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

Percentage Accurate: 61.0% → 90.4%

Time: 13.9s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := x + \left(y + t\right)\\ t_3 := y + \left(x + t\right)\\ t_4 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_3}\\ t_5 := a \cdot \frac{y + t}{t\_3} + z \cdot \frac{x + y}{t\_3}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(z, \frac{x + y}{b \cdot t\_2}, \frac{y + t}{t\_2} \cdot \frac{a}{b}\right) - \frac{y}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ x (+ y t)))
        (t_3 (+ y (+ x t)))
        (t_4 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_3))
        (t_5 (+ (* a (/ (+ y t) t_3)) (* z (/ (+ x y) t_3)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 5e+215)
       (/ (- (fma (+ x y) z t_1) (* y b)) t_2)
       (if (<= t_4 INFINITY)
         t_5
         (*
          b
          (-
           (fma z (/ (+ x y) (* b t_2)) (* (/ (+ y t) t_2) (/ a b)))
           (/ y t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = x + (y + t);
	double t_3 = y + (x + t);
	double t_4 = ((((x + y) * z) + t_1) - (y * b)) / t_3;
	double t_5 = (a * ((y + t) / t_3)) + (z * ((x + y) / t_3));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= 5e+215) {
		tmp = (fma((x + y), z, t_1) - (y * b)) / t_2;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = b * (fma(z, ((x + y) / (b * t_2)), (((y + t) / t_2) * (a / b))) - (y / t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(y + Float64(x + t))
	t_4 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_3)
	t_5 = Float64(Float64(a * Float64(Float64(y + t) / t_3)) + Float64(z * Float64(Float64(x + y) / t_3)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= 5e+215)
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / t_2);
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(b * Float64(fma(z, Float64(Float64(x + y) / Float64(b * t_2)), Float64(Float64(Float64(y + t) / t_2) * Float64(a / b))) - Float64(y / t_2)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, 5e+215], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(b * N[(N[(z * N[(N[(x + y), $MachinePrecision] / N[(b * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.0000000000000001e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < +inf.0

   1. Initial program 12.6%

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

   3. Taylor expanded in b around inf 17.6%

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

      1. +-commutative 17.6%

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

      2. mul-1-neg 17.6%

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

      3. unsub-neg 17.6%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in b around 0 12.2%

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

      1. associate-/l* 46.7%

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

      2. associate-+r+ 46.7%

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

      3. +-commutative 46.7%

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

      4. associate-/l* 82.0%

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

      5. +-commutative 82.0%

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

      6. associate-+r+ 82.0%

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

      7. +-commutative 82.0%

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

   8. Simplified 82.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e215

   1. Initial program 99.1%

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

      1. fma-define 99.1%

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

      2. +-commutative 99.1%

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

      3. associate-+l+ 99.1%

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

      4. +-commutative 99.1%

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

   3. Simplified 99.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 0.0%

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

      1. +-commutative 0.0%

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

      2. mul-1-neg 0.0%

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

      3. unsub-neg 0.0%

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

   5. Simplified 87.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq \infty:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(z, \frac{x + y}{b \cdot \left(x + \left(y + t\right)\right)}, \frac{y + t}{x + \left(y + t\right)} \cdot \frac{a}{b}\right) - \frac{y}{x + \left(y + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a \cdot \frac{y + t}{t\_2} + z \cdot \frac{x + y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 5e+215)))
     (+ (* a (/ (+ y t) t_2)) (* z (/ (+ x y) t_2)))
     (/ (- (fma (+ x y) z t_1) (* y b)) (+ x (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 5e+215)) {
		tmp = (a * ((y + t) / t_2)) + (z * ((x + y) / t_2));
	} else {
		tmp = (fma((x + y), z, t_1) - (y * b)) / (x + (y + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 5e+215))
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_2)) + Float64(z * Float64(Float64(x + y) / t_2)));
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $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, 5e+215]], $MachinePrecision]], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $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 5.0000000000000001e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.7%

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

   3. Taylor expanded in b around inf 15.1%

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

      1. +-commutative 15.1%

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

      2. mul-1-neg 15.1%

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

      3. unsub-neg 15.1%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in b around 0 10.7%

