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

Percentage Accurate: 60.1% → 90.1%

Time: 19.6s

Alternatives: 17

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: 60.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{x + y}{y}\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ t_4 := \frac{{\left(x + y\right)}^{2}}{y}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;t_3 \leq 10^{+263}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(z - \frac{b}{t_2}\right) + \mathsf{fma}\left(t, \frac{a}{x + y} + \left(\frac{b}{t_4} - \left(\frac{z}{x + y} + \frac{a}{t_4}\right)\right), \frac{a}{t_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (+ x y) y))
        (t_3 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_1))
        (t_4 (/ (pow (+ x y) 2.0) y)))
   (if (<= t_3 -5e+278)
     (+ (* a (+ (/ y t_1) (/ t t_1))) (/ z (/ (+ t (+ x y)) (+ x y))))
     (if (<= t_3 1e+263)
       t_3
       (+
        (- z (/ b t_2))
        (fma
         t
         (+ (/ a (+ x y)) (- (/ b t_4) (+ (/ z (+ x y)) (/ a t_4))))
         (/ a t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (x + y) / y;
	double t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double t_4 = pow((x + y), 2.0) / y;
	double tmp;
	if (t_3 <= -5e+278) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / ((t + (x + y)) / (x + y)));
	} else if (t_3 <= 1e+263) {
		tmp = t_3;
	} else {
		tmp = (z - (b / t_2)) + fma(t, ((a / (x + y)) + ((b / t_4) - ((z / (x + y)) + (a / t_4)))), (a / t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(x + y) / y)
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_4 = Float64((Float64(x + y) ^ 2.0) / y)
	tmp = 0.0
	if (t_3 <= -5e+278)
		tmp = Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))));
	elseif (t_3 <= 1e+263)
		tmp = t_3;
	else
		tmp = Float64(Float64(z - Float64(b / t_2)) + fma(t, Float64(Float64(a / Float64(x + y)) + Float64(Float64(b / t_4) - Float64(Float64(z / Float64(x + y)) + Float64(a / t_4)))), Float64(a / t_2)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[Power[N[(x + y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+278], N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+263], t$95$3, N[(N[(z - N[(b / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(b / t$95$4), $MachinePrecision] - N[(N[(z / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000029e278

   1. Initial program 8.5%

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

   3. Taylor expanded in a around 0 50.1%

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

      1. associate--l+ 50.1%

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

      2. +-commutative 50.1%

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

      3. associate-+r+ 50.1%

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

      4. associate-+r+ 50.1%

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

      5. div-sub 50.1%

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

      6. +-commutative 50.1%

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

      7. *-commutative 50.1%

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

      8. associate-+r+ 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around inf 49.5%

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

      1. associate-/l* 78.9%

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

      2. +-commutative 78.9%

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

      3. +-commutative 78.9%

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

   8. Simplified 78.9%

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

   if -5.00000000000000029e278 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000002e263

   1. Initial program 99.6%

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

   if 1.00000000000000002e263 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.0%

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

      1. associate--l+ 8.0%

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

      2. fma-define 8.9%

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

      3. cancel-sign-sub-inv 8.9%

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

      4. fma-define 9.3%

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

      5. +-commutative 9.3%

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

      6. distribute-lft-neg-out 9.3%

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

      7. distribute-rgt-neg-out 9.3%

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

      8. associate-+l+ 9.3%

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

      9. +-commutative 9.3%

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

   3. Simplified 9.3%

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

   5. Taylor expanded in t around 0 29.9%

      \[\leadsto \color{blue}{z + \left(-1 \cdot \frac{b \cdot y}{x + y} + \left(t \cdot \left(\frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right)\right) + \frac{a \cdot y}{x + y}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 29.9%

         \[\leadsto \color{blue}{\left(z + -1 \cdot \frac{b \cdot y}{x + y}\right) + \left(t \cdot \left(\frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right)\right) + \frac{a \cdot y}{x + y}\right)} \]

      2. mul-1-neg 29.9%

         \[\leadsto \left(z + \color{blue}{\left(-\frac{b \cdot y}{x + y}\right)}\right) + \left(t \cdot \left(\frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right)\right) + \frac{a \cdot y}{x + y}\right) \]

      3. unsub-neg 29.9%

         \[\leadsto \color{blue}{\left(z - \frac{b \cdot y}{x + y}\right)} + \left(t \cdot \left(\frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right)\right) + \frac{a \cdot y}{x + y}\right) \]

      4. associate-/l* 30.0%

         \[\leadsto \left(z - \color{blue}{\frac{b}{\frac{x + y}{y}}}\right) + \left(t \cdot \left(\frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right)\right) + \frac{a \cdot y}{x + y}\right) \]

      5. +-commutative 30.0%

         \[\leadsto \left(z - \frac{b}{\frac{\color{blue}{y + x}}{y}}\right) + \left(t \cdot \left(\frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right)\right) + \frac{a \cdot y}{x + y}\right) \]

      6. fma-define 30.0%

         \[\leadsto \left(z - \frac{b}{\frac{y + x}{y}}\right) + \color{blue}{\mathsf{fma}\left(t, \frac{a}{x + y} - \left(-1 \cdot \frac{b \cdot y}{{\left(x + y\right)}^{2}} + \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right), \frac{a \cdot y}{x + y}\right)} \]

   7. Simplified 83.5%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right) + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+263}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z - \frac{b}{\frac{x + y}{y}}\right) + \mathsf{fma}\left(t, \frac{a}{x + y} + \left(\frac{b}{\frac{{\left(x + y\right)}^{2}}{y}} - \left(\frac{z}{x + y} + \frac{a}{\frac{{\left(x + y\right)}^{2}}{y}}\right)\right), \frac{a}{\frac{x + y}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+278} \lor \neg \left(t_1 \leq 5 \cdot 10^{+269}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 -5e+278) (not (<= t_1 5e+269))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+278) || !(t_1 <= 5e+269)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t))
    if ((t_1 <= (-5d+278)) .or. (.not. (t_1 <= 5d+269))) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -5e+278) || !(t_1 <= 5e+269)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -5e+278) or not (t_1 <= 5e+269):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= -5e+278) || !(t_1 <= 5e+269))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -5e+278) || ~((t_1 <= 5e+269)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+278], N[Not[LessEqual[t$95$1, 5e+269]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000029e278 or 5.0000000000000002e269 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 78.9%

