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

Percentage Accurate: 59.9% → 97.4%

Time: 14.5s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathsf{fma}\left(z, \frac{y + x}{t\_1}, a \cdot \frac{y + t}{t\_1}\right) - y \cdot \frac{b}{t\_1} \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (- (fma z (/ (+ y x) t_1) (* a (/ (+ y t) t_1))) (* y (/ b t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	return fma(z, ((y + x) / t_1), (a * ((y + t) / t_1))) - (y * (b / t_1));
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	return Float64(fma(z, Float64(Float64(y + x) / t_1), Float64(a * Float64(Float64(y + t) / t_1))) - Float64(y * Float64(b / t_1)))
end

Wolfram

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

Derivation

1. Initial program 58.5%

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

3. Taylor expanded in b around 0 58.5%

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

   1. mul-1-neg 58.5%

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

   2. +-commutative 58.5%

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

   3. unsub-neg 58.5%

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

   4. +-commutative 58.5%

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

   5. associate-/l* 70.1%

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

   6. fma-define 70.1%

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

   7. +-commutative 70.1%

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

   8. associate-+r+ 70.1%

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

   9. associate-/l* 86.3%

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

   10. associate-+r+ 86.3%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+303} \lor \neg \left(t\_2 \leq 10^{+252}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{1}{\frac{t\_1}{y + x}}, a\right) - y \cdot \frac{b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 -2e+303) (not (<= t_2 1e+252)))
     (- (fma z (/ 1.0 (/ t_1 (+ y x))) a) (* y (/ b 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 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -2e+303) || !(t_2 <= 1e+252)) {
		tmp = fma(z, (1.0 / (t_1 / (y + x))), a) - (y * (b / 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(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -2e+303) || !(t_2 <= 1e+252))
		tmp = Float64(fma(z, Float64(1.0 / Float64(t_1 / Float64(y + x))), a) - Float64(y * Float64(b / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+303], N[Not[LessEqual[t$95$2, 1e+252]], $MachinePrecision]], N[(N[(z * N[(1.0 / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] - N[(y * N[(b / 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)) < -2e303 or 1.0000000000000001e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in b around 0 6.3%

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

      1. mul-1-neg 6.3%

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

      2. +-commutative 6.3%

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

      3. unsub-neg 6.3%

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

      4. +-commutative 6.3%

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

      5. associate-/l* 32.6%

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

      6. fma-define 32.6%

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

      7. +-commutative 32.6%

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

      8. associate-+r+ 32.6%

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

      9. associate-/l* 69.2%

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

      10. associate-+r+ 69.2%

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

   5. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. +-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in t around inf 88.8%

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

   if -2e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e252

   1. Initial program 99.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+303} \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+252}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{1}{\frac{y + \left(x + t\right)}{y + x}}, a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := y \cdot \frac{b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;\left(z + a\right) - t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+252}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\frac{y}{t\_1} + z \cdot \frac{y + x}{a \cdot t\_1}\right)\right) - t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (* y (/ b t_1))))
   (if (<= t_2 -2e+303)
     (- (+ z a) t_3)
     (if (<= t_2 1e+252)
       t_2
       (-
        (* a (+ (/ t t_1) (+ (/ y t_1) (* z (/ (+ y x) (* a t_1))))))
        t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = y * (b / t_1);
	double tmp;
	if (t_2 <= -2e+303) {
		tmp = (z + a) - t_3;
	} else if (t_2 <= 1e+252) {
		tmp = t_2;
	} else {
		tmp = (a * ((t / t_1) + ((y / t_1) + (z * ((y + x) / (a * t_1)))))) - t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
    t_3 = y * (b / t_1)
    if (t_2 <= (-2d+303)) then
        tmp = (z + a) - t_3
    else if (t_2 <= 1d+252) then
        tmp = t_2
    else
        tmp = (a * ((t / t_1) + ((y / t_1) + (z * ((y + x) / (a * t_1)))))) - t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = y * (b / t_1);
	double tmp;
	if (t_2 <= -2e+303) {
		tmp = (z + a) - t_3;
	} else if (t_2 <= 1e+252) {
		tmp = t_2;
	} else {
		tmp = (a * ((t / t_1) + ((y / t_1) + (z * ((y + x) / (a * t_1)))))) - t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = y * (b / t_1)
	tmp = 0
	if t_2 <= -2e+303:
		tmp = (z + a) - t_3
	elif t_2 <= 1e+252:
		tmp = t_2
	else:
		tmp = (a * ((t / t_1) + ((y / t_1) + (z * ((y + x) / (a * t_1)))))) - t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(y * Float64(b / t_1))
	tmp = 0.0
	if (t_2 <= -2e+303)
		tmp = Float64(Float64(z + a) - t_3);
	elseif (t_2 <= 1e+252)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * Float64(Float64(t / t_1) + Float64(Float64(y / t_1) + Float64(z * Float64(Float64(y + x) / Float64(a * t_1)))))) - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = y * (b / t_1);
	tmp = 0.0;
	if (t_2 <= -2e+303)
		tmp = (z + a) - t_3;
	elseif (t_2 <= 1e+252)
		tmp = t_2;
	else
		tmp = (a * ((t / t_1) + ((y / t_1) + (z * ((y + x) / (a * t_1)))))) - t_3;
	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[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+303], N[(N[(z + a), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 1e+252], t$95$2, N[(N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(y / t$95$1), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $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)) < -2e303

