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

Percentage Accurate: 60.7% → 84.7%

Time: 23.0s

Alternatives: 13

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.7% 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: 84.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := y + \left(t + x\right)\\ t_3 := a \cdot \left(b \cdot \mathsf{fma}\left(-1, \frac{y}{a \cdot t\_1}, \frac{z}{a} \cdot \frac{y + x}{b \cdot t\_1}\right) + \frac{t + y}{\left(t + y\right) + x}\right)\\ t_4 := \frac{y + x}{t\_2}\\ \mathbf{if}\;a \leq -4.15 \cdot 10^{+46}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_2}}{z} + t\_4\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(\frac{a \cdot \frac{t + y}{t\_2} + z \cdot t\_4}{b} - \frac{y}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (+ y (+ t x)))
        (t_3
         (*
          a
          (+
           (* b (fma -1.0 (/ y (* a t_1)) (* (/ z a) (/ (+ y x) (* b t_1)))))
           (/ (+ t y) (+ (+ t y) x)))))
        (t_4 (/ (+ y x) t_2)))
   (if (<= a -4.15e+46)
     t_3
     (if (<= a 5e-208)
       (* z (+ (/ (/ (- (* a (+ t y)) (* y b)) t_2) z) t_4))
       (if (<= a 9e+207)
         (* b (- (/ (+ (* a (/ (+ t y) t_2)) (* z t_4)) b) (/ y t_2)))
         t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = y + (t + x);
	double t_3 = a * ((b * fma(-1.0, (y / (a * t_1)), ((z / a) * ((y + x) / (b * t_1))))) + ((t + y) / ((t + y) + x)));
	double t_4 = (y + x) / t_2;
	double tmp;
	if (a <= -4.15e+46) {
		tmp = t_3;
	} else if (a <= 5e-208) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_2) / z) + t_4);
	} else if (a <= 9e+207) {
		tmp = b * ((((a * ((t + y) / t_2)) + (z * t_4)) / b) - (y / t_2));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(a * Float64(Float64(b * fma(-1.0, Float64(y / Float64(a * t_1)), Float64(Float64(z / a) * Float64(Float64(y + x) / Float64(b * t_1))))) + Float64(Float64(t + y) / Float64(Float64(t + y) + x))))
	t_4 = Float64(Float64(y + x) / t_2)
	tmp = 0.0
	if (a <= -4.15e+46)
		tmp = t_3;
	elseif (a <= 5e-208)
		tmp = Float64(z * Float64(Float64(Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_2) / z) + t_4));
	elseif (a <= 9e+207)
		tmp = Float64(b * Float64(Float64(Float64(Float64(a * Float64(Float64(t + y) / t_2)) + Float64(z * t_4)) / b) - Float64(y / t_2)));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * N[(-1.0 * N[(y / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(N[(y + x), $MachinePrecision] / N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] / N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[a, -4.15e+46], t$95$3, If[LessEqual[a, 5e-208], N[(z * N[(N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] / z), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+207], N[(b * N[(N[(N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$4), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.14999999999999976e46 or 9.00000000000000006e207 < a

   1. Initial program 39.2%

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

   3. Taylor expanded in a around -inf 78.7%

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

      1. associate-*r* 78.7%

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

      2. mul-1-neg 78.7%

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

      3. mul-1-neg 78.7%

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

      4. unsub-neg 78.7%

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

      5. mul-1-neg 78.7%

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

      6. distribute-neg-frac2 78.7%

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

      7. +-commutative 78.7%

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

      8. associate-+r+ 78.7%

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

      9. distribute-neg-in 78.7%

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

      10. +-commutative 78.7%

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

      11. unsub-neg 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in b around inf 78.0%

