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

Percentage Accurate: 59.9% → 90.7%

Time: 10.7s

Alternatives: 13

Speedup: 0.8×

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: 59.9% 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: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;z \leq -29000000000000 \lor \neg \left(z \leq 6 \cdot 10^{+151}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{t\_1}, \frac{y}{t\_1}\right) - \frac{b}{t\_1} \cdot \frac{y}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_2} + \left(\left(\frac{y}{t\_2} + \frac{z}{a} \cdot \frac{x + y}{t\_2}\right) - b \cdot \frac{y}{a \cdot t\_2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (+ t (+ x y))))
   (if (or (<= z -29000000000000.0) (not (<= z 6e+151)))
     (*
      z
      (+
       (/ x t_1)
       (- (fma (/ a z) (/ (+ y t) t_1) (/ y t_1)) (* (/ b t_1) (/ y z)))))
     (*
      a
      (+
       (/ t t_2)
       (- (+ (/ y t_2) (* (/ z a) (/ (+ x y) t_2))) (* b (/ y (* a t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = t + (x + y);
	double tmp;
	if ((z <= -29000000000000.0) || !(z <= 6e+151)) {
		tmp = z * ((x / t_1) + (fma((a / z), ((y + t) / t_1), (y / t_1)) - ((b / t_1) * (y / z))));
	} else {
		tmp = a * ((t / t_2) + (((y / t_2) + ((z / a) * ((x + y) / t_2))) - (b * (y / (a * t_2)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if ((z <= -29000000000000.0) || !(z <= 6e+151))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(fma(Float64(a / z), Float64(Float64(y + t) / t_1), Float64(y / t_1)) - Float64(Float64(b / t_1) * Float64(y / z)))));
	else
		tmp = Float64(a * Float64(Float64(t / t_2) + Float64(Float64(Float64(y / t_2) + Float64(Float64(z / a) * Float64(Float64(x + y) / t_2))) - Float64(b * Float64(y / Float64(a * t_2))))));
	end
	return 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[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -29000000000000.0], N[Not[LessEqual[z, 6e+151]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(N[(a / z), $MachinePrecision] * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(b / t$95$1), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t / t$95$2), $MachinePrecision] + N[(N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e13 or 5.9999999999999998e151 < z

   1. Initial program 38.7%

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

   3. Taylor expanded in z around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. +-commutative 68.8%

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

      3. associate-+r+ 68.8%

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

      4. +-commutative 68.8%

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

      5. associate-+l+ 68.8%

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

   5. Simplified 99.8%

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

   if -2.9e13 < z < 5.9999999999999998e151

   1. Initial program 73.3%

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

   3. Taylor expanded in a around inf 85.9%

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

      1. associate--l+ 85.9%

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

      2. +-commutative 85.9%

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

      3. +-commutative 85.9%

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

      4. times-frac 90.2%

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

      5. +-commutative 90.2%

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

      6. +-commutative 90.2%

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

      7. associate-/l* 95.3%

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

      8. +-commutative 95.3%

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

   5. Simplified 95.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29000000000000 \lor \neg \left(z \leq 6 \cdot 10^{+151}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{y + \left(x + t\right)}, \frac{y}{y + \left(x + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{z}{a} \cdot \frac{x + y}{t + \left(x + y\right)}\right) - b \cdot \frac{y}{a \cdot \left(t + \left(x + y\right)\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(a \cdot \left(y + t\right) + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2} + \frac{t\_1 - y \cdot b}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* a (+ y t)) t_1) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 4e+290)))
     (- (+ z a) b)
     (+ (* a (/ (+ y t) t_2)) (/ (- t_1 (* y b)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x + y);
	double t_2 = y + (x + t);
	double t_3 = (((a * (y + t)) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 4e+290)) {
		tmp = (z + a) - b;
	} else {
		tmp = (a * ((y + t) / t_2)) + ((t_1 - (y * b)) / t_2);
	}
	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);
	double t_2 = y + (x + t);
	double t_3 = (((a * (y + t)) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 4e+290)) {
		tmp = (z + a) - b;
	} else {
		tmp = (a * ((y + t) / t_2)) + ((t_1 - (y * b)) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x + y)
	t_2 = y + (x + t)
	t_3 = (((a * (y + t)) + t_1) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 4e+290):
		tmp = (z + a) - b
	else:
		tmp = (a * ((y + t) / t_2)) + ((t_1 - (y * b)) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 4e+290))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_2)) + Float64(Float64(t_1 - Float64(y * b)) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x + y);
	t_2 = y + (x + t);
	t_3 = (((a * (y + t)) + t_1) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 4e+290)))
		tmp = (z + a) - b;
	else
		tmp = (a * ((y + t) / t_2)) + ((t_1 - (y * b)) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 4e+290]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $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 4.00000000000000025e290 < (/.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 72.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000025e290