   1. Initial program 8.6%

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

   3. Taylor expanded in b around 0 8.6%

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

      1. mul-1-neg 8.6%

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

      2. +-commutative 8.6%

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

      3. unsub-neg 8.6%

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

      4. +-commutative 8.6%

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

      5. associate-/l* 40.5%

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

      6. fma-define 40.5%

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

      7. +-commutative 40.5%

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

      8. associate-+r+ 40.5%

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

      9. associate-/l* 72.2%

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

      10. associate-+r+ 72.2%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 79.3%

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

   if -2e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e252

   1. Initial program 99.7%

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

   if 1.0000000000000001e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.6%

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

   3. Taylor expanded in b around 0 4.6%

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

      1. mul-1-neg 4.6%

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

      2. +-commutative 4.6%

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

      3. unsub-neg 4.6%

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

      4. +-commutative 4.6%

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

      5. associate-/l* 27.0%

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

      6. fma-define 27.0%

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

      7. +-commutative 27.0%

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

      8. associate-+r+ 27.0%

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

      9. associate-/l* 67.0%

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

      10. associate-+r+ 67.0%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in a around inf 48.7%

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

      1. associate-+r+ 48.7%

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

      2. +-commutative 48.7%

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

      3. associate-+r+ 48.7%

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

      4. +-commutative 48.7%

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

      5. associate-/l* 81.2%

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

      6. +-commutative 81.2%

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

      7. associate-+r+ 81.2%

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

      8. +-commutative 81.2%

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

   8. Simplified 81.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+303}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+252}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{y + \left(x + t\right)} + \left(\frac{y}{y + \left(x + t\right)} + z \cdot \frac{y + x}{a \cdot \left(y + \left(x + t\right)\right)}\right)\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+303} \lor \neg \left(t\_2 \leq 10^{+252}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 -2e+303) (not (<= t_2 1e+252)))
     (- (+ z a) (* y (/ b 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 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -2e+303) || !(t_2 <= 1e+252)) {
		tmp = (z + a) - (y * (b / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
    if ((t_2 <= (-2d+303)) .or. (.not. (t_2 <= 1d+252))) then
        tmp = (z + a) - (y * (b / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -2e+303) || !(t_2 <= 1e+252)) {
		tmp = (z + a) - (y * (b / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -2e+303) or not (t_2 <= 1e+252):
		tmp = (z + a) - (y * (b / 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(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= -2e+303) || !(t_2 <= 1e+252))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / 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 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -2e+303) || ~((t_2 <= 1e+252)))
		tmp = (z + a) - (y * (b / 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[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+303], N[Not[LessEqual[t$95$2, 1e+252]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / 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)) < -2e303 or 1.0000000000000001e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in b around 0 6.3%

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

      1. mul-1-neg 6.3%

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

      2. +-commutative 6.3%

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

      3. unsub-neg 6.3%

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

      4. +-commutative 6.3%

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

      5. associate-/l* 32.6%

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

      6. fma-define 32.6%

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

      7. +-commutative 32.6%

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

      8. associate-+r+ 32.6%

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

      9. associate-/l* 69.2%

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

      10. associate-+r+ 69.2%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 75.4%

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

   if -2e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e252

   1. Initial program 99.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+303} \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+252}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\right) - \frac{y \cdot b}{x}\\ t_2 := \left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-190}:\\ \;\;\;\;\left(a + \frac{z \cdot y}{y + t}\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;x \leq 10^{+191}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z (* t (- (/ a x) (/ z x)))) (/ (* y b) x)))
        (t_2 (- (+ z a) (* y (/ b (+ y (+ x t)))))))
   (if (<= x -4.4e+184)
     t_1
     (if (<= x 5e-306)
       t_2
       (if (<= x 5.5e-190)
         (- (+ a (/ (* z y) (+ y t))) (/ (* y b) (+ y t)))
         (if (<= x 1e+191) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * ((a / x) - (z / x)))) - ((y * b) / x);
	double t_2 = (z + a) - (y * (b / (y + (x + t))));
	double tmp;
	if (x <= -4.4e+184) {
		tmp = t_1;
	} else if (x <= 5e-306) {
		tmp = t_2;
	} else if (x <= 5.5e-190) {
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t));
	} else if (x <= 1e+191) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + (t * ((a / x) - (z / x)))) - ((y * b) / x)
    t_2 = (z + a) - (y * (b / (y + (x + t))))
    if (x <= (-4.4d+184)) then
        tmp = t_1
    else if (x <= 5d-306) then
        tmp = t_2
    else if (x <= 5.5d-190) then
        tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t))
    else if (x <= 1d+191) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (t * ((a / x) - (z / x)))) - ((y * b) / x);
	double t_2 = (z + a) - (y * (b / (y + (x + t))));
	double tmp;
	if (x <= -4.4e+184) {
		tmp = t_1;
	} else if (x <= 5e-306) {
		tmp = t_2;
	} else if (x <= 5.5e-190) {
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t));
	} else if (x <= 1e+191) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (t * ((a / x) - (z / x)))) - ((y * b) / x)
	t_2 = (z + a) - (y * (b / (y + (x + t))))
	tmp = 0
	if x <= -4.4e+184:
		tmp = t_1
	elif x <= 5e-306:
		tmp = t_2
	elif x <= 5.5e-190:
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t))
	elif x <= 1e+191:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x)))) - Float64(Float64(y * b) / x))
	t_2 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(y + Float64(x + t)))))
	tmp = 0.0
	if (x <= -4.4e+184)
		tmp = t_1;
	elseif (x <= 5e-306)
		tmp = t_2;
	elseif (x <= 5.5e-190)
		tmp = Float64(Float64(a + Float64(Float64(z * y) / Float64(y + t))) - Float64(Float64(y * b) / Float64(y + t)));
	elseif (x <= 1e+191)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (t * ((a / x) - (z / x)))) - ((y * b) / x);
	t_2 = (z + a) - (y * (b / (y + (x + t))));
	tmp = 0.0;
	if (x <= -4.4e+184)
		tmp = t_1;
	elseif (x <= 5e-306)
		tmp = t_2;
	elseif (x <= 5.5e-190)
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t));
	elseif (x <= 1e+191)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.4e+184], t$95$1, If[LessEqual[x, 5e-306], t$95$2, If[LessEqual[x, 5.5e-190], N[(N[(a + N[(N[(z * y), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+191], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e184 or 1.00000000000000007e191 < x