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

      1. fma-define 78.0%

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

      2. times-frac 94.7%

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

   8. Simplified 94.7%

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

   if -4.14999999999999976e46 < a < 4.99999999999999963e-208

   1. Initial program 74.4%

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

   3. Taylor expanded in z around -inf 94.0%

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

      1. associate-*r* 94.0%

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

      2. mul-1-neg 94.0%

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

      3. mul-1-neg 94.0%

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

      4. unsub-neg 94.0%

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

      5. associate-*r/ 94.0%

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

      6. distribute-lft-in 94.0%

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

      7. neg-mul-1 94.0%

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

      8. unsub-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-+r+ 94.0%

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

   5. Simplified 94.0%

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

   if 4.99999999999999963e-208 < a < 9.00000000000000006e207

   1. Initial program 66.5%

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

   3. Taylor expanded in b around -inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. distribute-rgt-neg-in 74.9%

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

      3. +-commutative 74.9%

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

      4. mul-1-neg 74.9%

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

      5. unsub-neg 74.9%

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

      6. associate-+r+ 74.9%

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

   5. Simplified 95.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.15 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot \mathsf{fma}\left(-1, \frac{y}{a \cdot \left(t + \left(y + x\right)\right)}, \frac{z}{a} \cdot \frac{y + x}{b \cdot \left(t + \left(y + x\right)\right)}\right) + \frac{t + y}{\left(t + y\right) + x}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(t + x\right)}}{z} + \frac{y + x}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(\frac{a \cdot \frac{t + y}{y + \left(t + x\right)} + z \cdot \frac{y + x}{y + \left(t + x\right)}}{b} - \frac{y}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \mathsf{fma}\left(-1, \frac{y}{a \cdot \left(t + \left(y + x\right)\right)}, \frac{z}{a} \cdot \frac{y + x}{b \cdot \left(t + \left(y + x\right)\right)}\right) + \frac{t + y}{\left(t + y\right) + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+187}\right):\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t + \left(x \cdot z + y \cdot \left(\left(a + z\right) - b\right)\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (- (+ (* a (+ t y)) (* (+ y x) z)) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+187)))
     (+ a (- z b))
     (/ (+ (* a t) (+ (* x z) (* y (- (+ a z) b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (((a * (t + y)) + ((y + x) * z)) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+187)) {
		tmp = a + (z - b);
	} else {
		tmp = ((a * t) + ((x * z) + (y * ((a + z) - b)))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (((a * (t + y)) + ((y + x) * z)) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+187)) {
		tmp = a + (z - b);
	} else {
		tmp = ((a * t) + ((x * z) + (y * ((a + z) - b)))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (((a * (t + y)) + ((y + x) * z)) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+187):
		tmp = a + (z - b)
	else:
		tmp = ((a * t) + ((x * z) + (y * ((a + z) - b)))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(Float64(y + x) * z)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+187))
		tmp = Float64(a + Float64(z - b));
	else
		tmp = Float64(Float64(Float64(a * t) + Float64(Float64(x * z) + Float64(y * Float64(Float64(a + z) - b)))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = (((a * (t + y)) + ((y + x) * z)) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+187)))
		tmp = a + (z - b);
	else
		tmp = ((a * t) + ((x * z) + (y * ((a + z) - b)))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+187]], $MachinePrecision]], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 9.99999999999999907e186 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 16.2%