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

      1. associate-/l* 42.4%

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

      2. associate-+r+ 42.4%

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

      3. +-commutative 42.4%

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

      4. associate-/l* 78.7%

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

      5. +-commutative 78.7%

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

      6. associate-+r+ 78.7%

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

      7. +-commutative 78.7%

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

   8. Simplified 78.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e215

   1. Initial program 99.1%

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

      1. fma-define 99.1%

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

      2. +-commutative 99.1%

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

      3. associate-+l+ 99.1%

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

      4. +-commutative 99.1%

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

   3. Simplified 99.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} + z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+215)))
     (+ (* a (/ (+ y t) t_1)) (* z (/ (+ x y) t_1)))
     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 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+215)) {
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+215)) {
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+215):
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+215))
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(x + y) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+215)))
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+215]], $MachinePrecision]], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.0000000000000001e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.7%

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

   3. Taylor expanded in b around inf 15.1%

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

      1. +-commutative 15.1%

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

      2. mul-1-neg 15.1%

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

      3. unsub-neg 15.1%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in b around 0 10.7%

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

      1. associate-/l* 42.4%

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

      2. associate-+r+ 42.4%

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

      3. +-commutative 42.4%

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

      4. associate-/l* 78.7%

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

      5. +-commutative 78.7%

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

      6. associate-+r+ 78.7%

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

      7. +-commutative 78.7%

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

   8. Simplified 78.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e215

   1. Initial program 99.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -5e+305) (not (<= t_1 5e+215))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+305) || !(t_1 <= 5e+215)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-5d+305)) .or. (.not. (t_1 <= 5d+215))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+305) || !(t_1 <= 5e+215)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -5e+305) or not (t_1 <= 5e+215):
		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(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -5e+305) || !(t_1 <= 5e+215))
		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 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -5e+305) || ~((t_1 <= 5e+215)))
		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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+305], N[Not[LessEqual[t$95$1, 5e+215]], $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)) < -5.00000000000000009e305 or 5.0000000000000001e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.5%

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

   3. Taylor expanded in y around inf 72.2%

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

   if -5.00000000000000009e305 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e215

   1. Initial program 99.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+305} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+215}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{\left(-x\right) - \left(y + t\right)}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 10^{+116}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b (- (- x) (+ y t))))))
   (if (<= b -1.25e+148)
     t_1
     (if (<= b -4.2e+67)
       (* a (/ (+ y t) (+ x (+ y t))))
       (if (<= b -1.22e-151)
         (- (+ z a) b)
         (if (<= b 1e+116) (+ z (* a (/ y (+ x y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (-x - (y + t)));
	double tmp;
	if (b <= -1.25e+148) {
		tmp = t_1;
	} else if (b <= -4.2e+67) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else if (b <= -1.22e-151) {
		tmp = (z + a) - b;
	} else if (b <= 1e+116) {
		tmp = z + (a * (y / (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 = y * (b / (-x - (y + t)))
    if (b <= (-1.25d+148)) then
        tmp = t_1
    else if (b <= (-4.2d+67)) then
        tmp = a * ((y + t) / (x + (y + t)))
    else if (b <= (-1.22d-151)) then
        tmp = (z + a) - b
    else if (b <= 1d+116) then
        tmp = z + (a * (y / (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 = y * (b / (-x - (y + t)));
	double tmp;
	if (b <= -1.25e+148) {
		tmp = t_1;
	} else if (b <= -4.2e+67) {
		tmp = a * ((y + t) / (x + (y + t)));
	} else if (b <= -1.22e-151) {
		tmp = (z + a) - b;
	} else if (b <= 1e+116) {
		tmp = z + (a * (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / (-x - (y + t)))
	tmp = 0
	if b <= -1.25e+148:
		tmp = t_1
	elif b <= -4.2e+67:
		tmp = a * ((y + t) / (x + (y + t)))
	elif b <= -1.22e-151:
		tmp = (z + a) - b
	elif b <= 1e+116:
		tmp = z + (a * (y / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / Float64(Float64(-x) - Float64(y + t))))
	tmp = 0.0
	if (b <= -1.25e+148)
		tmp = t_1;
	elseif (b <= -4.2e+67)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(x + Float64(y + t))));
	elseif (b <= -1.22e-151)
		tmp = Float64(Float64(z + a) - b);
	elseif (b <= 1e+116)
		tmp = Float64(z + Float64(a * Float64(y / Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / (-x - (y + t)));
	tmp = 0.0;
	if (b <= -1.25e+148)
		tmp = t_1;
	elseif (b <= -4.2e+67)
		tmp = a * ((y + t) / (x + (y + t)));
	elseif (b <= -1.22e-151)
		tmp = (z + a) - b;
	elseif (b <= 1e+116)
		tmp = z + (a * (y / (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / N[((-x) - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+148], t$95$1, If[LessEqual[b, -4.2e+67], N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.22e-151], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 1e+116], N[(z + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.25000000000000006e148 or 1.00000000000000002e116 < b