   1. Initial program 47.5%

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

   3. Taylor expanded in x around inf 55.7%

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

   4. Taylor expanded in t around 0 77.0%

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

   5. Taylor expanded in t around inf 68.6%

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

   if -4.4e184 < x < 4.99999999999999998e-306 or 5.50000000000000048e-190 < x < 1.00000000000000007e191

   1. Initial program 56.3%

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

   3. Taylor expanded in b around 0 56.3%

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

      1. mul-1-neg 56.3%

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

      2. +-commutative 56.3%

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

      3. unsub-neg 56.3%

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

      4. +-commutative 56.3%

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

      5. associate-/l* 68.3%

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

      6. fma-define 68.3%

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

      7. +-commutative 68.3%

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

      8. associate-+r+ 68.3%

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

      9. associate-/l* 84.1%

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

      10. associate-+r+ 84.1%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around inf 75.2%

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

   if 4.99999999999999998e-306 < x < 5.50000000000000048e-190

   1. Initial program 87.0%

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

   3. Taylor expanded in b around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. unsub-neg 86.9%

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

      4. +-commutative 86.9%

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

      5. associate-/l* 87.0%

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

      6. fma-define 87.1%

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

      7. +-commutative 87.1%

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

      8. associate-+r+ 87.1%

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

      9. associate-/l* 96.6%

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

      10. associate-+r+ 96.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in x around 0 92.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+184}:\\ \;\;\;\;\left(z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\right) - \frac{y \cdot b}{x}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-306}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-190}:\\ \;\;\;\;\left(a + \frac{z \cdot y}{y + t}\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;x \leq 10^{+191}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\right) - \frac{y \cdot b}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - y \cdot \frac{b}{t\_1}\\ \mathbf{if}\;x \leq -2.75 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \frac{x}{t\_1}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-187}:\\ \;\;\;\;\left(a + \frac{z \cdot y}{y + t}\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+189}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) (* y (/ b t_1)))))
   (if (<= x -2.75e+144)
     (* z (/ x t_1))
     (if (<= x 5.5e-306)
       t_2
       (if (<= x 4.3e-187)
         (- (+ a (/ (* z y) (+ y t))) (/ (* y b) (+ y t)))
         (if (<= x 2.9e+189) t_2 (+ z (* t (- (/ a x) (/ z x))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - (y * (b / t_1));
	double tmp;
	if (x <= -2.75e+144) {
		tmp = z * (x / t_1);
	} else if (x <= 5.5e-306) {
		tmp = t_2;
	} else if (x <= 4.3e-187) {
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t));
	} else if (x <= 2.9e+189) {
		tmp = t_2;
	} else {
		tmp = z + (t * ((a / x) - (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - (y * (b / t_1))
    if (x <= (-2.75d+144)) then
        tmp = z * (x / t_1)
    else if (x <= 5.5d-306) then
        tmp = t_2
    else if (x <= 4.3d-187) then
        tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t))
    else if (x <= 2.9d+189) then
        tmp = t_2
    else
        tmp = z + (t * ((a / x) - (z / x)))
    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 + (x + t);
	double t_2 = (z + a) - (y * (b / t_1));
	double tmp;
	if (x <= -2.75e+144) {
		tmp = z * (x / t_1);
	} else if (x <= 5.5e-306) {
		tmp = t_2;
	} else if (x <= 4.3e-187) {
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t));
	} else if (x <= 2.9e+189) {
		tmp = t_2;
	} else {
		tmp = z + (t * ((a / x) - (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - (y * (b / t_1))
	tmp = 0
	if x <= -2.75e+144:
		tmp = z * (x / t_1)
	elif x <= 5.5e-306:
		tmp = t_2
	elif x <= 4.3e-187:
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t))
	elif x <= 2.9e+189:
		tmp = t_2
	else:
		tmp = z + (t * ((a / x) - (z / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - Float64(y * Float64(b / t_1)))
	tmp = 0.0
	if (x <= -2.75e+144)
		tmp = Float64(z * Float64(x / t_1));
	elseif (x <= 5.5e-306)
		tmp = t_2;
	elseif (x <= 4.3e-187)
		tmp = Float64(Float64(a + Float64(Float64(z * y) / Float64(y + t))) - Float64(Float64(y * b) / Float64(y + t)));
	elseif (x <= 2.9e+189)
		tmp = t_2;
	else
		tmp = Float64(z + Float64(t * Float64(Float64(a / x) - Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - (y * (b / t_1));
	tmp = 0.0;
	if (x <= -2.75e+144)
		tmp = z * (x / t_1);
	elseif (x <= 5.5e-306)
		tmp = t_2;
	elseif (x <= 4.3e-187)
		tmp = (a + ((z * y) / (y + t))) - ((y * b) / (y + t));
	elseif (x <= 2.9e+189)
		tmp = t_2;
	else
		tmp = z + (t * ((a / x) - (z / x)));
	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[(z + a), $MachinePrecision] - N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.75e+144], N[(z * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-306], t$95$2, If[LessEqual[x, 4.3e-187], N[(N[(a + N[(N[(z * y), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+189], t$95$2, N[(z + N[(t * N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.75000000000000011e144