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

   3. Taylor expanded in y around inf 72.3%

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

      1. associate--l+ 72.3%

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

   5. Simplified 72.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999907e186

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - y \cdot b}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - y \cdot b}{y + \left(t + x\right)} \leq 10^{+187}\right):\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t + \left(x \cdot z + y \cdot \left(\left(a + z\right) - b\right)\right)}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{y}{t\_1}\\ t_3 := \frac{y + x}{t\_1}\\ t_4 := a \cdot \left(\frac{t}{t\_1} + \left(\left(t\_2 + \frac{z}{a} \cdot t\_3\right) - \frac{y \cdot b}{a \cdot t\_1}\right)\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-48}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_1}}{z} + t\_3\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(\frac{a \cdot \frac{t + y}{t\_1} + z \cdot t\_3}{b} - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ y t_1))
        (t_3 (/ (+ y x) t_1))
        (t_4
         (*
          a
          (+ (/ t t_1) (- (+ t_2 (* (/ z a) t_3)) (/ (* y b) (* a t_1)))))))
   (if (<= a -6.5e-48)
     t_4
     (if (<= a 7.5e-207)
       (* z (+ (/ (/ (- (* a (+ t y)) (* y b)) t_1) z) t_3))
       (if (<= a 1.2e+209)
         (* b (- (/ (+ (* a (/ (+ t y) t_1)) (* z t_3)) b) t_2))
         t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = y / t_1;
	double t_3 = (y + x) / t_1;
	double t_4 = a * ((t / t_1) + ((t_2 + ((z / a) * t_3)) - ((y * b) / (a * t_1))));
	double tmp;
	if (a <= -6.5e-48) {
		tmp = t_4;
	} else if (a <= 7.5e-207) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_3);
	} else if (a <= 1.2e+209) {
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_3)) / b) - 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 = y + (t + x)
    t_2 = y / t_1
    t_3 = (y + x) / t_1
    t_4 = a * ((t / t_1) + ((t_2 + ((z / a) * t_3)) - ((y * b) / (a * t_1))))
    if (a <= (-6.5d-48)) then
        tmp = t_4
    else if (a <= 7.5d-207) then
        tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_3)
    else if (a <= 1.2d+209) then
        tmp = b * ((((a * ((t + y) / t_1)) + (z * t_3)) / b) - 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 = y + (t + x);
	double t_2 = y / t_1;
	double t_3 = (y + x) / t_1;
	double t_4 = a * ((t / t_1) + ((t_2 + ((z / a) * t_3)) - ((y * b) / (a * t_1))));
	double tmp;
	if (a <= -6.5e-48) {
		tmp = t_4;
	} else if (a <= 7.5e-207) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_3);
	} else if (a <= 1.2e+209) {
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_3)) / b) - t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = y / t_1
	t_3 = (y + x) / t_1
	t_4 = a * ((t / t_1) + ((t_2 + ((z / a) * t_3)) - ((y * b) / (a * t_1))))
	tmp = 0
	if a <= -6.5e-48:
		tmp = t_4
	elif a <= 7.5e-207:
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_3)
	elif a <= 1.2e+209:
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_3)) / b) - t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(y + x) / t_1)
	t_4 = Float64(a * Float64(Float64(t / t_1) + Float64(Float64(t_2 + Float64(Float64(z / a) * t_3)) - Float64(Float64(y * b) / Float64(a * t_1)))))
	tmp = 0.0
	if (a <= -6.5e-48)
		tmp = t_4;
	elseif (a <= 7.5e-207)
		tmp = Float64(z * Float64(Float64(Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_1) / z) + t_3));
	elseif (a <= 1.2e+209)
		tmp = Float64(b * Float64(Float64(Float64(Float64(a * Float64(Float64(t + y) / t_1)) + Float64(z * t_3)) / b) - t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = y / t_1;
	t_3 = (y + x) / t_1;
	t_4 = a * ((t / t_1) + ((t_2 + ((z / a) * t_3)) - ((y * b) / (a * t_1))));
	tmp = 0.0;
	if (a <= -6.5e-48)
		tmp = t_4;
	elseif (a <= 7.5e-207)
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_3);
	elseif (a <= 1.2e+209)
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_3)) / b) - t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(t$95$2 + N[(N[(z / a), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-48], t$95$4, If[LessEqual[a, 7.5e-207], N[(z * N[(N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] / z), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+209], N[(b * N[(N[(N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e-48 or 1.19999999999999998e209 < a