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

   if -5.00000000000000029e278 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e269

   1. Initial program 99.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+278} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+269}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_2 -5e+278)
     (+ (* a (+ (/ y t_1) (/ t t_1))) (/ z (/ (+ t (+ x y)) (+ x y))))
     (if (<= t_2 5e+269) t_2 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -5e+278) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / ((t + (x + y)) / (x + y)));
	} else if (t_2 <= 5e+269) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1
    if (t_2 <= (-5d+278)) then
        tmp = (a * ((y / t_1) + (t / t_1))) + (z / ((t + (x + y)) / (x + y)))
    else if (t_2 <= 5d+269) then
        tmp = t_2
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -5e+278) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / ((t + (x + y)) / (x + y)));
	} else if (t_2 <= 5e+269) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -5e+278:
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / ((t + (x + y)) / (x + y)))
	elif t_2 <= 5e+269:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -5e+278)
		tmp = Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))));
	elseif (t_2 <= 5e+269)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -5e+278)
		tmp = (a * ((y / t_1) + (t / t_1))) + (z / ((t + (x + y)) / (x + y)));
	elseif (t_2 <= 5e+269)
		tmp = t_2;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+278], N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+269], t$95$2, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000029e278

   1. Initial program 8.5%

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

   3. Taylor expanded in a around 0 50.1%

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

      1. associate--l+ 50.1%

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

      2. +-commutative 50.1%

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

      3. associate-+r+ 50.1%

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

      4. associate-+r+ 50.1%

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

      5. div-sub 50.1%

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

      6. +-commutative 50.1%

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

      7. *-commutative 50.1%

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

      8. associate-+r+ 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around inf 49.5%

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

      1. associate-/l* 78.9%

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

      2. +-commutative 78.9%

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

      3. +-commutative 78.9%

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

   8. Simplified 78.9%

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

   if -5.00000000000000029e278 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e269

   1. Initial program 99.6%

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

   if 5.0000000000000002e269 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.6%

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

   3. Taylor expanded in y around inf 79.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+278}:\\ \;\;\;\;a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right) + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+269}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -0.00062:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot z + y \cdot \left(z - b\right)}{t_1}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-154}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-128}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 11000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ a (/ z (/ (+ t (+ x y)) (+ x y)))))
        (t_3 (- (+ z a) b)))
   (if (<= y -3.8e+155)
     t_3
     (if (<= y -0.00062)
       t_2
       (if (<= y -1.8e-144)
         (/ (+ (* x z) (* y (- z b))) t_1)
         (if (<= y 3.05e-304)
           t_2
           (if (<= y 1.25e-198)
             (/ (+ (* t a) (* x z)) (+ x t))
             (if (<= y 5.7e-154)
               (- a (/ (* y b) t))
               (if (<= y 1.72e-128)
                 (/ (- (* x z) (* y b)) t_1)
                 (if (<= y 11000000000.0) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z / ((t + (x + y)) / (x + y)));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.8e+155) {
		tmp = t_3;
	} else if (y <= -0.00062) {
		tmp = t_2;
	} else if (y <= -1.8e-144) {
		tmp = ((x * z) + (y * (z - b))) / t_1;
	} else if (y <= 3.05e-304) {
		tmp = t_2;
	} else if (y <= 1.25e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5.7e-154) {
		tmp = a - ((y * b) / t);
	} else if (y <= 1.72e-128) {
		tmp = ((x * z) - (y * b)) / t_1;
	} else if (y <= 11000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a + (z / ((t + (x + y)) / (x + y)))
    t_3 = (z + a) - b
    if (y <= (-3.8d+155)) then
        tmp = t_3
    else if (y <= (-0.00062d0)) then
        tmp = t_2
    else if (y <= (-1.8d-144)) then
        tmp = ((x * z) + (y * (z - b))) / t_1
    else if (y <= 3.05d-304) then
        tmp = t_2
    else if (y <= 1.25d-198) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 5.7d-154) then
        tmp = a - ((y * b) / t)
    else if (y <= 1.72d-128) then
        tmp = ((x * z) - (y * b)) / t_1
    else if (y <= 11000000000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z / ((t + (x + y)) / (x + y)));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -3.8e+155) {
		tmp = t_3;
	} else if (y <= -0.00062) {
		tmp = t_2;
	} else if (y <= -1.8e-144) {
		tmp = ((x * z) + (y * (z - b))) / t_1;
	} else if (y <= 3.05e-304) {
		tmp = t_2;
	} else if (y <= 1.25e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5.7e-154) {
		tmp = a - ((y * b) / t);
	} else if (y <= 1.72e-128) {
		tmp = ((x * z) - (y * b)) / t_1;
	} else if (y <= 11000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + (z / ((t + (x + y)) / (x + y)))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -3.8e+155:
		tmp = t_3
	elif y <= -0.00062:
		tmp = t_2
	elif y <= -1.8e-144:
		tmp = ((x * z) + (y * (z - b))) / t_1
	elif y <= 3.05e-304:
		tmp = t_2
	elif y <= 1.25e-198:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 5.7e-154:
		tmp = a - ((y * b) / t)
	elif y <= 1.72e-128:
		tmp = ((x * z) - (y * b)) / t_1
	elif y <= 11000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.8e+155)
		tmp = t_3;
	elseif (y <= -0.00062)
		tmp = t_2;
	elseif (y <= -1.8e-144)
		tmp = Float64(Float64(Float64(x * z) + Float64(y * Float64(z - b))) / t_1);
	elseif (y <= 3.05e-304)
		tmp = t_2;
	elseif (y <= 1.25e-198)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 5.7e-154)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	elseif (y <= 1.72e-128)
		tmp = Float64(Float64(Float64(x * z) - Float64(y * b)) / t_1);
	elseif (y <= 11000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a + (z / ((t + (x + y)) / (x + y)));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.8e+155)
		tmp = t_3;
	elseif (y <= -0.00062)
		tmp = t_2;
	elseif (y <= -1.8e-144)
		tmp = ((x * z) + (y * (z - b))) / t_1;
	elseif (y <= 3.05e-304)
		tmp = t_2;
	elseif (y <= 1.25e-198)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 5.7e-154)
		tmp = a - ((y * b) / t);
	elseif (y <= 1.72e-128)
		tmp = ((x * z) - (y * b)) / t_1;
	elseif (y <= 11000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.8e+155], t$95$3, If[LessEqual[y, -0.00062], t$95$2, If[LessEqual[y, -1.8e-144], N[(N[(N[(x * z), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 3.05e-304], t$95$2, If[LessEqual[y, 1.25e-198], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e-154], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.72e-128], N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 11000000000.0], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.8000000000000001e155 or 1.1e10 < y

