168:
		tmp = a
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.4e+168)
		tmp = a;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.4e+168)
		tmp = a;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.4e+168], a, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.40000000000000018e168

   1. Initial program 29.4%

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

   3. Taylor expanded in t around inf 48.6%

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

   if -7.40000000000000018e168 < t

   1. Initial program 54.4%

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

   3. Taylor expanded in y around inf 61.8%

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

   4. Taylor expanded in b around 0 63.0%

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

      1. +-commutative 63.0%

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

   6. Simplified 63.0%

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

Alternative 13: 32.7% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 51.2%

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

3. Taylor expanded in t around inf 35.0%

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

Developer Target 1: 81.8% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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