   1. Initial program 49.1%

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

   3. Taylor expanded in a around inf 77.2%

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

      1. associate--l+ 77.2%

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

      2. associate-+r+ 77.2%

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

      3. associate-+r+ 77.2%

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

      4. *-commutative 77.2%

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

      5. *-commutative 77.2%

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

      6. times-frac 93.2%

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

      7. +-commutative 93.2%

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

      8. associate-+r+ 93.2%

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

      9. *-commutative 93.2%

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

   5. Simplified 93.2%

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

   if -6.5e-48 < a < 7.5000000000000006e-207

   1. Initial program 73.5%

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

   3. Taylor expanded in z around -inf 94.5%

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

      1. associate-*r* 94.5%

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

      2. mul-1-neg 94.5%

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

      3. mul-1-neg 94.5%

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

      4. unsub-neg 94.5%

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

      5. associate-*r/ 94.5%

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

      6. distribute-lft-in 94.5%

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

      7. neg-mul-1 94.5%

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

      8. unsub-neg 94.5%

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

      9. neg-mul-1 94.5%

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

      10. associate-+r+ 94.5%

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

   5. Simplified 94.5%

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

   if 7.5000000000000006e-207 < a < 1.19999999999999998e209

   1. Initial program 66.9%

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

   3. Taylor expanded in b around -inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-rgt-neg-in 75.2%

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

      3. +-commutative 75.2%

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

      4. mul-1-neg 75.2%

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

      5. unsub-neg 75.2%

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

      6. associate-+r+ 75.2%

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

   5. Simplified 95.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(\frac{t}{y + \left(t + x\right)} + \left(\left(\frac{y}{y + \left(t + x\right)} + \frac{z}{a} \cdot \frac{y + x}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{a \cdot \left(y + \left(t + x\right)\right)}\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(t + x\right)}}{z} + \frac{y + x}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(\frac{a \cdot \frac{t + y}{y + \left(t + x\right)} + z \cdot \frac{y + x}{y + \left(t + x\right)}}{b} - \frac{y}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{y + \left(t + x\right)} + \left(\left(\frac{y}{y + \left(t + x\right)} + \frac{z}{a} \cdot \frac{y + x}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{a \cdot \left(y + \left(t + x\right)\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{y + x}{t\_1}\\ t_3 := a \cdot \left(\frac{t + y}{\left(t + y\right) + x} - \frac{b}{a} \cdot \frac{y}{t + \left(y + x\right)}\right)\\ \mathbf{if}\;a \leq -1.62 \cdot 10^{+49}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{t\_1}}{z} + t\_2\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(\frac{a \cdot \frac{t + y}{t\_1} + z \cdot t\_2}{b} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x)))
        (t_2 (/ (+ y x) t_1))
        (t_3
         (* a (- (/ (+ t y) (+ (+ t y) x)) (* (/ b a) (/ y (+ t (+ y x))))))))
   (if (<= a -1.62e+49)
     t_3
     (if (<= a 1.6e-207)
       (* z (+ (/ (/ (- (* a (+ t y)) (* y b)) t_1) z) t_2))
       (if (<= a 8.2e+207)
         (* b (- (/ (+ (* a (/ (+ t y) t_1)) (* z t_2)) b) (/ y t_1)))
         t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (y + x) / t_1;
	double t_3 = a * (((t + y) / ((t + y) + x)) - ((b / a) * (y / (t + (y + x)))));
	double tmp;
	if (a <= -1.62e+49) {
		tmp = t_3;
	} else if (a <= 1.6e-207) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2);
	} else if (a <= 8.2e+207) {
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_2)) / b) - (y / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (t + x)
    t_2 = (y + x) / t_1
    t_3 = a * (((t + y) / ((t + y) + x)) - ((b / a) * (y / (t + (y + x)))))
    if (a <= (-1.62d+49)) then
        tmp = t_3
    else if (a <= 1.6d-207) then
        tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2)
    else if (a <= 8.2d+207) then
        tmp = b * ((((a * ((t + y) / t_1)) + (z * t_2)) / b) - (y / t_1))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = (y + x) / t_1;
	double t_3 = a * (((t + y) / ((t + y) + x)) - ((b / a) * (y / (t + (y + x)))));
	double tmp;
	if (a <= -1.62e+49) {
		tmp = t_3;
	} else if (a <= 1.6e-207) {
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2);
	} else if (a <= 8.2e+207) {
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_2)) / b) - (y / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = (y + x) / t_1
	t_3 = a * (((t + y) / ((t + y) + x)) - ((b / a) * (y / (t + (y + x)))))
	tmp = 0
	if a <= -1.62e+49:
		tmp = t_3
	elif a <= 1.6e-207:
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2)
	elif a <= 8.2e+207:
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_2)) / b) - (y / t_1))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(Float64(y + x) / t_1)
	t_3 = Float64(a * Float64(Float64(Float64(t + y) / Float64(Float64(t + y) + x)) - Float64(Float64(b / a) * Float64(y / Float64(t + Float64(y + x))))))
	tmp = 0.0
	if (a <= -1.62e+49)
		tmp = t_3;
	elseif (a <= 1.6e-207)
		tmp = Float64(z * Float64(Float64(Float64(Float64(Float64(a * Float64(t + y)) - Float64(y * b)) / t_1) / z) + t_2));
	elseif (a <= 8.2e+207)
		tmp = Float64(b * Float64(Float64(Float64(Float64(a * Float64(Float64(t + y) / t_1)) + Float64(z * t_2)) / b) - Float64(y / t_1)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = (y + x) / t_1;
	t_3 = a * (((t + y) / ((t + y) + x)) - ((b / a) * (y / (t + (y + x)))));
	tmp = 0.0;
	if (a <= -1.62e+49)
		tmp = t_3;
	elseif (a <= 1.6e-207)
		tmp = z * (((((a * (t + y)) - (y * b)) / t_1) / z) + t_2);
	elseif (a <= 8.2e+207)
		tmp = b * ((((a * ((t + y) / t_1)) + (z * t_2)) / b) - (y / t_1));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(N[(t + y), $MachinePrecision] / N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * N[(y / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.62e+49], t$95$3, If[LessEqual[a, 1.6e-207], N[(z * N[(N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] / z), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+207], N[(b * N[(N[(N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.62e49 or 8.2e207 < a

   1. Initial program 39.2%

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

   3. Taylor expanded in a around -inf 78.7%

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

      1. associate-*r* 78.7%

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

      2. mul-1-neg 78.7%

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

      3. mul-1-neg 78.7%

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

      4. unsub-neg 78.7%

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

      5. mul-1-neg 78.7%

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

      6. distribute-neg-frac2 78.7%

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

      7. +-commutative 78.7%

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

      8. associate-+r+ 78.7%

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

      9. distribute-neg-in 78.7%

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

      10. +-commutative 78.7%

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

      11. unsub-neg 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in b around inf 78.0%