   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 b around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-/l* 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l+ 99.8%

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

      9. sub-neg 99.8%

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

      10. div-sub 99.8%

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

      11. +-commutative 99.8%

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

      12. *-commutative 99.8%

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

      13. +-commutative 99.8%

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

      14. associate-+r+ 99.8%

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

      15. +-commutative 99.8%

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

      16. associate-+l+ 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + \frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+290))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+290)) {
		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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+290)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+290):
		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(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+290))
		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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+290)))
		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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + 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$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+290]], $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 4.00000000000000025e290 < (/.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 72.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000025e290

   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. Recombined 2 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{z}{a} \cdot \frac{x + y}{t\_1}\right) - b \cdot \frac{y}{a \cdot t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))))
   (if (<= z -3.5e+151)
     (- (+ z a) b)
     (if (<= z 8.5e+157)
       (*
        a
        (+
         (/ t t_1)
         (- (+ (/ y t_1) (* (/ z a) (/ (+ x y) t_1))) (* b (/ y (* a t_1))))))
       (* z (/ (+ x y) (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double tmp;
	if (z <= -3.5e+151) {
		tmp = (z + a) - b;
	} else if (z <= 8.5e+157) {
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))));
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x + y)
    if (z <= (-3.5d+151)) then
        tmp = (z + a) - b
    else if (z <= 8.5d+157) then
        tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))))
    else
        tmp = z * ((x + y) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double tmp;
	if (z <= -3.5e+151) {
		tmp = (z + a) - b;
	} else if (z <= 8.5e+157) {
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))));
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	tmp = 0
	if z <= -3.5e+151:
		tmp = (z + a) - b
	elif z <= 8.5e+157:
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))))
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (z <= -3.5e+151)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 8.5e+157)
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(Float64(Float64(y / t_1) + Float64(Float64(z / a) * Float64(Float64(x + y) / t_1))) - Float64(b * Float64(y / Float64(a * t_1))))));
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	tmp = 0.0;
	if (z <= -3.5e+151)
		tmp = (z + a) - b;
	elseif (z <= 8.5e+157)
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * ((x + y) / t_1))) - (b * (y / (a * t_1)))));
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+151], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 8.5e+157], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000003e151