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf 29.6%

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

      1. *-commutative 29.6%

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

   5. Simplified 29.6%

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

      1. associate-/l* 60.8%

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

      2. +-commutative 60.8%

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

      3. +-commutative 60.8%

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

   7. Applied egg-rr 60.8%

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

   if -2.75000000000000011e144 < x < 5.49999999999999992e-306 or 4.3e-187 < x < 2.90000000000000019e189

   1. Initial program 55.7%

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

   3. Taylor expanded in b around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. +-commutative 55.7%

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

      3. unsub-neg 55.7%

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

      4. +-commutative 55.7%

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

      5. associate-/l* 67.8%

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

      6. fma-define 67.8%

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

      7. +-commutative 67.8%

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

      8. associate-+r+ 67.8%

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

      9. associate-/l* 83.3%

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

      10. associate-+r+ 83.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around inf 76.1%

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

   if 5.49999999999999992e-306 < x < 4.3e-187

   1. Initial program 87.0%

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

   3. Taylor expanded in b around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. unsub-neg 86.9%

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

      4. +-commutative 86.9%

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

      5. associate-/l* 87.0%

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

      6. fma-define 87.1%

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

      7. +-commutative 87.1%

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

      8. associate-+r+ 87.1%

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

      9. associate-/l* 96.6%

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

      10. associate-+r+ 96.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in x around 0 92.8%

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

   if 2.90000000000000019e189 < x

   1. Initial program 54.6%

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

   3. Taylor expanded in y around 0 44.9%

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

   4. Taylor expanded in t around 0 71.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-187}:\\ \;\;\;\;\left(a + \frac{z \cdot y}{y + t}\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+189}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := z \cdot \frac{y + x}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-284}:\\ \;\;\;\;a - \frac{y \cdot b}{t\_1}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (* z (/ (+ y x) t_1))) (t_3 (- (+ z a) b)))
   (if (<= y -8.5e+24)
     t_3
     (if (<= y -3.4e-272)
       t_2
       (if (<= y 3e-284)
         (- a (/ (* y b) t_1))
         (if (<= y 3.8e-147) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = z * ((y + x) / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -8.5e+24) {
		tmp = t_3;
	} else if (y <= -3.4e-272) {
		tmp = t_2;
	} else if (y <= 3e-284) {
		tmp = a - ((y * b) / t_1);
	} else if (y <= 3.8e-147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y + x) + t
    t_2 = z * ((y + x) / t_1)
    t_3 = (z + a) - b
    if (y <= (-8.5d+24)) then
        tmp = t_3
    else if (y <= (-3.4d-272)) then
        tmp = t_2
    else if (y <= 3d-284) then
        tmp = a - ((y * b) / t_1)
    else if (y <= 3.8d-147) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = z * ((y + x) / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -8.5e+24) {
		tmp = t_3;
	} else if (y <= -3.4e-272) {
		tmp = t_2;
	} else if (y <= 3e-284) {
		tmp = a - ((y * b) / t_1);
	} else if (y <= 3.8e-147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + x) + t
	t_2 = z * ((y + x) / t_1)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -8.5e+24:
		tmp = t_3
	elif y <= -3.4e-272:
		tmp = t_2
	elif y <= 3e-284:
		tmp = a - ((y * b) / t_1)
	elif y <= 3.8e-147:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(z * Float64(Float64(y + x) / t_1))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -8.5e+24)
		tmp = t_3;
	elseif (y <= -3.4e-272)
		tmp = t_2;
	elseif (y <= 3e-284)
		tmp = Float64(a - Float64(Float64(y * b) / t_1));
	elseif (y <= 3.8e-147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + x) + t;
	t_2 = z * ((y + x) / t_1);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -8.5e+24)
		tmp = t_3;
	elseif (y <= -3.4e-272)
		tmp = t_2;
	elseif (y <= 3e-284)
		tmp = a - ((y * b) / t_1);
	elseif (y <= 3.8e-147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.5e+24], t$95$3, If[LessEqual[y, -3.4e-272], t$95$2, If[LessEqual[y, 3e-284], N[(a - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-147], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999959e24 or 3.80000000000000028e-147 < y