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

      1. fma-define 78.0%

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

      2. times-frac 94.7%

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

   8. Simplified 94.7%

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

   9. Taylor expanded in b around inf 76.5%

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

       1. mul-1-neg 76.5%

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

       2. times-frac 82.9%

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

   11. Simplified 82.9%

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

   if -1.62e49 < a < 1.6000000000000002e-207

   1. Initial program 74.4%

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

   3. Taylor expanded in z around -inf 94.0%

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

      1. associate-*r* 94.0%

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

      2. mul-1-neg 94.0%

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

      3. mul-1-neg 94.0%

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

      4. unsub-neg 94.0%

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

      5. associate-*r/ 94.0%

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

      6. distribute-lft-in 94.0%

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

      7. neg-mul-1 94.0%

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

      8. unsub-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-+r+ 94.0%

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

   5. Simplified 94.0%

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

   if 1.6000000000000002e-207 < a < 8.2e207

   1. Initial program 66.5%

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

   3. Taylor expanded in b around -inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. distribute-rgt-neg-in 74.9%

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

      3. +-commutative 74.9%

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

      4. mul-1-neg 74.9%

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

      5. unsub-neg 74.9%

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

      6. associate-+r+ 74.9%

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

   5. Simplified 95.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(\frac{t + y}{\left(t + y\right) + x} - \frac{b}{a} \cdot \frac{y}{t + \left(y + x\right)}\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(\frac{\frac{a \cdot \left(t + y\right) - y \cdot b}{y + \left(t + x\right)}}{z} + \frac{y + x}{y + \left(t + x\right)}\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(\frac{a \cdot \frac{t + y}{y + \left(t + x\right)} + z \cdot \frac{y + x}{y + \left(t + x\right)}}{b} - \frac{y}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t + y}{\left(t + y\right) + x} - \frac{b}{a} \cdot \frac{y}{t + \left(y + x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := a \cdot \frac{t + y}{t\_1}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} \cdot \frac{z}{t + x} + \frac{t}{t + x}\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+208}:\\ \;\;\;\;b \cdot \left(\frac{a + z}{b} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))) (t_2 (* a (/ (+ t y) t_1))))
   (if (<= a -2e+151)
     t_2
     (if (<= a -8.8e-20)
       (* a (+ (* (/ x a) (/ z (+ t x))) (/ t (+ t x))))
       (if (<= a 1.42e-201)
         (* z (/ (+ y x) t_1))
         (if (<= a 1.85e+208) (* b (- (/ (+ a z) b) (/ y t_1))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double t_2 = a * ((t + y) / t_1);
	double tmp;
	if (a <= -2e+151) {
		tmp = t_2;
	} else if (a <= -8.8e-20) {
		tmp = a * (((x / a) * (z / (t + x))) + (t / (t + x)));
	} else if (a <= 1.42e-201) {
		tmp = z * ((y + x) / t_1);
	} else if (a <= 1.85e+208) {
		tmp = b * (((a + z) / b) - (y / 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 + (t + x)
    t_2 = a * ((t + y) / t_1)
    if (a <= (-2d+151)) then
        tmp = t_2
    else if (a <= (-8.8d-20)) then
        tmp = a * (((x / a) * (z / (t + x))) + (t / (t + x)))
    else if (a <= 1.42d-201) then
        tmp = z * ((y + x) / t_1)
    else if (a <= 1.85d+208) then
        tmp = b * (((a + z) / b) - (y / 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 + (t + x);
	double t_2 = a * ((t + y) / t_1);
	double tmp;
	if (a <= -2e+151) {
		tmp = t_2;
	} else if (a <= -8.8e-20) {
		tmp = a * (((x / a) * (z / (t + x))) + (t / (t + x)));
	} else if (a <= 1.42e-201) {
		tmp = z * ((y + x) / t_1);
	} else if (a <= 1.85e+208) {
		tmp = b * (((a + z) / b) - (y / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	t_2 = a * ((t + y) / t_1)
	tmp = 0
	if a <= -2e+151:
		tmp = t_2
	elif a <= -8.8e-20:
		tmp = a * (((x / a) * (z / (t + x))) + (t / (t + x)))
	elif a <= 1.42e-201:
		tmp = z * ((y + x) / t_1)
	elif a <= 1.85e+208:
		tmp = b * (((a + z) / b) - (y / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	t_2 = Float64(a * Float64(Float64(t + y) / t_1))
	tmp = 0.0
	if (a <= -2e+151)
		tmp = t_2;
	elseif (a <= -8.8e-20)
		tmp = Float64(a * Float64(Float64(Float64(x / a) * Float64(z / Float64(t + x))) + Float64(t / Float64(t + x))));
	elseif (a <= 1.42e-201)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif (a <= 1.85e+208)
		tmp = Float64(b * Float64(Float64(Float64(a + z) / b) - Float64(y / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	t_2 = a * ((t + y) / t_1);
	tmp = 0.0;
	if (a <= -2e+151)
		tmp = t_2;
	elseif (a <= -8.8e-20)
		tmp = a * (((x / a) * (z / (t + x))) + (t / (t + x)));
	elseif (a <= 1.42e-201)
		tmp = z * ((y + x) / t_1);
	elseif (a <= 1.85e+208)
		tmp = b * (((a + z) / b) - (y / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+151], t$95$2, If[LessEqual[a, -8.8e-20], N[(a * N[(N[(N[(x / a), $MachinePrecision] * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e-201], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+208], N[(b * N[(N[(N[(a + z), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.00000000000000003e151 or 1.84999999999999994e208 < a

   1. Initial program 29.7%

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

   3. Taylor expanded in a around inf 22.7%

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

      1. associate-/l* 81.5%

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

      2. associate-+r+ 81.5%

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

   5. Simplified 81.5%

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

   if -2.00000000000000003e151 < a < -8.79999999999999964e-20

   1. Initial program 66.4%

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

   3. Taylor expanded in a around -inf 78.6%

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

      1. associate-*r* 78.6%

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

      2. mul-1-neg 78.6%

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

      3. mul-1-neg 78.6%

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

      4. unsub-neg 78.6%

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

      5. mul-1-neg 78.6%

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

      6. distribute-neg-frac2 78.6%

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

      7. +-commutative 78.6%

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

      8. associate-+r+ 78.6%

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

      9. distribute-neg-in 78.6%

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

      10. +-commutative 78.6%

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

      11. unsub-neg 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in b around inf 75.6%