   1. Initial program 55.8%

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

   3. Taylor expanded in b around inf 35.1%

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

      1. *-commutative 35.1%

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

      2. +-commutative 35.1%

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

      3. associate-+r+ 35.1%

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

      4. associate-*r/ 58.3%

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

      5. neg-mul-1 58.3%

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

      6. distribute-lft-neg-in 58.3%

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

   5. Simplified 58.3%

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

   if -1.25000000000000006e148 < b < -4.2000000000000003e67

   1. Initial program 75.8%

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

   3. Taylor expanded in a around inf 43.1%

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

      1. associate-/l* 66.4%

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

      2. +-commutative 66.4%

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

      3. +-commutative 66.4%

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

      4. associate-+r+ 66.4%

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

   5. Simplified 66.4%

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

   if -4.2000000000000003e67 < b < -1.21999999999999997e-151

   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 y around inf 73.5%

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

   if -1.21999999999999997e-151 < b < 1.00000000000000002e116

   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 b around inf 39.9%

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

      1. +-commutative 39.9%

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

      2. mul-1-neg 39.9%

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

      3. unsub-neg 39.9%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in b around 0 54.4%

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

      1. associate-/l* 71.7%

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

      2. associate-+r+ 71.7%

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

      3. +-commutative 71.7%

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

      4. associate-/l* 93.3%

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

      5. +-commutative 93.3%

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

      6. associate-+r+ 93.3%

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

      7. +-commutative 93.3%

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

   8. Simplified 93.3%

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

   9. Taylor expanded in t around 0 54.7%

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

       1. associate-/l* 67.4%

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

   11. Simplified 67.4%

       \[\leadsto \color{blue}{z + a \cdot \frac{y}{x + y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \frac{b}{\left(-x\right) - \left(y + t\right)}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 10^{+116}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{b}{\left(-x\right) - \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{\left(-x\right) - \left(y + t\right)}\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+115}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b (- (- x) (+ y t))))))
   (if (<= b -2.3e+155)
     t_1
     (if (<= b -9e-152)
       (- (+ z a) b)
       (if (<= b 8.5e+115) (+ z (* a (/ y (+ x y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (-x - (y + t)));
	double tmp;
	if (b <= -2.3e+155) {
		tmp = t_1;
	} else if (b <= -9e-152) {
		tmp = (z + a) - b;
	} else if (b <= 8.5e+115) {
		tmp = z + (a * (y / (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 = y * (b / (-x - (y + t)))
    if (b <= (-2.3d+155)) then
        tmp = t_1
    else if (b <= (-9d-152)) then
        tmp = (z + a) - b
    else if (b <= 8.5d+115) then
        tmp = z + (a * (y / (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 = y * (b / (-x - (y + t)));
	double tmp;
	if (b <= -2.3e+155) {
		tmp = t_1;
	} else if (b <= -9e-152) {
		tmp = (z + a) - b;
	} else if (b <= 8.5e+115) {
		tmp = z + (a * (y / (x + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / (-x - (y + t)))
	tmp = 0
	if b <= -2.3e+155:
		tmp = t_1
	elif b <= -9e-152:
		tmp = (z + a) - b
	elif b <= 8.5e+115:
		tmp = z + (a * (y / (x + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / Float64(Float64(-x) - Float64(y + t))))
	tmp = 0.0
	if (b <= -2.3e+155)
		tmp = t_1;
	elseif (b <= -9e-152)
		tmp = Float64(Float64(z + a) - b);
	elseif (b <= 8.5e+115)
		tmp = Float64(z + Float64(a * Float64(y / Float64(x + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / (-x - (y + t)));
	tmp = 0.0;
	if (b <= -2.3e+155)
		tmp = t_1;
	elseif (b <= -9e-152)
		tmp = (z + a) - b;
	elseif (b <= 8.5e+115)
		tmp = z + (a * (y / (x + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / N[((-x) - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+155], t$95$1, If[LessEqual[b, -9e-152], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 8.5e+115], N[(z + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.29999999999999998e155 or 8.50000000000000057e115 < b