   1. Initial program 18.6%

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

   3. Taylor expanded in y around inf 85.2%

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

   if -3.5000000000000003e151 < z < 8.4999999999999998e157

   1. Initial program 71.1%

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

   3. Taylor expanded in a around inf 82.6%

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

      1. associate--l+ 82.6%

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

      2. +-commutative 82.6%

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

      3. +-commutative 82.6%

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

      4. times-frac 88.4%

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

      5. +-commutative 88.4%

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

      6. +-commutative 88.4%

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

      7. associate-/l* 93.4%

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

      8. +-commutative 93.4%

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

   5. Simplified 93.4%

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

   if 8.4999999999999998e157 < z

   1. Initial program 44.9%

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

   3. Taylor expanded in z around inf 31.5%

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

      1. associate-/l* 80.2%

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

      2. +-commutative 80.2%

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

      3. +-commutative 80.2%

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

      4. associate-+r+ 80.2%

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

      5. +-commutative 80.2%

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

      6. associate-+l+ 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(\frac{t}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{z}{a} \cdot \frac{x + y}{t + \left(x + y\right)}\right) - b \cdot \frac{y}{a \cdot \left(t + \left(x + y\right)\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot a + z \cdot x}{x + t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + t \cdot \frac{1}{x + t}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-44} \lor \neg \left(y \leq 10^{+72}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t a) (* z x)) (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -9.5e-39)
     t_2
     (if (<= y -1.4e-209)
       t_1
       (if (<= y 1.65e-110)
         (* a (+ (/ z a) (* t (/ 1.0 (+ x t)))))
         (if (<= y 7.5e-82)
           t_1
           (if (or (<= y 9.8e-44) (not (<= y 1e+72)))
             t_2
             (* a (/ (+ y t) (+ y (+ x t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (z * x)) / (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -9.5e-39) {
		tmp = t_2;
	} else if (y <= -1.4e-209) {
		tmp = t_1;
	} else if (y <= 1.65e-110) {
		tmp = a * ((z / a) + (t * (1.0 / (x + t))));
	} else if (y <= 7.5e-82) {
		tmp = t_1;
	} else if ((y <= 9.8e-44) || !(y <= 1e+72)) {
		tmp = t_2;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t * a) + (z * x)) / (x + t)
    t_2 = (z + a) - b
    if (y <= (-9.5d-39)) then
        tmp = t_2
    else if (y <= (-1.4d-209)) then
        tmp = t_1
    else if (y <= 1.65d-110) then
        tmp = a * ((z / a) + (t * (1.0d0 / (x + t))))
    else if (y <= 7.5d-82) then
        tmp = t_1
    else if ((y <= 9.8d-44) .or. (.not. (y <= 1d+72))) then
        tmp = t_2
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (z * x)) / (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -9.5e-39) {
		tmp = t_2;
	} else if (y <= -1.4e-209) {
		tmp = t_1;
	} else if (y <= 1.65e-110) {
		tmp = a * ((z / a) + (t * (1.0 / (x + t))));
	} else if (y <= 7.5e-82) {
		tmp = t_1;
	} else if ((y <= 9.8e-44) || !(y <= 1e+72)) {
		tmp = t_2;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (z * x)) / (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -9.5e-39:
		tmp = t_2
	elif y <= -1.4e-209:
		tmp = t_1
	elif y <= 1.65e-110:
		tmp = a * ((z / a) + (t * (1.0 / (x + t))))
	elif y <= 7.5e-82:
		tmp = t_1
	elif (y <= 9.8e-44) or not (y <= 1e+72):
		tmp = t_2
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9.5e-39)
		tmp = t_2;
	elseif (y <= -1.4e-209)
		tmp = t_1;
	elseif (y <= 1.65e-110)
		tmp = Float64(a * Float64(Float64(z / a) + Float64(t * Float64(1.0 / Float64(x + t)))));
	elseif (y <= 7.5e-82)
		tmp = t_1;
	elseif ((y <= 9.8e-44) || !(y <= 1e+72))
		tmp = t_2;
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (z * x)) / (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9.5e-39)
		tmp = t_2;
	elseif (y <= -1.4e-209)
		tmp = t_1;
	elseif (y <= 1.65e-110)
		tmp = a * ((z / a) + (t * (1.0 / (x + t))));
	elseif (y <= 7.5e-82)
		tmp = t_1;
	elseif ((y <= 9.8e-44) || ~((y <= 1e+72)))
		tmp = t_2;
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.5e-39], t$95$2, If[LessEqual[y, -1.4e-209], t$95$1, If[LessEqual[y, 1.65e-110], N[(a * N[(N[(z / a), $MachinePrecision] + N[(t * N[(1.0 / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-82], t$95$1, If[Or[LessEqual[y, 9.8e-44], N[Not[LessEqual[y, 1e+72]], $MachinePrecision]], t$95$2, N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.4999999999999999e-39 or 7.4999999999999997e-82 < y < 9.8000000000000006e-44 or 9.99999999999999944e71 < y