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

      1. fma-define 75.6%

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

      2. times-frac 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in y around 0 65.9%

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

       1. associate-*r* 65.9%

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

       2. neg-mul-1 65.9%

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

       3. associate-*r/ 65.9%

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

       4. mul-1-neg 65.9%

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

       5. times-frac 80.1%

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

   11. Simplified 80.1%

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

   if -8.79999999999999964e-20 < a < 1.42e-201

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf 47.8%

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

      1. associate-/l* 71.1%

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

      2. +-commutative 71.1%

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

      3. associate-+r+ 71.1%

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

   5. Simplified 71.1%

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

   if 1.42e-201 < a < 1.84999999999999994e208

   1. Initial program 66.5%

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

   3. Taylor expanded in b around -inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. distribute-rgt-neg-in 74.9%

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

      3. +-commutative 74.9%

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

      4. mul-1-neg 74.9%

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

      5. unsub-neg 74.9%

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

      6. associate-+r+ 74.9%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in y around inf 71.0%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(t + x\right)}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} \cdot \frac{z}{t + x} + \frac{t}{t + x}\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+208}:\\ \;\;\;\;b \cdot \left(\frac{a + z}{b} - \frac{y}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-103} \lor \neg \left(b \leq 1.65 \cdot 10^{-44}\right):\\ \;\;\;\;b \cdot \left(\frac{a + z}{b} - \frac{y}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.8e-103) (not (<= b 1.65e-44)))
   (* b (- (/ (+ a z) b) (/ y (+ y (+ t x)))))
   (+ a (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e-103) || !(b <= 1.65e-44)) {
		tmp = b * (((a + z) / b) - (y / (y + (t + x))));
	} else {
		tmp = a + (z - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.8d-103)) .or. (.not. (b <= 1.65d-44))) then
        tmp = b * (((a + z) / b) - (y / (y + (t + x))))
    else
        tmp = a + (z - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e-103) || !(b <= 1.65e-44)) {
		tmp = b * (((a + z) / b) - (y / (y + (t + x))));
	} else {
		tmp = a + (z - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.8e-103) or not (b <= 1.65e-44):
		tmp = b * (((a + z) / b) - (y / (y + (t + x))))
	else:
		tmp = a + (z - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.8e-103) || !(b <= 1.65e-44))
		tmp = Float64(b * Float64(Float64(Float64(a + z) / b) - Float64(y / Float64(y + Float64(t + x)))));
	else
		tmp = Float64(a + Float64(z - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.8e-103) || ~((b <= 1.65e-44)))
		tmp = b * (((a + z) / b) - (y / (y + (t + x))));
	else
		tmp = a + (z - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.8e-103], N[Not[LessEqual[b, 1.65e-44]], $MachinePrecision]], N[(b * N[(N[(N[(a + z), $MachinePrecision] / b), $MachinePrecision] - N[(y / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8000000000000001e-103 or 1.65000000000000003e-44 < b

   1. Initial program 66.6%

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

   3. Taylor expanded in b around -inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-rgt-neg-in 70.3%

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

      3. +-commutative 70.3%

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

      4. mul-1-neg 70.3%

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

      5. unsub-neg 70.3%

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

      6. associate-+r+ 70.3%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in y around inf 70.8%