   1. Initial program 55.3%

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

   3. Taylor expanded in b around inf 35.5%

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

      1. *-commutative 35.5%

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

      2. +-commutative 35.5%

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

      3. associate-+r+ 35.5%

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

      4. associate-*r/ 59.0%

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

      5. neg-mul-1 59.0%

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

      6. distribute-lft-neg-in 59.0%

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

   5. Simplified 59.0%

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

   if -2.29999999999999998e155 < b < -9.0000000000000008e-152

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 63.1%

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

   if -9.0000000000000008e-152 < b < 8.50000000000000057e115

   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 b around inf 39.9%

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

      1. +-commutative 39.9%

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

      2. mul-1-neg 39.9%

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

      3. unsub-neg 39.9%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in b around 0 54.4%

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

      1. associate-/l* 71.7%

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

      2. associate-+r+ 71.7%

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

      3. +-commutative 71.7%

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

      4. associate-/l* 93.3%

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

      5. +-commutative 93.3%

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

      6. associate-+r+ 93.3%

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

      7. +-commutative 93.3%

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

   8. Simplified 93.3%

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

   9. Taylor expanded in t around 0 54.7%

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

       1. associate-/l* 67.4%

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

   11. Simplified 67.4%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{b}{\left(-x\right) - \left(y + t\right)}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-152}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+115}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{b}{\left(-x\right) - \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1620000:\\ \;\;\;\;a + z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.9e-28)
     t_1
     (if (<= y 1620000.0)
       (+ a (* z (/ x (+ x t))))
       (if (<= y 5.8e+174) (+ z (* a (/ y (+ 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 <= -4.9e-28) {
		tmp = t_1;
	} else if (y <= 1620000.0) {
		tmp = a + (z * (x / (x + t)));
	} else if (y <= 5.8e+174) {
		tmp = z + (a * (y / (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 <= (-4.9d-28)) then
        tmp = t_1
    else if (y <= 1620000.0d0) then
        tmp = a + (z * (x / (x + t)))
    else if (y <= 5.8d+174) then
        tmp = z + (a * (y / (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 <= -4.9e-28) {
		tmp = t_1;
	} else if (y <= 1620000.0) {
		tmp = a + (z * (x / (x + t)));
	} else if (y <= 5.8e+174) {
		tmp = z + (a * (y / (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 <= -4.9e-28:
		tmp = t_1
	elif y <= 1620000.0:
		tmp = a + (z * (x / (x + t)))
	elif y <= 5.8e+174:
		tmp = z + (a * (y / (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 <= -4.9e-28)
		tmp = t_1;
	elseif (y <= 1620000.0)
		tmp = Float64(a + Float64(z * Float64(x / Float64(x + t))));
	elseif (y <= 5.8e+174)
		tmp = Float64(z + Float64(a * Float64(y / 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 <= -4.9e-28)
		tmp = t_1;
	elseif (y <= 1620000.0)
		tmp = a + (z * (x / (x + t)));
	elseif (y <= 5.8e+174)
		tmp = z + (a * (y / (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, -4.9e-28], t$95$1, If[LessEqual[y, 1620000.0], N[(a + N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+174], N[(z + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9000000000000003e-28 or 5.7999999999999999e174 < y

   1. Initial program 39.1%

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

   3. Taylor expanded in y around inf 74.4%

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

   if -4.9000000000000003e-28 < y < 1.62e6

   1. Initial program 72.5%

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

   3. Taylor expanded in b around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in b around 0 56.6%

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

      1. associate-/l* 64.8%

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

      2. associate-+r+ 64.7%

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

      3. +-commutative 64.7%

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

      4. associate-/l* 82.3%

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

      5. +-commutative 82.3%

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

      6. associate-+r+ 82.3%

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

      7. +-commutative 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in t around inf 65.2%