   1. Initial program 37.8%

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

   3. Taylor expanded in y around inf 87.0%

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

   if -3.8000000000000001e155 < y < -6.2e-4 or -1.8e-144 < y < 3.0500000000000002e-304 or 1.71999999999999992e-128 < y < 1.1e10

   1. Initial program 72.4%

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

   3. Taylor expanded in a around 0 82.7%

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

      1. associate--l+ 82.7%

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

      2. +-commutative 82.7%

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

      3. associate-+r+ 82.7%

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

      4. associate-+r+ 82.7%

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

      5. div-sub 82.7%

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

      6. +-commutative 82.7%

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

      7. *-commutative 82.7%

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

      8. associate-+r+ 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 86.3%

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

      2. +-commutative 86.3%

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

      3. +-commutative 86.3%

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

   8. Simplified 86.3%

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

   9. Taylor expanded in y around inf 75.5%

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

   if -6.2e-4 < y < -1.8e-144

   1. Initial program 86.1%

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

   3. Taylor expanded in a around 0 72.8%

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

      1. +-commutative 72.8%

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

      2. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around 0 72.8%

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

   if 3.0500000000000002e-304 < y < 1.25e-198

   1. Initial program 87.1%

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

   3. Taylor expanded in y around 0 83.8%

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

   if 1.25e-198 < y < 5.6999999999999998e-154

   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 z around 0 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around 0 53.0%

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

   7. Taylor expanded in t around inf 99.7%

      \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. neg-mul-1 99.7%

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

      4. *-commutative 99.7%

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

   9. Simplified 99.7%

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

   if 5.6999999999999998e-154 < y < 1.71999999999999992e-128

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around 0 80.1%

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

      1. *-commutative 80.1%

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

   8. Simplified 80.1%

      \[\leadsto \frac{\color{blue}{z \cdot x} - y \cdot b}{\left(x + t\right) + y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -0.00062:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{x \cdot z + y \cdot \left(z - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-304}:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-154}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-128}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 11000000000:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-153}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-128}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 48000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (/ z (/ (+ t (+ x y)) (+ x y))))) (t_2 (- (+ z a) b)))
   (if (<= y -3.5e+155)
     t_2
     (if (<= y 5.5e-305)
       t_1
       (if (<= y 4.6e-198)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 4.1e-153)
           (- a (/ (* y b) t))
           (if (<= y 1.95e-128)
             (/ (- (* x z) (* y b)) (+ y (+ x t)))
             (if (<= y 48000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((t + (x + y)) / (x + y)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -3.5e+155) {
		tmp = t_2;
	} else if (y <= 5.5e-305) {
		tmp = t_1;
	} else if (y <= 4.6e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.1e-153) {
		tmp = a - ((y * b) / t);
	} else if (y <= 1.95e-128) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else if (y <= 48000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z / ((t + (x + y)) / (x + y)))
    t_2 = (z + a) - b
    if (y <= (-3.5d+155)) then
        tmp = t_2
    else if (y <= 5.5d-305) then
        tmp = t_1
    else if (y <= 4.6d-198) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4.1d-153) then
        tmp = a - ((y * b) / t)
    else if (y <= 1.95d-128) then
        tmp = ((x * z) - (y * b)) / (y + (x + t))
    else if (y <= 48000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((t + (x + y)) / (x + y)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -3.5e+155) {
		tmp = t_2;
	} else if (y <= 5.5e-305) {
		tmp = t_1;
	} else if (y <= 4.6e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4.1e-153) {
		tmp = a - ((y * b) / t);
	} else if (y <= 1.95e-128) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else if (y <= 48000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z / ((t + (x + y)) / (x + y)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -3.5e+155:
		tmp = t_2
	elif y <= 5.5e-305:
		tmp = t_1
	elif y <= 4.6e-198:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4.1e-153:
		tmp = a - ((y * b) / t)
	elif y <= 1.95e-128:
		tmp = ((x * z) - (y * b)) / (y + (x + t))
	elif y <= 48000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.5e+155)
		tmp = t_2;
	elseif (y <= 5.5e-305)
		tmp = t_1;
	elseif (y <= 4.6e-198)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4.1e-153)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	elseif (y <= 1.95e-128)
		tmp = Float64(Float64(Float64(x * z) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 48000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z / ((t + (x + y)) / (x + y)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.5e+155)
		tmp = t_2;
	elseif (y <= 5.5e-305)
		tmp = t_1;
	elseif (y <= 4.6e-198)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4.1e-153)
		tmp = a - ((y * b) / t);
	elseif (y <= 1.95e-128)
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	elseif (y <= 48000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.5e+155], t$95$2, If[LessEqual[y, 5.5e-305], t$95$1, If[LessEqual[y, 4.6e-198], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-153], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-128], N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 48000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.49999999999999985e155 or 4.8e10 < y

   1. Initial program 37.8%

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

   3. Taylor expanded in y around inf 87.0%

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

   if -3.49999999999999985e155 < y < 5.5e-305 or 1.94999999999999998e-128 < y < 4.8e10