   1. Initial program 45.2%

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

   3. Taylor expanded in y around inf 78.3%

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

   if -9.4999999999999999e-39 < y < -1.40000000000000006e-209 or 1.65e-110 < y < 7.4999999999999997e-82

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0 68.6%

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

   if -1.40000000000000006e-209 < y < 1.65e-110

   1. Initial program 69.4%

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

   3. Taylor expanded in a around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. +-commutative 83.8%

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

      3. +-commutative 83.8%

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

      4. times-frac 92.4%

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

      5. +-commutative 92.4%

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

      6. +-commutative 92.4%

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

      7. associate-/l* 92.4%

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

      8. +-commutative 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in y around 0 77.6%

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

      1. associate-/l* 79.3%

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

      2. associate-/r* 80.0%

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

   8. Simplified 80.0%

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

      1. div-inv 79.9%

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

      2. +-commutative 79.9%

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

   10. Applied egg-rr 79.9%

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

   11. Taylor expanded in x around inf 80.5%

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

   if 9.8000000000000006e-44 < y < 9.99999999999999944e71

   1. Initial program 79.4%

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

   3. Taylor expanded in a around inf 42.2%

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

      1. associate-/l* 54.4%

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

      2. +-commutative 54.4%

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

      3. associate-+r+ 54.4%

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

      4. +-commutative 54.4%

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

      5. associate-+l+ 54.4%

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

   5. Simplified 54.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-209}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(\frac{z}{a} + t \cdot \frac{1}{x + t}\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-44} \lor \neg \left(y \leq 10^{+72}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-43} \lor \neg \left(y \leq 9.5 \cdot 10^{+79}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.4e-39)
     t_1
     (if (<= y 9.5e-83)
       (/ (+ (* t a) (* z x)) (+ x t))
       (if (or (<= y 3e-43) (not (<= y 9.5e+79)))
         t_1
         (* a (/ (+ y t) (+ y (+ x t)))))))))

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 <= -4.4e-39) {
		tmp = t_1;
	} else if (y <= 9.5e-83) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if ((y <= 3e-43) || !(y <= 9.5e+79)) {
		tmp = t_1;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.4d-39)) then
        tmp = t_1
    else if (y <= 9.5d-83) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if ((y <= 3d-43) .or. (.not. (y <= 9.5d+79))) then
        tmp = t_1
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.4e-39) {
		tmp = t_1;
	} else if (y <= 9.5e-83) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if ((y <= 3e-43) || !(y <= 9.5e+79)) {
		tmp = t_1;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.4e-39:
		tmp = t_1
	elif y <= 9.5e-83:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif (y <= 3e-43) or not (y <= 9.5e+79):
		tmp = t_1
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.4e-39)
		tmp = t_1;
	elseif (y <= 9.5e-83)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif ((y <= 3e-43) || !(y <= 9.5e+79))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	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 <= -4.4e-39)
		tmp = t_1;
	elseif (y <= 9.5e-83)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif ((y <= 3e-43) || ~((y <= 9.5e+79)))
		tmp = t_1;
	else
		tmp = a * ((y + t) / (y + (x + t)));
	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, -4.4e-39], t$95$1, If[LessEqual[y, 9.5e-83], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3e-43], N[Not[LessEqual[y, 9.5e+79]], $MachinePrecision]], t$95$1, N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.40000000000000002e-39 or 9.50000000000000051e-83 < y < 3.00000000000000003e-43 or 9.49999999999999994e79 < y