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

   10. Taylor expanded in y around 0 61.2%

       \[\leadsto a \cdot 1 + z \cdot \color{blue}{\frac{x}{t + x}} \]
   11. Step-by-step derivation

       1. +-commutative 61.2%

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

   12. Simplified 61.2%

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

   if 1.62e6 < y < 5.7999999999999999e174

   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 b around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in b around 0 49.6%

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

      1. associate-/l* 71.0%

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

      2. associate-+r+ 71.0%

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

      3. +-commutative 71.0%

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

      4. associate-/l* 78.2%

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

      5. +-commutative 78.2%

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

      6. associate-+r+ 78.2%

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

      7. +-commutative 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in t around 0 57.0%

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

       1. associate-/l* 71.0%

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

   11. Simplified 71.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-28}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1620000:\\ \;\;\;\;a + z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;a + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.5e+145)
   (+ z (* t (- (/ a x) (/ z x))))
   (if (<= x 2.8e+101)
     (+ a (* z (/ (+ x y) (+ y (+ x t)))))
     (+ z (* a (/ y (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e+145) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else if (x <= 2.8e+101) {
		tmp = a + (z * ((x + y) / (y + (x + t))));
	} else {
		tmp = z + (a * (y / (x + y)));
	}
	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 <= (-7.5d+145)) then
        tmp = z + (t * ((a / x) - (z / x)))
    else if (x <= 2.8d+101) then
        tmp = a + (z * ((x + y) / (y + (x + t))))
    else
        tmp = z + (a * (y / (x + y)))
    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 <= -7.5e+145) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else if (x <= 2.8e+101) {
		tmp = a + (z * ((x + y) / (y + (x + t))));
	} else {
		tmp = z + (a * (y / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.5e+145:
		tmp = z + (t * ((a / x) - (z / x)))
	elif x <= 2.8e+101:
		tmp = a + (z * ((x + y) / (y + (x + t))))
	else:
		tmp = z + (a * (y / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.5e+145)
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	elseif (x <= 2.8e+101)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t)))));
	else
		tmp = Float64(z + Float64(a * Float64(y / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.5e+145)
		tmp = z + (t * ((a / x) - (z / x)));
	elseif (x <= 2.8e+101)
		tmp = a + (z * ((x + y) / (y + (x + t))));
	else
		tmp = z + (a * (y / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.5e+145], N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+101], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000006e145

   1. Initial program 52.0%

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

   3. Taylor expanded in y around 0 40.5%

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

   4. Taylor expanded in t around 0 70.8%

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

   if -7.50000000000000006e145 < x < 2.79999999999999981e101

   1. Initial program 67.0%

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

   3. Taylor expanded in b around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in b around 0 49.9%

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

      1. associate-/l* 65.4%

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

      2. associate-+r+ 65.4%

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

      3. +-commutative 65.4%

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

      4. associate-/l* 74.5%

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

      5. +-commutative 74.5%

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

      6. associate-+r+ 74.5%

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

      7. +-commutative 74.5%

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

   8. Simplified 74.5%

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

   9. Taylor expanded in t around inf 70.7%

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

   if 2.79999999999999981e101 < x

   1. Initial program 43.4%

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

   3. Taylor expanded in b around inf 33.5%

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

      1. +-commutative 33.5%

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

      2. mul-1-neg 33.5%

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

      3. unsub-neg 33.5%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in b around 0 32.8%

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

      1. associate-/l* 45.5%

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

      2. associate-+r+ 45.5%

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

      3. +-commutative 45.5%

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

      4. associate-/l* 79.2%

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

      5. +-commutative 79.2%

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

      6. associate-+r+ 79.2%

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

      7. +-commutative 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in t around 0 47.4%