   1. Initial program 47.3%

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

   3. Taylor expanded in y around inf 74.2%

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

   if -8.49999999999999959e24 < y < -3.4000000000000003e-272 or 3e-284 < y < 3.80000000000000028e-147

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf 42.0%

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

      1. associate-/l* 58.9%

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

      2. +-commutative 58.9%

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

      3. +-commutative 58.9%

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

   5. Simplified 58.9%

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

   if -3.4000000000000003e-272 < y < 3e-284

   1. Initial program 82.7%

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

   3. Taylor expanded in b around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. +-commutative 82.7%

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

      3. unsub-neg 82.7%

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

      4. +-commutative 82.7%

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

      5. associate-/l* 82.7%

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

      6. fma-define 82.7%

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

      7. +-commutative 82.7%

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

      8. associate-+r+ 82.7%

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

      9. associate-/l* 99.9%

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

      10. associate-+r+ 99.9%

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

   5. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. inv-pow 91.4%

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

      3. +-commutative 91.4%

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

      4. +-commutative 91.4%

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

      5. +-commutative 91.4%

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

   7. Applied egg-rr 91.4%

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

      1. unpow-1 91.4%

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

   9. Simplified 91.4%

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

   10. Taylor expanded in t around inf 71.0%

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

   11. Taylor expanded in z around 0 79.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-284}:\\ \;\;\;\;a - \frac{y \cdot b}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -2.12 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_2}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \frac{x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ y (+ x t))))
   (if (<= y -2.12e+24)
     t_1
     (if (<= y -2.6e-272)
       (* z (/ (+ y x) (+ (+ y x) t)))
       (if (<= y 4.2e-214)
         (* a (/ (+ y t) t_2))
         (if (<= y 4.8e-146) (* z (/ x t_2)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -2.12e+24) {
		tmp = t_1;
	} else if (y <= -2.6e-272) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 4.2e-214) {
		tmp = a * ((y + t) / t_2);
	} else if (y <= 4.8e-146) {
		tmp = z * (x / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    if (y <= (-2.12d+24)) then
        tmp = t_1
    else if (y <= (-2.6d-272)) then
        tmp = z * ((y + x) / ((y + x) + t))
    else if (y <= 4.2d-214) then
        tmp = a * ((y + t) / t_2)
    else if (y <= 4.8d-146) then
        tmp = z * (x / t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -2.12e+24) {
		tmp = t_1;
	} else if (y <= -2.6e-272) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 4.2e-214) {
		tmp = a * ((y + t) / t_2);
	} else if (y <= 4.8e-146) {
		tmp = z * (x / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	tmp = 0
	if y <= -2.12e+24:
		tmp = t_1
	elif y <= -2.6e-272:
		tmp = z * ((y + x) / ((y + x) + t))
	elif y <= 4.2e-214:
		tmp = a * ((y + t) / t_2)
	elif y <= 4.8e-146:
		tmp = z * (x / t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -2.12e+24)
		tmp = t_1;
	elseif (y <= -2.6e-272)
		tmp = Float64(z * Float64(Float64(y + x) / Float64(Float64(y + x) + t)));
	elseif (y <= 4.2e-214)
		tmp = Float64(a * Float64(Float64(y + t) / t_2));
	elseif (y <= 4.8e-146)
		tmp = Float64(z * Float64(x / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	tmp = 0.0;
	if (y <= -2.12e+24)
		tmp = t_1;
	elseif (y <= -2.6e-272)
		tmp = z * ((y + x) / ((y + x) + t));
	elseif (y <= 4.2e-214)
		tmp = a * ((y + t) / t_2);
	elseif (y <= 4.8e-146)
		tmp = z * (x / t_2);
	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]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.12e+24], t$95$1, If[LessEqual[y, -2.6e-272], N[(z * N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-214], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-146], N[(z * N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1200000000000001e24 or 4.8000000000000003e-146 < y

   1. Initial program 47.3%

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

   3. Taylor expanded in y around inf 74.2%

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

   if -2.1200000000000001e24 < y < -2.59999999999999992e-272

   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 z around inf 43.5%

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

      1. associate-/l* 60.0%

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

      2. +-commutative 60.0%

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

      3. +-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -2.59999999999999992e-272 < y < 4.19999999999999984e-214