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

   if -3.8000000000000001e-103 < b < 1.65000000000000003e-44

   1. Initial program 53.0%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. associate--l+ 67.5%

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

   5. Simplified 67.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-103} \lor \neg \left(b \leq 1.65 \cdot 10^{-44}\right):\\ \;\;\;\;b \cdot \left(\frac{a + z}{b} - \frac{y}{y + \left(t + x\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t + x}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8200:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(t + x\right)}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+28}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ x (+ t x)))))
   (if (<= x -5.5e+89)
     t_1
     (if (<= x -8200.0)
       (* a (/ (+ t y) (+ y (+ t x))))
       (if (<= x 1.95e+28) (+ a (- z b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (t + x));
	double tmp;
	if (x <= -5.5e+89) {
		tmp = t_1;
	} else if (x <= -8200.0) {
		tmp = a * ((t + y) / (y + (t + x)));
	} else if (x <= 1.95e+28) {
		tmp = a + (z - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / (t + x))
    if (x <= (-5.5d+89)) then
        tmp = t_1
    else if (x <= (-8200.0d0)) then
        tmp = a * ((t + y) / (y + (t + x)))
    else if (x <= 1.95d+28) then
        tmp = a + (z - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (t + x));
	double tmp;
	if (x <= -5.5e+89) {
		tmp = t_1;
	} else if (x <= -8200.0) {
		tmp = a * ((t + y) / (y + (t + x)));
	} else if (x <= 1.95e+28) {
		tmp = a + (z - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x / (t + x))
	tmp = 0
	if x <= -5.5e+89:
		tmp = t_1
	elif x <= -8200.0:
		tmp = a * ((t + y) / (y + (t + x)))
	elif x <= 1.95e+28:
		tmp = a + (z - b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x / Float64(t + x)))
	tmp = 0.0
	if (x <= -5.5e+89)
		tmp = t_1;
	elseif (x <= -8200.0)
		tmp = Float64(a * Float64(Float64(t + y) / Float64(y + Float64(t + x))));
	elseif (x <= 1.95e+28)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x / (t + x));
	tmp = 0.0;
	if (x <= -5.5e+89)
		tmp = t_1;
	elseif (x <= -8200.0)
		tmp = a * ((t + y) / (y + (t + x)));
	elseif (x <= 1.95e+28)
		tmp = a + (z - b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+89], t$95$1, If[LessEqual[x, -8200.0], N[(a * N[(N[(t + y), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+28], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.49999999999999976e89 or 1.9499999999999999e28 < x

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 31.9%

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

      1. associate-/l* 62.4%

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

      2. +-commutative 62.4%

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

      3. associate-+r+ 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in y around 0 60.5%

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

   if -5.49999999999999976e89 < x < -8200

   1. Initial program 58.3%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 66.0%

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

      2. associate-+r+ 66.0%

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

   5. Simplified 66.0%

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

   if -8200 < x < 1.9499999999999999e28

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. associate--l+ 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \mathbf{elif}\;x \leq -8200:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(t + x\right)}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+28}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + x\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{elif}\;x \leq -20000000:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t x))))
   (if (<= x -4.2e+82)
     (* z (/ (+ y x) t_1))
     (if (<= x -20000000.0)
       (* a (/ (+ t y) t_1))
       (if (<= x 2.5e+28) (+ a (- z b)) (* z (/ x (+ t x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + x);
	double tmp;
	if (x <= -4.2e+82) {
		tmp = z * ((y + x) / t_1);
	} else if (x <= -20000000.0) {
		tmp = a * ((t + y) / t_1);
	} else if (x <= 2.5e+28) {
		tmp = a + (z - b);
	} else {
		tmp = z * (x / (t + 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) :: tmp
    t_1 = y + (t + x)
    if (x <= (-4.2d+82)) then
        tmp = z * ((y + x) / t_1)
    else if (x <= (-20000000.0d0)) then
        tmp = a * ((t + y) / t_1)
    else if (x <= 2.5d+28) then
        tmp = a + (z - b)
    else
        tmp = z * (x / (t + 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 + (t + x);
	double tmp;
	if (x <= -4.2e+82) {
		tmp = z * ((y + x) / t_1);
	} else if (x <= -20000000.0) {
		tmp = a * ((t + y) / t_1);
	} else if (x <= 2.5e+28) {
		tmp = a + (z - b);
	} else {
		tmp = z * (x / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (t + x)
	tmp = 0
	if x <= -4.2e+82:
		tmp = z * ((y + x) / t_1)
	elif x <= -20000000.0:
		tmp = a * ((t + y) / t_1)
	elif x <= 2.5e+28:
		tmp = a + (z - b)
	else:
		tmp = z * (x / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + x))
	tmp = 0.0
	if (x <= -4.2e+82)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif (x <= -20000000.0)
		tmp = Float64(a * Float64(Float64(t + y) / t_1));
	elseif (x <= 2.5e+28)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = Float64(z * Float64(x / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (t + x);
	tmp = 0.0;
	if (x <= -4.2e+82)
		tmp = z * ((y + x) / t_1);
	elseif (x <= -20000000.0)
		tmp = a * ((t + y) / t_1);
	elseif (x <= 2.5e+28)
		tmp = a + (z - b);
	else
		tmp = z * (x / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+82], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -20000000.0], N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+28], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e82