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

       1. associate-/l* 62.2%

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

   11. Simplified 62.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;a + z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t}{x + t}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ t (+ x t)))))
   (if (<= t -1.1e+180)
     t_1
     (if (<= t 2.65e+73)
       (+ z (* a (/ y (+ x y))))
       (if (<= t 9.5e+178) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t / (x + t));
	double tmp;
	if (t <= -1.1e+180) {
		tmp = t_1;
	} else if (t <= 2.65e+73) {
		tmp = z + (a * (y / (x + y)));
	} else if (t <= 9.5e+178) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t / (x + t))
    if (t <= (-1.1d+180)) then
        tmp = t_1
    else if (t <= 2.65d+73) then
        tmp = z + (a * (y / (x + y)))
    else if (t <= 9.5d+178) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t / (x + t));
	double tmp;
	if (t <= -1.1e+180) {
		tmp = t_1;
	} else if (t <= 2.65e+73) {
		tmp = z + (a * (y / (x + y)));
	} else if (t <= 9.5e+178) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t / (x + t))
	tmp = 0
	if t <= -1.1e+180:
		tmp = t_1
	elif t <= 2.65e+73:
		tmp = z + (a * (y / (x + y)))
	elif t <= 9.5e+178:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t / Float64(x + t)))
	tmp = 0.0
	if (t <= -1.1e+180)
		tmp = t_1;
	elseif (t <= 2.65e+73)
		tmp = Float64(z + Float64(a * Float64(y / Float64(x + y))));
	elseif (t <= 9.5e+178)
		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 * (t / (x + t));
	tmp = 0.0;
	if (t <= -1.1e+180)
		tmp = t_1;
	elseif (t <= 2.65e+73)
		tmp = z + (a * (y / (x + y)));
	elseif (t <= 9.5e+178)
		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[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+180], t$95$1, If[LessEqual[t, 2.65e+73], N[(z + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+178], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e180 or 9.5e178 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in y around 0 32.8%

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

   4. Taylor expanded in a around inf 29.3%

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

      1. associate-/l* 67.9%

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

   6. Simplified 67.9%

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

   if -1.1e180 < t < 2.64999999999999998e73

   1. Initial program 65.1%

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

   3. Taylor expanded in b around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in b around 0 50.5%

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

      1. associate-/l* 58.6%

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

      2. associate-+r+ 58.5%

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

      3. +-commutative 58.5%

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

      4. associate-/l* 76.9%

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

      5. +-commutative 76.9%

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

      6. associate-+r+ 76.9%

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

      7. +-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in t around 0 51.4%

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

       1. associate-/l* 62.3%

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

   11. Simplified 62.3%

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

   if 2.64999999999999998e73 < t < 9.5e178

   1. Initial program 46.9%

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

   3. Taylor expanded in y around inf 62.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+73}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.1e+124)
   (+ z (* t (- (/ a x) (/ z x))))
   (if (<= x 5.2e+63) (- (+ z a) b) (+ z (* a (/ y (+ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e+124) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else if (x <= 5.2e+63) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * (y / (x + y)));
	}
	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 <= (-1.1d+124)) then
        tmp = z + (t * ((a / x) - (z / x)))
    else if (x <= 5.2d+63) then
        tmp = (z + a) - b
    else
        tmp = z + (a * (y / (x + y)))
    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 <= -1.1e+124) {
		tmp = z + (t * ((a / x) - (z / x)));
	} else if (x <= 5.2e+63) {
		tmp = (z + a) - b;
	} else {
		tmp = z + (a * (y / (x + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.1e+124:
		tmp = z + (t * ((a / x) - (z / x)))
	elif x <= 5.2e+63:
		tmp = (z + a) - b
	else:
		tmp = z + (a * (y / (x + y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.1e+124)
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	elseif (x <= 5.2e+63)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z + Float64(a * Float64(y / Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.1e+124)
		tmp = z + (t * ((a / x) - (z / x)));
	elseif (x <= 5.2e+63)
		tmp = (z + a) - b;
	else
		tmp = z + (a * (y / (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.1e+124], N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+63], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e124

   1. Initial program 55.3%

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

   3. Taylor expanded in y around 0 42.4%

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

   4. Taylor expanded in t around 0 66.6%

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

   if -1.1e124 < x < 5.2000000000000002e63

   1. Initial program 66.7%

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

   3. Taylor expanded in y around inf 62.9%

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

   if 5.2000000000000002e63 < x

   1. Initial program 47.0%

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

   3. Taylor expanded in b around inf 35.2%

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

      1. +-commutative 35.2%

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

      2. mul-1-neg 35.2%

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

      3. unsub-neg 35.2%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in b around 0 38.5%

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

      1. associate-/l* 52.4%

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

      2. associate-+r+ 52.4%

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

      3. +-commutative 52.4%

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

      4. associate-/l* 83.2%

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

      5. +-commutative 83.2%

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

      6. associate-+r+ 83.2%

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

      7. +-commutative 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in t around 0 50.1%