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 40.3%

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

      1. associate-/l* 56.4%

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

      2. associate-+r+ 56.4%

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

   5. Simplified 56.4%

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

   if 4.19999999999999984e-214 < y < 4.8000000000000003e-146

   1. Initial program 56.5%

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

   3. Taylor expanded in x around inf 41.6%

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

      1. *-commutative 41.6%

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

   5. Simplified 41.6%

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

      1. associate-/l* 76.5%

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

      2. +-commutative 76.5%

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

      3. +-commutative 76.5%

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

   7. Applied egg-rr 76.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.12 \cdot 10^{+24}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{-70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-148}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ x t_1))) (t_3 (- (+ z a) b)))
   (if (<= y -2.85e-70)
     t_3
     (if (<= y -1.08e-271)
       t_2
       (if (<= y 1.8e-216)
         (* a (/ (+ y t) t_1))
         (if (<= y 3.2e-148) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -2.85e-70) {
		tmp = t_3;
	} else if (y <= -1.08e-271) {
		tmp = t_2;
	} else if (y <= 1.8e-216) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= 3.2e-148) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * (x / t_1)
    t_3 = (z + a) - b
    if (y <= (-2.85d-70)) then
        tmp = t_3
    else if (y <= (-1.08d-271)) then
        tmp = t_2
    else if (y <= 1.8d-216) then
        tmp = a * ((y + t) / t_1)
    else if (y <= 3.2d-148) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -2.85e-70) {
		tmp = t_3;
	} else if (y <= -1.08e-271) {
		tmp = t_2;
	} else if (y <= 1.8e-216) {
		tmp = a * ((y + t) / t_1);
	} else if (y <= 3.2e-148) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * (x / t_1)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -2.85e-70:
		tmp = t_3
	elif y <= -1.08e-271:
		tmp = t_2
	elif y <= 1.8e-216:
		tmp = a * ((y + t) / t_1)
	elif y <= 3.2e-148:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(x / t_1))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.85e-70)
		tmp = t_3;
	elseif (y <= -1.08e-271)
		tmp = t_2;
	elseif (y <= 1.8e-216)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	elseif (y <= 3.2e-148)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * (x / t_1);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.85e-70)
		tmp = t_3;
	elseif (y <= -1.08e-271)
		tmp = t_2;
	elseif (y <= 1.8e-216)
		tmp = a * ((y + t) / t_1);
	elseif (y <= 3.2e-148)
		tmp = t_2;
	else
		tmp = t_3;
	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[(z * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.85e-70], t$95$3, If[LessEqual[y, -1.08e-271], t$95$2, If[LessEqual[y, 1.8e-216], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-148], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.85000000000000014e-70 or 3.19999999999999993e-148 < y

   1. Initial program 50.4%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -2.85000000000000014e-70 < y < -1.07999999999999997e-271 or 1.7999999999999999e-216 < y < 3.19999999999999993e-148

   1. Initial program 71.0%

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

   3. Taylor expanded in x around inf 40.0%

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

      1. *-commutative 40.0%

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

   5. Simplified 40.0%

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

      1. associate-/l* 62.1%

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

      2. +-commutative 62.1%

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

      3. +-commutative 62.1%

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

   7. Applied egg-rr 62.1%

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

   if -1.07999999999999997e-271 < y < 1.7999999999999999e-216

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 40.3%

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

      1. associate-/l* 56.4%

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

      2. associate-+r+ 56.4%

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

   5. Simplified 56.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-70}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-271}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2 \cdot 10^{-69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-233}:\\ \;\;\;\;\frac{t \cdot a}{t\_1}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-146}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ x t_1))) (t_3 (- (+ z a) b)))
   (if (<= y -2e-69)
     t_3
     (if (<= y -1.5e-272)
       t_2
       (if (<= y 1.9e-233) (/ (* t a) t_1) (if (<= y 3.7e-146) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -2e-69) {
		tmp = t_3;
	} else if (y <= -1.5e-272) {
		tmp = t_2;
	} else if (y <= 1.9e-233) {
		tmp = (t * a) / t_1;
	} else if (y <= 3.7e-146) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * (x / t_1)
    t_3 = (z + a) - b
    if (y <= (-2d-69)) then
        tmp = t_3
    else if (y <= (-1.5d-272)) then
        tmp = t_2
    else if (y <= 1.9d-233) then
        tmp = (t * a) / t_1
    else if (y <= 3.7d-146) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x / t_1);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -2e-69) {
		tmp = t_3;
	} else if (y <= -1.5e-272) {
		tmp = t_2;
	} else if (y <= 1.9e-233) {
		tmp = (t * a) / t_1;
	} else if (y <= 3.7e-146) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * (x / t_1)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -2e-69:
		tmp = t_3
	elif y <= -1.5e-272:
		tmp = t_2
	elif y <= 1.9e-233:
		tmp = (t * a) / t_1
	elif y <= 3.7e-146:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(x / t_1))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2e-69)
		tmp = t_3;
	elseif (y <= -1.5e-272)
		tmp = t_2;
	elseif (y <= 1.9e-233)
		tmp = Float64(Float64(t * a) / t_1);
	elseif (y <= 3.7e-146)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * (x / t_1);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2e-69)
		tmp = t_3;
	elseif (y <= -1.5e-272)
		tmp = t_2;
	elseif (y <= 1.9e-233)
		tmp = (t * a) / t_1;
	elseif (y <= 3.7e-146)
		tmp = t_2;
	else
		tmp = t_3;
	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[(z * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2e-69], t$95$3, If[LessEqual[y, -1.5e-272], t$95$2, If[LessEqual[y, 1.9e-233], N[(N[(t * a), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3.7e-146], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e-69 or 3.69999999999999986e-146 < y

   1. Initial program 50.4%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -1.9999999999999999e-69 < y < -1.5000000000000001e-272 or 1.9e-233 < y < 3.69999999999999986e-146