   1. Initial program 75.4%

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

   3. Taylor expanded in a around 0 85.6%

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

      1. associate--l+ 85.6%

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

      2. +-commutative 85.6%

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

      3. associate-+r+ 85.6%

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

      4. associate-+r+ 85.6%

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

      5. div-sub 85.6%

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

      6. +-commutative 85.6%

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

      7. *-commutative 85.6%

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

      8. associate-+r+ 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in z around inf 69.9%

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

      1. associate-/l* 81.1%

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

      2. +-commutative 81.1%

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

      3. +-commutative 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in y around inf 70.4%

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

   if 5.5e-305 < y < 4.60000000000000027e-198

   1. Initial program 87.1%

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

   3. Taylor expanded in y around 0 83.8%

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

   if 4.60000000000000027e-198 < y < 4.1e-153

   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 z around 0 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around 0 53.0%

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

   7. Taylor expanded in t around inf 99.7%

      \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. neg-mul-1 99.7%

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

      4. *-commutative 99.7%

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

   9. Simplified 99.7%

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

   if 4.1e-153 < y < 1.94999999999999998e-128

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around 0 80.1%

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

      1. *-commutative 80.1%

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

   8. Simplified 80.1%

      \[\leadsto \frac{\color{blue}{z \cdot x} - y \cdot b}{\left(x + t\right) + y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-305}:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-153}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-128}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 48000000000:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-154}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (/ z (/ (+ t (+ x y)) (+ x y))))) (t_2 (- (+ z a) b)))
   (if (<= y -6.6e+155)
     t_2
     (if (<= y 2e-304)
       t_1
       (if (<= y 2.7e-198)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 5.7e-154)
           (- a (/ (* y b) t))
           (if (<= y 5.8e-127)
             (/ (- (* (+ y t) a) (* y b)) (+ y (+ x t)))
             (if (<= y 52000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((t + (x + y)) / (x + y)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.6e+155) {
		tmp = t_2;
	} else if (y <= 2e-304) {
		tmp = t_1;
	} else if (y <= 2.7e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5.7e-154) {
		tmp = a - ((y * b) / t);
	} else if (y <= 5.8e-127) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (y <= 52000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z / ((t + (x + y)) / (x + y)))
    t_2 = (z + a) - b
    if (y <= (-6.6d+155)) then
        tmp = t_2
    else if (y <= 2d-304) then
        tmp = t_1
    else if (y <= 2.7d-198) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 5.7d-154) then
        tmp = a - ((y * b) / t)
    else if (y <= 5.8d-127) then
        tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
    else if (y <= 52000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((t + (x + y)) / (x + y)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.6e+155) {
		tmp = t_2;
	} else if (y <= 2e-304) {
		tmp = t_1;
	} else if (y <= 2.7e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5.7e-154) {
		tmp = a - ((y * b) / t);
	} else if (y <= 5.8e-127) {
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	} else if (y <= 52000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z / ((t + (x + y)) / (x + y)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -6.6e+155:
		tmp = t_2
	elif y <= 2e-304:
		tmp = t_1
	elif y <= 2.7e-198:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 5.7e-154:
		tmp = a - ((y * b) / t)
	elif y <= 5.8e-127:
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t))
	elif y <= 52000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.6e+155)
		tmp = t_2;
	elseif (y <= 2e-304)
		tmp = t_1;
	elseif (y <= 2.7e-198)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 5.7e-154)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	elseif (y <= 5.8e-127)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 52000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z / ((t + (x + y)) / (x + y)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.6e+155)
		tmp = t_2;
	elseif (y <= 2e-304)
		tmp = t_1;
	elseif (y <= 2.7e-198)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 5.7e-154)
		tmp = a - ((y * b) / t);
	elseif (y <= 5.8e-127)
		tmp = (((y + t) * a) - (y * b)) / (y + (x + t));
	elseif (y <= 52000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.6e+155], t$95$2, If[LessEqual[y, 2e-304], t$95$1, If[LessEqual[y, 2.7e-198], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e-154], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-127], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 52000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.5999999999999997e155 or 5.2e10 < y

   1. Initial program 37.8%

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

   3. Taylor expanded in y around inf 87.0%

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

   if -6.5999999999999997e155 < y < 1.99999999999999994e-304 or 5.8000000000000001e-127 < y < 5.2e10

   1. Initial program 75.4%

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

   3. Taylor expanded in a around 0 85.6%

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

      1. associate--l+ 85.6%

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

      2. +-commutative 85.6%

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

      3. associate-+r+ 85.6%

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

      4. associate-+r+ 85.6%

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

      5. div-sub 85.6%

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

      6. +-commutative 85.6%

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

      7. *-commutative 85.6%

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

      8. associate-+r+ 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in z around inf 69.9%

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

      1. associate-/l* 81.1%

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

      2. +-commutative 81.1%

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

      3. +-commutative 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in y around inf 70.4%

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

   if 1.99999999999999994e-304 < y < 2.7000000000000002e-198

   1. Initial program 87.1%

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

   3. Taylor expanded in y around 0 83.8%

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

   if 2.7000000000000002e-198 < y < 5.6999999999999998e-154

   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 z around 0 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around 0 53.0%