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

       1. associate-/l* 63.9%

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

   11. Simplified 63.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{y}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+181} \lor \neg \left(t \leq 1.12 \cdot 10^{+179}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.35e+181) (not (<= t 1.12e+179)))
   (* 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 <= -1.35e+181) || !(t <= 1.12e+179)) {
		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 <= (-1.35d+181)) .or. (.not. (t <= 1.12d+179))) 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 <= -1.35e+181) || !(t <= 1.12e+179)) {
		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 <= -1.35e+181) or not (t <= 1.12e+179):
		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 <= -1.35e+181) || !(t <= 1.12e+179))
		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 <= -1.35e+181) || ~((t <= 1.12e+179)))
		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, -1.35e+181], N[Not[LessEqual[t, 1.12e+179]], $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 < -1.35000000000000004e181 or 1.11999999999999997e179 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in y around 0 32.8%

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

   4. Taylor expanded in a around inf 29.3%

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

      1. associate-/l* 67.9%

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

   6. Simplified 67.9%

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

   if -1.35000000000000004e181 < t < 1.11999999999999997e179

   1. Initial program 62.8%

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

   3. Taylor expanded in y around inf 59.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+181} \lor \neg \left(t \leq 1.12 \cdot 10^{+179}\right):\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+180}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2e+180) a (if (<= t 8.8e+178) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e+180) {
		tmp = a;
	} else if (t <= 8.8e+178) {
		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 <= (-2d+180)) then
        tmp = a
    else if (t <= 8.8d+178) 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 <= -2e+180) {
		tmp = a;
	} else if (t <= 8.8e+178) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2e+180:
		tmp = a
	elif t <= 8.8e+178:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2e+180)
		tmp = a;
	elseif (t <= 8.8e+178)
		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 <= -2e+180)
		tmp = a;
	elseif (t <= 8.8e+178)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2e+180], a, If[LessEqual[t, 8.8e+178], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -2e180 or 8.79999999999999989e178 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in t around inf 57.9%

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

   if -2e180 < t < 8.79999999999999989e178

   1. Initial program 62.8%

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

   3. Taylor expanded in y around inf 59.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+180}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+178}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+20}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+170) z (if (<= z 2.5e+20) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+170) {
		tmp = z;
	} else if (z <= 2.5e+20) {
		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 <= (-1.05d+170)) then
        tmp = z
    else if (z <= 2.5d+20) 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 <= -1.05e+170) {
		tmp = z;
	} else if (z <= 2.5e+20) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.05e+170:
		tmp = z
	elif z <= 2.5e+20:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+170)
		tmp = z;
	elseif (z <= 2.5e+20)
		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 <= -1.05e+170)
		tmp = z;
	elseif (z <= 2.5e+20)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+170], z, If[LessEqual[z, 2.5e+20], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999999e170 or 2.5e20 < z

   1. Initial program 46.9%

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

   3. Taylor expanded in x around inf 54.3%

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

   if -1.04999999999999999e170 < z < 2.5e20

   1. Initial program 68.8%

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

   3. Taylor expanded in t around inf 43.8%

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

Alternative 14: 52.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -9.5e+111) z (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+111) {
		tmp = z;
	} 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 (x <= (-9.5d+111)) then
        tmp = z
    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 (x <= -9.5e+111) {
		tmp = z;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+111:
		tmp = z
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+111)
		tmp = z;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e+111)
		tmp = z;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+111], z, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000019e111

   1. Initial program 50.2%

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

   3. Taylor expanded in x around inf 47.7%

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

   if -9.50000000000000019e111 < x

   1. Initial program 63.2%

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

   3. Taylor expanded in b around inf 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in b around 0 47.3%

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

      1. associate-/l* 62.9%

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

      2. associate-+r+ 62.9%

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

      3. +-commutative 62.9%

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

      4. associate-/l* 75.9%

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

      5. +-commutative 75.9%

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

      6. associate-+r+ 75.9%

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

      7. +-commutative 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in y around inf 53.5%

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

       1. +-commutative 53.5%

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

   11. Simplified 53.5%

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

Alternative 15: 32.1% 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 60.8%

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

3. Taylor expanded in t around inf 34.1%

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

Developer Target 1: 82.3% 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 2024133 
(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)))