   1. Initial program 69.3%

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

   3. Taylor expanded in x around inf 39.8%

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

      1. *-commutative 39.8%

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

   5. Simplified 39.8%

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

      1. associate-/l* 60.8%

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

      2. +-commutative 60.8%

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

      3. +-commutative 60.8%

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

   7. Applied egg-rr 60.8%

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

   if -1.5000000000000001e-272 < y < 1.9e-233

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf 44.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-69}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-233}:\\ \;\;\;\;\frac{t \cdot a}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-217}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ x (+ y (+ x t))))) (t_2 (- (+ z a) b)))
   (if (<= y -8.5e-70)
     t_2
     (if (<= y -1.7e-272)
       t_1
       (if (<= y 1.16e-217) a (if (<= y 1.05e-147) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -8.5e-70) {
		tmp = t_2;
	} else if (y <= -1.7e-272) {
		tmp = t_1;
	} else if (y <= 1.16e-217) {
		tmp = a;
	} else if (y <= 1.05e-147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x / (y + (x + t)))
    t_2 = (z + a) - b
    if (y <= (-8.5d-70)) then
        tmp = t_2
    else if (y <= (-1.7d-272)) then
        tmp = t_1
    else if (y <= 1.16d-217) then
        tmp = a
    else if (y <= 1.05d-147) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -8.5e-70) {
		tmp = t_2;
	} else if (y <= -1.7e-272) {
		tmp = t_1;
	} else if (y <= 1.16e-217) {
		tmp = a;
	} else if (y <= 1.05e-147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x / (y + (x + t)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -8.5e-70:
		tmp = t_2
	elif y <= -1.7e-272:
		tmp = t_1
	elif y <= 1.16e-217:
		tmp = a
	elif y <= 1.05e-147:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x / Float64(y + Float64(x + t))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -8.5e-70)
		tmp = t_2;
	elseif (y <= -1.7e-272)
		tmp = t_1;
	elseif (y <= 1.16e-217)
		tmp = a;
	elseif (y <= 1.05e-147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x / (y + (x + t)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -8.5e-70)
		tmp = t_2;
	elseif (y <= -1.7e-272)
		tmp = t_1;
	elseif (y <= 1.16e-217)
		tmp = a;
	elseif (y <= 1.05e-147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.5e-70], t$95$2, If[LessEqual[y, -1.7e-272], t$95$1, If[LessEqual[y, 1.16e-217], a, If[LessEqual[y, 1.05e-147], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000002e-70 or 1.05e-147 < y

   1. Initial program 50.4%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -8.5000000000000002e-70 < y < -1.7000000000000002e-272 or 1.1600000000000001e-217 < y < 1.05e-147

   1. Initial program 71.0%

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

   3. Taylor expanded in x around inf 40.0%

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

      1. *-commutative 40.0%

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

   5. Simplified 40.0%

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

      1. associate-/l* 62.1%

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

      2. +-commutative 62.1%

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

      3. +-commutative 62.1%

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

   7. Applied egg-rr 62.1%

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

   if -1.7000000000000002e-272 < y < 1.1600000000000001e-217

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 43.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-70}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-217}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \frac{x}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-262}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-80}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) (* y (/ b (+ y (+ x t)))))))
   (if (<= y -1e-137)
     t_1
     (if (<= y -6.2e-262)
       (* z (/ (+ y x) (+ (+ y x) t)))
       (if (<= y 2.9e-80) (/ (+ (* t a) (* z x)) (+ x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - (y * (b / (y + (x + t))));
	double tmp;
	if (y <= -1e-137) {
		tmp = t_1;
	} else if (y <= -6.2e-262) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 2.9e-80) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - (y * (b / (y + (x + t))))
    if (y <= (-1d-137)) then
        tmp = t_1
    else if (y <= (-6.2d-262)) then
        tmp = z * ((y + x) / ((y + x) + t))
    else if (y <= 2.9d-80) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - (y * (b / (y + (x + t))));
	double tmp;
	if (y <= -1e-137) {
		tmp = t_1;
	} else if (y <= -6.2e-262) {
		tmp = z * ((y + x) / ((y + x) + t));
	} else if (y <= 2.9e-80) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - (y * (b / (y + (x + t))))
	tmp = 0
	if y <= -1e-137:
		tmp = t_1
	elif y <= -6.2e-262:
		tmp = z * ((y + x) / ((y + x) + t))
	elif y <= 2.9e-80:
		tmp = ((t * a) + (z * x)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(y + Float64(x + t)))))
	tmp = 0.0
	if (y <= -1e-137)
		tmp = t_1;
	elseif (y <= -6.2e-262)
		tmp = Float64(z * Float64(Float64(y + x) / Float64(Float64(y + x) + t)));
	elseif (y <= 2.9e-80)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - (y * (b / (y + (x + t))));
	tmp = 0.0;
	if (y <= -1e-137)
		tmp = t_1;
	elseif (y <= -6.2e-262)
		tmp = z * ((y + x) / ((y + x) + t));
	elseif (y <= 2.9e-80)
		tmp = ((t * a) + (z * x)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-137], t$95$1, If[LessEqual[y, -6.2e-262], N[(z * N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-80], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999978e-138 or 2.89999999999999998e-80 < y