   1. Initial program 45.2%

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

   3. Taylor expanded in y around inf 78.3%

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

   if -4.40000000000000002e-39 < y < 9.50000000000000051e-83

   1. Initial program 76.7%

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

   3. Taylor expanded in y around 0 65.6%

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

   if 3.00000000000000003e-43 < y < 9.49999999999999994e79

   1. Initial program 79.4%

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

   3. Taylor expanded in a around inf 42.2%

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

      1. associate-/l* 54.4%

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

      2. +-commutative 54.4%

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

      3. associate-+r+ 54.4%

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

      4. +-commutative 54.4%

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

      5. associate-+l+ 54.4%

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

   5. Simplified 54.4%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-43} \lor \neg \left(y \leq 9.5 \cdot 10^{+79}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+55} \lor \neg \left(y \leq 0.00021\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + x \cdot \frac{\frac{z}{a}}{x + t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e+55) (not (<= y 0.00021)))
   (- (+ z a) b)
   (* a (+ (/ t (+ x t)) (* x (/ (/ z a) (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e+55) || !(y <= 0.00021)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.6d+55)) .or. (.not. (y <= 0.00021d0))) then
        tmp = (z + a) - b
    else
        tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e+55) || !(y <= 0.00021)) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e+55) or not (y <= 0.00021):
		tmp = (z + a) - b
	else:
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e+55) || !(y <= 0.00021))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(t / Float64(x + t)) + Float64(x * Float64(Float64(z / a) / Float64(x + t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.6e+55) || ~((y <= 0.00021)))
		tmp = (z + a) - b;
	else
		tmp = a * ((t / (x + t)) + (x * ((z / a) / (x + t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e+55], N[Not[LessEqual[y, 0.00021]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z / a), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e55 or 2.1000000000000001e-4 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 75.1%

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

   if -2.6e55 < y < 2.1000000000000001e-4

   1. Initial program 74.1%

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

   3. Taylor expanded in a around inf 82.4%

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

      1. associate--l+ 82.4%

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

      2. +-commutative 82.4%

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

      3. +-commutative 82.4%

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

      4. times-frac 89.5%

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

      5. +-commutative 89.5%

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

      6. +-commutative 89.5%

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

      7. associate-/l* 88.9%

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

      8. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in y around 0 69.7%

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

      1. associate-/l* 73.8%

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

      2. associate-/r* 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+55} \lor \neg \left(y \leq 0.00021\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{x + t} + x \cdot \frac{\frac{z}{a}}{x + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0105 \lor \neg \left(t \leq 490000\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -0.0105) (not (<= t 490000.0)))
   (* a (/ (+ y t) (+ y (+ x t))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.0105) || !(t <= 490000.0)) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-0.0105d0)) .or. (.not. (t <= 490000.0d0))) then
        tmp = a * ((y + t) / (y + (x + t)))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.0105) || !(t <= 490000.0)) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -0.0105) or not (t <= 490000.0):
		tmp = a * ((y + t) / (y + (x + t)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -0.0105) || !(t <= 490000.0))
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -0.0105) || ~((t <= 490000.0)))
		tmp = a * ((y + t) / (y + (x + t)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -0.0105], N[Not[LessEqual[t, 490000.0]], $MachinePrecision]], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0105000000000000007 or 4.9e5 < t

   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 a around inf 38.0%

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

      1. associate-/l* 65.3%

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

      2. +-commutative 65.3%

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

      3. associate-+r+ 65.3%

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

      4. +-commutative 65.3%

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

      5. associate-+l+ 65.3%

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

   5. Simplified 65.3%

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

   if -0.0105000000000000007 < t < 4.9e5

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf 68.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0105 \lor \neg \left(t \leq 490000\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+138}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;t \leq 490000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.4e+138)
   (+ a (* y (- (/ z t) (/ b t))))
   (if (<= t 490000.0) (- (+ z a) b) (* a (/ (+ y t) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.4e+138) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else if (t <= 490000.0) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.4d+138)) then
        tmp = a + (y * ((z / t) - (b / t)))
    else if (t <= 490000.0d0) then
        tmp = (z + a) - b
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.4e+138) {
		tmp = a + (y * ((z / t) - (b / t)));
	} else if (t <= 490000.0) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.4e+138:
		tmp = a + (y * ((z / t) - (b / t)))
	elif t <= 490000.0:
		tmp = (z + a) - b
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.4e+138)
		tmp = Float64(a + Float64(y * Float64(Float64(z / t) - Float64(b / t))));
	elseif (t <= 490000.0)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.4e+138)
		tmp = a + (y * ((z / t) - (b / t)));
	elseif (t <= 490000.0)
		tmp = (z + a) - b;
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.4e+138], N[(a + N[(y * N[(N[(z / t), $MachinePrecision] - N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 490000.0], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.40000000000000018e138