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

   7. Taylor expanded in t around inf 99.7%

      \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. neg-mul-1 99.7%

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

      4. *-commutative 99.7%

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

   9. Simplified 99.7%

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

   if 5.6999999999999998e-154 < y < 5.8000000000000001e-127

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 80.9%

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

      1. *-commutative 80.9%

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

   5. Simplified 80.9%

      \[\leadsto \frac{\color{blue}{a \cdot \left(t + y\right) - y \cdot b}}{\left(x + t\right) + y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-304}:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-154}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := x + \left(y + t\right)\\ t_3 := z + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-52}:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;a \leq 0.00013:\\ \;\;\;\;z \cdot \frac{x + y}{t_2} - \frac{b}{\frac{t_2}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ x (+ y t)))
        (t_3 (+ z (* a (+ (/ y t_1) (/ t t_1))))))
   (if (<= a -6e+139)
     t_3
     (if (<= a -1.6e-52)
       (+ a (/ z (/ (+ t (+ x y)) (+ x y))))
       (if (<= a 0.00013) (- (* z (/ (+ x y) t_2)) (/ b (/ t_2 y))) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = x + (y + t);
	double t_3 = z + (a * ((y / t_1) + (t / t_1)));
	double tmp;
	if (a <= -6e+139) {
		tmp = t_3;
	} else if (a <= -1.6e-52) {
		tmp = a + (z / ((t + (x + y)) / (x + y)));
	} else if (a <= 0.00013) {
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = x + (y + t)
    t_3 = z + (a * ((y / t_1) + (t / t_1)))
    if (a <= (-6d+139)) then
        tmp = t_3
    else if (a <= (-1.6d-52)) then
        tmp = a + (z / ((t + (x + y)) / (x + y)))
    else if (a <= 0.00013d0) then
        tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = x + (y + t);
	double t_3 = z + (a * ((y / t_1) + (t / t_1)));
	double tmp;
	if (a <= -6e+139) {
		tmp = t_3;
	} else if (a <= -1.6e-52) {
		tmp = a + (z / ((t + (x + y)) / (x + y)));
	} else if (a <= 0.00013) {
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = x + (y + t)
	t_3 = z + (a * ((y / t_1) + (t / t_1)))
	tmp = 0
	if a <= -6e+139:
		tmp = t_3
	elif a <= -1.6e-52:
		tmp = a + (z / ((t + (x + y)) / (x + y)))
	elif a <= 0.00013:
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))))
	tmp = 0.0
	if (a <= -6e+139)
		tmp = t_3;
	elseif (a <= -1.6e-52)
		tmp = Float64(a + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))));
	elseif (a <= 0.00013)
		tmp = Float64(Float64(z * Float64(Float64(x + y) / t_2)) - Float64(b / Float64(t_2 / y)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = x + (y + t);
	t_3 = z + (a * ((y / t_1) + (t / t_1)));
	tmp = 0.0;
	if (a <= -6e+139)
		tmp = t_3;
	elseif (a <= -1.6e-52)
		tmp = a + (z / ((t + (x + y)) / (x + y)));
	elseif (a <= 0.00013)
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+139], t$95$3, If[LessEqual[a, -1.6e-52], N[(a + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00013], N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.9999999999999999e139 or 1.29999999999999989e-4 < a

   1. Initial program 47.3%

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

   3. Taylor expanded in a around 0 75.2%

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

      1. associate--l+ 75.2%

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

      2. +-commutative 75.2%

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

      3. associate-+r+ 75.2%

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

      4. associate-+r+ 75.2%

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

      5. div-sub 75.2%

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

      6. +-commutative 75.2%

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

      7. *-commutative 75.2%

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

      8. associate-+r+ 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in x around inf 84.1%

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

   if -5.9999999999999999e139 < a < -1.60000000000000005e-52

   1. Initial program 68.0%

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

   3. Taylor expanded in a around 0 78.1%

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

      1. associate--l+ 78.1%

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

      2. +-commutative 78.1%

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

      3. associate-+r+ 78.1%

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

      4. associate-+r+ 78.1%

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

      5. div-sub 78.1%

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

      6. +-commutative 78.1%

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

      7. *-commutative 78.1%

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

      8. associate-+r+ 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 68.1%

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

      1. associate-/l* 77.9%

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

      2. +-commutative 77.9%

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

      3. +-commutative 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in y around inf 70.2%

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

   if -1.60000000000000005e-52 < a < 1.29999999999999989e-4

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 65.9%

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

      1. +-commutative 65.9%

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

      2. *-commutative 65.9%

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

   5. Simplified 65.9%

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

      1. div-sub 65.9%

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

      2. associate-*l/ 68.6%

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

      3. +-commutative 68.6%

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

      4. associate-+r+ 68.6%

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

      5. +-commutative 68.6%

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

      6. associate-/r/ 77.4%

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

      7. div-inv 77.3%

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

      8. clear-num 77.3%

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

      9. +-commutative 77.3%

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

      10. associate-+r+ 77.3%

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

      11. +-commutative 77.3%

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

      12. associate-+l+ 77.3%

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

      13. *-commutative 77.3%

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

      14. associate-/l* 90.7%

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

      15. associate-+l+ 90.7%

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

   7. Applied egg-rr 90.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+139}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-52}:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;a \leq 0.00013:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)} - \frac{b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := x + \left(y + t\right)\\ t_3 := z + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{t_1}\\ \mathbf{elif}\;a \leq 24000:\\ \;\;\;\;z \cdot \frac{x + y}{t_2} - \frac{b}{\frac{t_2}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ x (+ y t)))
        (t_3 (+ z (* a (+ (/ y t_1) (/ t t_1))))))
   (if (<= a -3.5e+88)
     t_3
     (if (<= a -4.8e-53)
       (/ (+ (* t a) (+ (* x z) (* y (- (+ z a) b)))) t_1)
       (if (<= a 24000.0) (- (* z (/ (+ x y) t_2)) (/ b (/ t_2 y))) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = x + (y + t);
	double t_3 = z + (a * ((y / t_1) + (t / t_1)));
	double tmp;
	if (a <= -3.5e+88) {
		tmp = t_3;
	} else if (a <= -4.8e-53) {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_1;
	} else if (a <= 24000.0) {
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = x + (y + t)
    t_3 = z + (a * ((y / t_1) + (t / t_1)))
    if (a <= (-3.5d+88)) then
        tmp = t_3
    else if (a <= (-4.8d-53)) then
        tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_1
    else if (a <= 24000.0d0) then
        tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = x + (y + t);
	double t_3 = z + (a * ((y / t_1) + (t / t_1)));
	double tmp;
	if (a <= -3.5e+88) {
		tmp = t_3;
	} else if (a <= -4.8e-53) {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_1;
	} else if (a <= 24000.0) {
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = x + (y + t)
	t_3 = z + (a * ((y / t_1) + (t / t_1)))
	tmp = 0
	if a <= -3.5e+88:
		tmp = t_3
	elif a <= -4.8e-53:
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_1
	elif a <= 24000.0:
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))))
	tmp = 0.0
	if (a <= -3.5e+88)
		tmp = t_3;
	elseif (a <= -4.8e-53)
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * Float64(Float64(z + a) - b)))) / t_1);
	elseif (a <= 24000.0)
		tmp = Float64(Float64(z * Float64(Float64(x + y) / t_2)) - Float64(b / Float64(t_2 / y)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = x + (y + t);
	t_3 = z + (a * ((y / t_1) + (t / t_1)));
	tmp = 0.0;
	if (a <= -3.5e+88)
		tmp = t_3;
	elseif (a <= -4.8e-53)
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_1;
	elseif (a <= 24000.0)
		tmp = (z * ((x + y) / t_2)) - (b / (t_2 / y));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+88], t$95$3, If[LessEqual[a, -4.8e-53], N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[a, 24000.0], N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4999999999999998e88 or 24000 < a