   1. Initial program 50.7%

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

   3. Taylor expanded in b around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. +-commutative 50.7%

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

      3. unsub-neg 50.7%

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

      4. +-commutative 50.7%

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

      5. associate-/l* 62.6%

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

      6. fma-define 62.6%

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

      7. +-commutative 62.6%

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

      8. associate-+r+ 62.6%

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

      9. associate-/l* 79.6%

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

      10. associate-+r+ 79.6%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in y around inf 78.9%

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

   if -9.99999999999999978e-138 < y < -6.1999999999999997e-262

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 45.7%

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

      1. associate-/l* 72.1%

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

      2. +-commutative 72.1%

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

      3. +-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -6.1999999999999997e-262 < y < 2.89999999999999998e-80

   1. Initial program 79.2%

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

   3. Taylor expanded in y around 0 60.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-137}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-262}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + x\right) + t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-80}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-76} \lor \neg \left(y \leq 1.95 \cdot 10^{-72}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.75e-76) (not (<= y 1.95e-72)))
   (- (+ z a) b)
   (/ (+ (* t a) (* z x)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.75e-76) || !(y <= 1.95e-72)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.75d-76)) .or. (.not. (y <= 1.95d-72))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (z * x)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.75e-76) || !(y <= 1.95e-72)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.75e-76) or not (y <= 1.95e-72):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (z * x)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.75e-76) || !(y <= 1.95e-72))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.75e-76) || ~((y <= 1.95e-72)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (z * x)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.75e-76], N[Not[LessEqual[y, 1.95e-72]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.75000000000000007e-76 or 1.95e-72 < y

   1. Initial program 46.9%

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

   3. Taylor expanded in y around inf 73.0%

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

   if -2.75000000000000007e-76 < y < 1.95e-72

   1. Initial program 76.8%

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

   3. Taylor expanded in y around 0 59.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-76} \lor \neg \left(y \leq 1.95 \cdot 10^{-72}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+201}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+139)
   (* x (/ z (+ x t)))
   (if (<= x 3.4e+201) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+139) {
		tmp = x * (z / (x + t));
	} else if (x <= 3.4e+201) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+139)) then
        tmp = x * (z / (x + t))
    else if (x <= 3.4d+201) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+139) {
		tmp = x * (z / (x + t));
	} else if (x <= 3.4e+201) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+139:
		tmp = x * (z / (x + t))
	elif x <= 3.4e+201:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+139)
		tmp = Float64(x * Float64(z / Float64(x + t)));
	elseif (x <= 3.4e+201)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+139)
		tmp = x * (z / (x + t));
	elseif (x <= 3.4e+201)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+139], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+201], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -8.7999999999999998e139

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf 29.6%

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

      1. *-commutative 29.6%

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

   5. Simplified 29.6%

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

   6. Taylor expanded in y around 0 29.6%

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

      1. associate-/l* 51.0%

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

      2. +-commutative 51.0%

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

   8. Simplified 51.0%

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

   if -8.7999999999999998e139 < x < 3.4e201

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 62.6%

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

   if 3.4e201 < x

   1. Initial program 55.4%

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

   3. Taylor expanded in x around inf 59.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+201}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+202}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.2e+167) z (if (<= x 5.2e+202) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.2e+167) {
		tmp = z;
	} else if (x <= 5.2e+202) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5.2d+167)) then
        tmp = z
    else if (x <= 5.2d+202) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.2e+167) {
		tmp = z;
	} else if (x <= 5.2e+202) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.2e+167:
		tmp = z
	elif x <= 5.2e+202:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.2e+167)
		tmp = z;
	elseif (x <= 5.2e+202)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.2e+167)
		tmp = z;
	elseif (x <= 5.2e+202)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.2e+167], z, If[LessEqual[x, 5.2e+202], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000004e167 or 5.2000000000000004e202 < x

   1. Initial program 49.8%

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

   3. Taylor expanded in x around inf 54.6%

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

   if -5.2000000000000004e167 < x < 5.2000000000000004e202

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 61.8%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+202}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.8e+14) a (if (<= t 1.7e+48) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+14) {
		tmp = a;
	} else if (t <= 1.7e+48) {
		tmp = z;
	} 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 <= (-3.8d+14)) then
        tmp = a
    else if (t <= 1.7d+48) then
        tmp = z
    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 <= -3.8e+14) {
		tmp = a;
	} else if (t <= 1.7e+48) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.8e+14:
		tmp = a
	elif t <= 1.7e+48:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.8e+14)
		tmp = a;
	elseif (t <= 1.7e+48)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.8e+14)
		tmp = a;
	elseif (t <= 1.7e+48)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.8e+14], a, If[LessEqual[t, 1.7e+48], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e14 or 1.7000000000000002e48 < t

   1. Initial program 47.4%

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

   3. Taylor expanded in t around inf 48.8%

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

   if -3.8e14 < t < 1.7000000000000002e48

   1. Initial program 66.8%

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

   3. Taylor expanded in x around inf 41.8%

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

Alternative 17: 32.2% 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 58.5%

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

3. Taylor expanded in t around inf 31.6%

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

Developer target: 81.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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