   1. Initial program 43.3%

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

   3. Taylor expanded in z around inf 25.1%

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

      1. associate-/l* 62.0%

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

      2. +-commutative 62.0%

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

      3. associate-+r+ 62.0%

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

   5. Simplified 62.0%

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

   if -4.2e82 < x < -2e7

   1. Initial program 58.3%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 66.0%

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

      2. associate-+r+ 66.0%

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

   5. Simplified 66.0%

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

   if -2e7 < x < 2.49999999999999979e28

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. associate--l+ 70.3%

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

   5. Simplified 70.3%

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

   if 2.49999999999999979e28 < x

   1. Initial program 53.4%

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

   3. Taylor expanded in z around inf 37.9%

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

      1. associate-/l* 62.8%

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

      2. +-commutative 62.8%

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

      3. associate-+r+ 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in y around 0 62.8%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(t + x\right)}\\ \mathbf{elif}\;x \leq -20000000:\\ \;\;\;\;a \cdot \frac{t + y}{y + \left(t + x\right)}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+56} \lor \neg \left(x \leq 3.1 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.5e+56) (not (<= x 3.1e+28)))
   (* z (/ x (+ t x)))
   (+ a (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.5e+56) || !(x <= 3.1e+28)) {
		tmp = z * (x / (t + x));
	} else {
		tmp = a + (z - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.5d+56)) .or. (.not. (x <= 3.1d+28))) then
        tmp = z * (x / (t + x))
    else
        tmp = a + (z - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.5e+56) || !(x <= 3.1e+28)) {
		tmp = z * (x / (t + x));
	} else {
		tmp = a + (z - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.5e+56) or not (x <= 3.1e+28):
		tmp = z * (x / (t + x))
	else:
		tmp = a + (z - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.5e+56) || !(x <= 3.1e+28))
		tmp = Float64(z * Float64(x / Float64(t + x)));
	else
		tmp = Float64(a + Float64(z - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.5e+56) || ~((x <= 3.1e+28)))
		tmp = z * (x / (t + x));
	else
		tmp = a + (z - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.5e+56], N[Not[LessEqual[x, 3.1e+28]], $MachinePrecision]], N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000003e56 or 3.1000000000000001e28 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in z around inf 31.2%

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

      1. associate-/l* 59.8%

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

      2. +-commutative 59.8%

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

      3. associate-+r+ 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in y around 0 58.0%

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

   if -1.50000000000000003e56 < x < 3.1000000000000001e28

   1. Initial program 69.6%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. associate--l+ 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+56} \lor \neg \left(x \leq 3.1 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+98}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+73}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4e+98) z (if (<= x 4.2e+73) (+ a (- z b)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4e+98) {
		tmp = z;
	} else if (x <= 4.2e+73) {
		tmp = a + (z - 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 <= (-4d+98)) then
        tmp = z
    else if (x <= 4.2d+73) then
        tmp = a + (z - 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 <= -4e+98) {
		tmp = z;
	} else if (x <= 4.2e+73) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4e+98:
		tmp = z
	elif x <= 4.2e+73:
		tmp = a + (z - b)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4e+98)
		tmp = z;
	elseif (x <= 4.2e+73)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4e+98)
		tmp = z;
	elseif (x <= 4.2e+73)
		tmp = a + (z - b);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4e+98], z, If[LessEqual[x, 4.2e+73], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999999e98 or 4.2000000000000003e73 < x

   1. Initial program 45.9%

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

   3. Taylor expanded in x around inf 54.8%

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

   if -3.99999999999999999e98 < x < 4.2000000000000003e73

   1. Initial program 69.7%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. associate--l+ 65.2%

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

   5. Simplified 65.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+98}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+73}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+62}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.45e+16) a (if (<= t 5.8e+62) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e+16) {
		tmp = a;
	} else if (t <= 5.8e+62) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.45d+16)) then
        tmp = a
    else if (t <= 5.8d+62) then
        tmp = z - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e+16) {
		tmp = a;
	} else if (t <= 5.8e+62) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.45e+16:
		tmp = a
	elif t <= 5.8e+62:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.45e+16)
		tmp = a;
	elseif (t <= 5.8e+62)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.45e+16)
		tmp = a;
	elseif (t <= 5.8e+62)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.45e+16], a, If[LessEqual[t, 5.8e+62], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e16 or 5.79999999999999968e62 < t

   1. Initial program 52.3%

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

   3. Taylor expanded in t around inf 55.2%

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

   if -1.45e16 < t < 5.79999999999999968e62

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf 55.4%

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

      1. +-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in y around inf 57.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+62}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -106000000000:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -106000000000.0) a (if (<= t 1.75e+53) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -106000000000.0) {
		tmp = a;
	} else if (t <= 1.75e+53) {
		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 <= (-106000000000.0d0)) then
        tmp = a
    else if (t <= 1.75d+53) 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 <= -106000000000.0) {
		tmp = a;
	} else if (t <= 1.75e+53) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -106000000000.0:
		tmp = a
	elif t <= 1.75e+53:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -106000000000.0)
		tmp = a;
	elseif (t <= 1.75e+53)
		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 <= -106000000000.0)
		tmp = a;
	elseif (t <= 1.75e+53)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -106000000000.0], a, If[LessEqual[t, 1.75e+53], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.06e11 or 1.75000000000000009e53 < t

   1. Initial program 52.7%

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

   3. Taylor expanded in t around inf 54.7%

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

   if -1.06e11 < t < 1.75000000000000009e53

   1. Initial program 67.7%

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

   3. Taylor expanded in x around inf 52.0%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -106000000000:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.5%

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

3. Taylor expanded in t around inf 29.9%

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

4. Final simplification 29.9%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.6% 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 2024055 
(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)))