   1. Initial program 45.2%

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

   3. Taylor expanded in a around 0 75.0%

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

      1. associate--l+ 75.0%

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

      2. +-commutative 75.0%

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

      3. associate-+r+ 75.0%

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

      4. associate-+r+ 75.0%

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

      5. div-sub 75.0%

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

      6. +-commutative 75.0%

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

      7. *-commutative 75.0%

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

      8. associate-+r+ 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around inf 82.3%

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

   if -3.4999999999999998e88 < a < -4.80000000000000015e-53

   1. Initial program 78.9%

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

   3. Taylor expanded in y around 0 79.4%

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

   if -4.80000000000000015e-53 < a < 24000

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 65.9%

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

      1. +-commutative 65.9%

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

      2. *-commutative 65.9%

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

   5. Simplified 65.9%

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

      1. div-sub 65.9%

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

      2. associate-*l/ 68.6%

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

      3. +-commutative 68.6%

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

      4. associate-+r+ 68.6%

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

      5. +-commutative 68.6%

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

      6. associate-/r/ 77.4%

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

      7. div-inv 77.3%

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

      8. clear-num 77.3%

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

      9. +-commutative 77.3%

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

      10. associate-+r+ 77.3%

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

      11. +-commutative 77.3%

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

      12. associate-+l+ 77.3%

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

      13. *-commutative 77.3%

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

      14. associate-/l* 90.7%

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

      15. associate-+l+ 90.7%

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

   7. Applied egg-rr 90.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+88}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 24000:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)} - \frac{b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-180}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (/ z (/ (+ t (+ x y)) (+ x y))))) (t_2 (- (+ z a) b)))
   (if (<= y -2.05e+156)
     t_2
     (if (<= y 8e-305)
       t_1
       (if (<= y 2.7e-180)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 52000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((t + (x + y)) / (x + y)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.05e+156) {
		tmp = t_2;
	} else if (y <= 8e-305) {
		tmp = t_1;
	} else if (y <= 2.7e-180) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 52000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z / ((t + (x + y)) / (x + y)))
    t_2 = (z + a) - b
    if (y <= (-2.05d+156)) then
        tmp = t_2
    else if (y <= 8d-305) then
        tmp = t_1
    else if (y <= 2.7d-180) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 52000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z / ((t + (x + y)) / (x + y)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.05e+156) {
		tmp = t_2;
	} else if (y <= 8e-305) {
		tmp = t_1;
	} else if (y <= 2.7e-180) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 52000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z / ((t + (x + y)) / (x + y)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -2.05e+156:
		tmp = t_2
	elif y <= 8e-305:
		tmp = t_1
	elif y <= 2.7e-180:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 52000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z / Float64(Float64(t + Float64(x + y)) / Float64(x + y))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.05e+156)
		tmp = t_2;
	elseif (y <= 8e-305)
		tmp = t_1;
	elseif (y <= 2.7e-180)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 52000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z / ((t + (x + y)) / (x + y)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.05e+156)
		tmp = t_2;
	elseif (y <= 8e-305)
		tmp = t_1;
	elseif (y <= 2.7e-180)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 52000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z / N[(N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.05e+156], t$95$2, If[LessEqual[y, 8e-305], t$95$1, If[LessEqual[y, 2.7e-180], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 52000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0500000000000001e156 or 5.2e10 < y

   1. Initial program 37.8%

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

   3. Taylor expanded in y around inf 87.0%

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

   if -2.0500000000000001e156 < y < 7.99999999999999997e-305 or 2.70000000000000014e-180 < y < 5.2e10

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 86.5%

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

      1. associate--l+ 86.5%

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

      2. +-commutative 86.5%

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

      3. associate-+r+ 86.5%

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

      4. associate-+r+ 86.5%

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

      5. div-sub 86.5%

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

      6. +-commutative 86.5%

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

      7. *-commutative 86.5%

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

      8. associate-+r+ 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around inf 69.1%