   1. Initial program 55.9%

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

   3. Taylor expanded in x around 0 49.7%

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

   4. Taylor expanded in y around 0 83.0%

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

   if -5.40000000000000018e138 < t < 4.9e5

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 66.3%

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

   if 4.9e5 < t

   1. Initial program 59.0%

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

   3. Taylor expanded in a around inf 41.8%

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

      1. associate-/l* 66.5%

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

      2. +-commutative 66.5%

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

      3. associate-+r+ 66.5%

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

      4. +-commutative 66.5%

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

      5. associate-+l+ 66.5%

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

   5. Simplified 66.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+138}:\\ \;\;\;\;a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{elif}\;t \leq 490000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+139} \lor \neg \left(t \leq 490000\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.9e+139) (not (<= t 490000.0)))
   (* a (/ t (+ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+139) || !(t <= 490000.0)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.9d+139)) .or. (.not. (t <= 490000.0d0))) then
        tmp = a * (t / (x + t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+139) || !(t <= 490000.0)) {
		tmp = a * (t / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.9e+139) or not (t <= 490000.0):
		tmp = a * (t / (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.9e+139) || !(t <= 490000.0))
		tmp = Float64(a * Float64(t / Float64(x + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.9e+139) || ~((t <= 490000.0)))
		tmp = a * (t / (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.9e+139], N[Not[LessEqual[t, 490000.0]], $MachinePrecision]], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999999e139 or 4.9e5 < t

   1. Initial program 58.1%

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

   3. Taylor expanded in a around inf 38.9%

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

   4. Taylor expanded in y around 0 40.5%

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

      1. associate-/l* 65.3%

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

   6. Simplified 65.3%

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

   if -2.8999999999999999e139 < t < 4.9e5

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 66.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+139} \lor \neg \left(t \leq 490000\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+139}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+147}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.9e+139) a (if (<= t 9e+147) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e+139) {
		tmp = a;
	} else if (t <= 9e+147) {
		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 <= (-2.9d+139)) then
        tmp = a
    else if (t <= 9d+147) 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 <= -2.9e+139) {
		tmp = a;
	} else if (t <= 9e+147) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.9e+139:
		tmp = a
	elif t <= 9e+147:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.9e+139)
		tmp = a;
	elseif (t <= 9e+147)
		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 <= -2.9e+139)
		tmp = a;
	elseif (t <= 9e+147)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.9e+139], a, If[LessEqual[t, 9e+147], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999999e139 or 9.00000000000000016e147 < t

   1. Initial program 57.0%

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

   3. Taylor expanded in t around inf 66.5%

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

   if -2.8999999999999999e139 < t < 9.00000000000000016e147

   1. Initial program 63.4%

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

   3. Taylor expanded in y around inf 63.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+139}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+147}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+52}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-65}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.6e+52) z (if (<= x 5.2e-65) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.6e+52) {
		tmp = z;
	} else if (x <= 5.2e-65) {
		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 (x <= (-1.6d+52)) then
        tmp = z
    else if (x <= 5.2d-65) 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 (x <= -1.6e+52) {
		tmp = z;
	} else if (x <= 5.2e-65) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.6e+52:
		tmp = z
	elif x <= 5.2e-65:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.6e+52)
		tmp = z;
	elseif (x <= 5.2e-65)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.6e+52)
		tmp = z;
	elseif (x <= 5.2e-65)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.6e+52], z, If[LessEqual[x, 5.2e-65], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e52 or 5.20000000000000019e-65 < x

   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 x around inf 47.8%

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

   if -1.6e52 < x < 5.20000000000000019e-65

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 58.6%

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

Alternative 13: 31.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.8%

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

3. Taylor expanded in t around inf 38.9%

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

Developer target: 81.8% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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