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

      1. associate-/l* 79.6%

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

      2. +-commutative 79.6%

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

      3. +-commutative 79.6%

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

   8. Simplified 79.6%

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

   9. Taylor expanded in y around inf 68.9%

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

   if 7.99999999999999997e-305 < y < 2.70000000000000014e-180

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0 81.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+156}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-305}:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-180}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;a + \frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{y + t}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-141} \lor \neg \left(y \leq 1.6 \cdot 10^{-132}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.5e+64)
     t_1
     (if (<= y -5.4e-110)
       (/ (* y (- z b)) (+ y t))
       (if (or (<= y -2.3e-141) (not (<= y 1.6e-132)))
         t_1
         (/ a (/ (+ y (+ x t)) (+ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.5e+64) {
		tmp = t_1;
	} else if (y <= -5.4e-110) {
		tmp = (y * (z - b)) / (y + t);
	} else if ((y <= -2.3e-141) || !(y <= 1.6e-132)) {
		tmp = t_1;
	} else {
		tmp = a / ((y + (x + t)) / (y + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-2.5d+64)) then
        tmp = t_1
    else if (y <= (-5.4d-110)) then
        tmp = (y * (z - b)) / (y + t)
    else if ((y <= (-2.3d-141)) .or. (.not. (y <= 1.6d-132))) then
        tmp = t_1
    else
        tmp = a / ((y + (x + t)) / (y + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.5e+64) {
		tmp = t_1;
	} else if (y <= -5.4e-110) {
		tmp = (y * (z - b)) / (y + t);
	} else if ((y <= -2.3e-141) || !(y <= 1.6e-132)) {
		tmp = t_1;
	} else {
		tmp = a / ((y + (x + t)) / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.5e+64:
		tmp = t_1
	elif y <= -5.4e-110:
		tmp = (y * (z - b)) / (y + t)
	elif (y <= -2.3e-141) or not (y <= 1.6e-132):
		tmp = t_1
	else:
		tmp = a / ((y + (x + t)) / (y + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.5e+64)
		tmp = t_1;
	elseif (y <= -5.4e-110)
		tmp = Float64(Float64(y * Float64(z - b)) / Float64(y + t));
	elseif ((y <= -2.3e-141) || !(y <= 1.6e-132))
		tmp = t_1;
	else
		tmp = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.5e+64)
		tmp = t_1;
	elseif (y <= -5.4e-110)
		tmp = (y * (z - b)) / (y + t);
	elseif ((y <= -2.3e-141) || ~((y <= 1.6e-132)))
		tmp = t_1;
	else
		tmp = a / ((y + (x + t)) / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.5e+64], t$95$1, If[LessEqual[y, -5.4e-110], N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.3e-141], N[Not[LessEqual[y, 1.6e-132]], $MachinePrecision]], t$95$1, N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5e64 or -5.3999999999999996e-110 < y < -2.29999999999999995e-141 or 1.6000000000000001e-132 < y

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 77.9%

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

   if -2.5e64 < y < -5.3999999999999996e-110

   1. Initial program 80.3%

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

   3. Taylor expanded in a around 0 63.6%

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

      1. +-commutative 63.6%

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

      2. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in x around 0 51.2%

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

      1. *-commutative 51.2%

         \[\leadsto \frac{y \cdot z - \color{blue}{y \cdot b}}{t + y} \]

      2. distribute-lft-out-- 51.1%

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

      3. +-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -2.29999999999999995e-141 < y < 1.6000000000000001e-132

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 37.3%

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

      1. associate-/l* 46.2%

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

      2. associate-+r+ 46.2%

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

   5. Simplified 46.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+64}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{y + t}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-141} \lor \neg \left(y \leq 1.6 \cdot 10^{-132}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-145}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-122}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -9.2e-57)
     t_1
     (if (<= y 4.6e-198)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 1.6e-145) (- a (/ (* y b) t)) (if (<= y 3e-122) z t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -9.2e-57) {
		tmp = t_1;
	} else if (y <= 4.6e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.6e-145) {
		tmp = a - ((y * b) / t);
	} else if (y <= 3e-122) {
		tmp = z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-9.2d-57)) then
        tmp = t_1
    else if (y <= 4.6d-198) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1.6d-145) then
        tmp = a - ((y * b) / t)
    else if (y <= 3d-122) then
        tmp = z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -9.2e-57) {
		tmp = t_1;
	} else if (y <= 4.6e-198) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.6e-145) {
		tmp = a - ((y * b) / t);
	} else if (y <= 3e-122) {
		tmp = z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -9.2e-57:
		tmp = t_1
	elif y <= 4.6e-198:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1.6e-145:
		tmp = a - ((y * b) / t)
	elif y <= 3e-122:
		tmp = z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9.2e-57)
		tmp = t_1;
	elseif (y <= 4.6e-198)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1.6e-145)
		tmp = Float64(a - Float64(Float64(y * b) / t));
	elseif (y <= 3e-122)
		tmp = z;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9.2e-57)
		tmp = t_1;
	elseif (y <= 4.6e-198)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1.6e-145)
		tmp = a - ((y * b) / t);
	elseif (y <= 3e-122)
		tmp = z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.2e-57], t$95$1, If[LessEqual[y, 4.6e-198], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-145], N[(a - N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-122], z, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.2000000000000001e-57 or 3.00000000000000004e-122 < y

   1. Initial program 52.8%

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

   3. Taylor expanded in y around inf 74.7%

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

   if -9.2000000000000001e-57 < y < 4.60000000000000027e-198

   1. Initial program 81.9%

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

   3. Taylor expanded in y around 0 66.9%

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

   if 4.60000000000000027e-198 < y < 1.60000000000000004e-145

   1. Initial program 64.8%

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

   3. Taylor expanded in z around 0 64.8%

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

      1. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in x around 0 52.4%

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

   7. Taylor expanded in t around inf 87.5%

      \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 87.5%

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

      2. associate-*r* 87.5%

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

      3. neg-mul-1 87.5%

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

      4. *-commutative 87.5%

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

   9. Simplified 87.5%

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

   if 1.60000000000000004e-145 < y < 3.00000000000000004e-122

   1. Initial program 80.3%

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

   3. Taylor expanded in x around inf 62.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-198}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-145}:\\ \;\;\;\;a - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-122}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-56}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-48} \lor \neg \left(a \leq 2.15 \cdot 10^{-14}\right) \land a \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.4e-56)
   a
   (if (or (<= a 3.2e-48) (and (not (<= a 2.15e-14)) (<= a 6.1e+119)))
     z
     (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.4e-56) {
		tmp = a;
	} else if ((a <= 3.2e-48) || (!(a <= 2.15e-14) && (a <= 6.1e+119))) {
		tmp = z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.4d-56)) then
        tmp = a
    else if ((a <= 3.2d-48) .or. (.not. (a <= 2.15d-14)) .and. (a <= 6.1d+119)) then
        tmp = z
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.4e-56) {
		tmp = a;
	} else if ((a <= 3.2e-48) || (!(a <= 2.15e-14) && (a <= 6.1e+119))) {
		tmp = z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.4e-56:
		tmp = a
	elif (a <= 3.2e-48) or (not (a <= 2.15e-14) and (a <= 6.1e+119)):
		tmp = z
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.4e-56)
		tmp = a;
	elseif ((a <= 3.2e-48) || (!(a <= 2.15e-14) && (a <= 6.1e+119)))
		tmp = z;
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.4e-56)
		tmp = a;
	elseif ((a <= 3.2e-48) || (~((a <= 2.15e-14)) && (a <= 6.1e+119)))
		tmp = z;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.4e-56], a, If[Or[LessEqual[a, 3.2e-48], And[N[Not[LessEqual[a, 2.15e-14]], $MachinePrecision], LessEqual[a, 6.1e+119]]], z, N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.39999999999999982e-56

   1. Initial program 52.0%

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

   3. Taylor expanded in t around inf 57.5%

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

   if -3.39999999999999982e-56 < a < 3.1999999999999998e-48 or 2.14999999999999999e-14 < a < 6.1e119

   1. Initial program 75.7%

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

   3. Taylor expanded in x around inf 41.0%

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

   if 3.1999999999999998e-48 < a < 2.14999999999999999e-14 or 6.1e119 < a

   1. Initial program 47.8%

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

   3. Taylor expanded in z around 0 35.7%

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

      1. *-commutative 35.7%

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

   5. Simplified 35.7%

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

   6. Taylor expanded in y around inf 64.3%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-56}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-48} \lor \neg \left(a \leq 2.15 \cdot 10^{-14}\right) \land a \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+162} \lor \neg \left(t \leq 3.5 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.2e+162) (not (<= t 3.5e+141)))
   (/ a (/ (+ x t) t))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+162) || !(t <= 3.5e+141)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.2d+162)) .or. (.not. (t <= 3.5d+141))) then
        tmp = a / ((x + t) / t)
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+162) || !(t <= 3.5e+141)) {
		tmp = a / ((x + t) / t);
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.2e+162) or not (t <= 3.5e+141):
		tmp = a / ((x + t) / t)
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.2e+162) || !(t <= 3.5e+141))
		tmp = Float64(a / Float64(Float64(x + t) / t));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.2e+162) || ~((t <= 3.5e+141)))
		tmp = a / ((x + t) / t);
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.2e+162], N[Not[LessEqual[t, 3.5e+141]], $MachinePrecision]], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000002e162 or 3.5e141 < t

   1. Initial program 47.7%

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

   3. Taylor expanded in z around 0 31.9%

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

      1. *-commutative 31.9%

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

   5. Simplified 31.9%

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

   6. Taylor expanded in t around inf 25.1%

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

      1. *-commutative 25.1%

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

   8. Simplified 25.1%

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

   9. Taylor expanded in y around 0 25.1%

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

       1. associate-/l* 59.6%

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

       2. +-commutative 59.6%

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

   11. Simplified 59.6%

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

   if -2.2000000000000002e162 < t < 3.5e141

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 62.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+162} \lor \neg \left(t \leq 3.5 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-52}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+121}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.3e-52) a (if (<= a 2.9e+121) (- z b) (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.3e-52) {
		tmp = a;
	} else if (a <= 2.9e+121) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.3d-52)) then
        tmp = a
    else if (a <= 2.9d+121) then
        tmp = z - b
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.3e-52) {
		tmp = a;
	} else if (a <= 2.9e+121) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.3e-52:
		tmp = a
	elif a <= 2.9e+121:
		tmp = z - b
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.3e-52)
		tmp = a;
	elseif (a <= 2.9e+121)
		tmp = Float64(z - b);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.3e-52)
		tmp = a;
	elseif (a <= 2.9e+121)
		tmp = z - b;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.3e-52], a, If[LessEqual[a, 2.9e+121], N[(z - b), $MachinePrecision], N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.29999999999999995e-52

   1. Initial program 52.6%

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

   3. Taylor expanded in t around inf 58.3%

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

   if -3.29999999999999995e-52 < a < 2.8999999999999999e121

   1. Initial program 74.3%

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

   3. Taylor expanded in a around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in y around inf 50.1%

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

   if 2.8999999999999999e121 < a

   1. Initial program 45.8%

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

   3. Taylor expanded in z around 0 31.4%

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

      1. *-commutative 31.4%

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

   5. Simplified 31.4%

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

   6. Taylor expanded in y around inf 62.8%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-52}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+121}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-57}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.8e-57) a (if (<= a 2.9e+118) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.8e-57) {
		tmp = a;
	} else if (a <= 2.9e+118) {
		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 (a <= (-7.8d-57)) then
        tmp = a
    else if (a <= 2.9d+118) 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 (a <= -7.8e-57) {
		tmp = a;
	} else if (a <= 2.9e+118) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.8e-57:
		tmp = a
	elif a <= 2.9e+118:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.8e-57)
		tmp = a;
	elseif (a <= 2.9e+118)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.8e-57)
		tmp = a;
	elseif (a <= 2.9e+118)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.8e-57], a, If[LessEqual[a, 2.9e+118], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -7.80000000000000013e-57 or 2.90000000000000016e118 < a

   1. Initial program 49.9%

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

   3. Taylor expanded in t around inf 57.8%

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

   if -7.80000000000000013e-57 < a < 2.90000000000000016e118

   1. Initial program 74.8%

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

   3. Taylor expanded in x around inf 39.1%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-57}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+162}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+162) a (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+162) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.2d+162)) then
        tmp = a
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+162) {
		tmp = a;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e+162:
		tmp = a
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e+162)
		tmp = a;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e+162)
		tmp = a;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+162], a, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000001e162

   1. Initial program 46.4%

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

   3. Taylor expanded in t around inf 66.9%

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

   if -3.2000000000000001e162 < t

   1. Initial program 66.2%

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

   3. Taylor expanded in y around inf 58.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+162}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.8% 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 63.9%

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

3. Taylor expanded in t around inf 31.4%

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

4. Final simplification 31.4%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.0% 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 2024026 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (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)))