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

Percentage Accurate: 60.9% → 88.3%

Time: 15.4s

Alternatives: 15

Speedup: 1.2×

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: 60.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \mathsf{fma}\left(y + t, a, b \cdot \left(-y\right)\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (+ t (+ x y))))
   (if (<= t_1 (- INFINITY))
     (+ z (* a (+ (/ y t_2) (/ t t_2))))
     (if (<= t_1 5e+274)
       (/ (fma (+ x y) z (fma (+ y t) a (* b (- y)))) (+ x (+ y t)))
       (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (x + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	} else if (t_1 <= 5e+274) {
		tmp = fma((x + y), z, fma((y + t), a, (b * -y))) / (x + (y + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))));
	elseif (t_1 <= 5e+274)
		tmp = Float64(fma(Float64(x + y), z, fma(Float64(y + t), a, Float64(b * Float64(-y)))) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return 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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z + N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(N[(N[(x + y), $MachinePrecision] * z + N[(N[(y + t), $MachinePrecision] * a + N[(b * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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)) < -inf.0

   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. Taylor expanded in a around 0 39.2%

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

      1. associate--l+ 39.2%

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

      2. +-commutative 39.2%

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

      3. +-commutative 39.2%

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

      4. +-commutative 39.2%

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

      5. div-sub 39.2%

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

      6. +-commutative 39.2%

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

      7. *-commutative 39.2%

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

      8. +-commutative 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in x around inf 82.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999998e274

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. fma-def 99.7%

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

      3. fma-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. *-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   if 4.9999999999999998e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.9%

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

   2. Taylor expanded in y around inf 77.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \mathsf{fma}\left(y + t, a, b \cdot \left(-y\right)\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 2: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (+ t (+ x y))))
   (if (<= t_1 (- INFINITY))
     (+ z (* a (+ (/ y t_2) (/ t t_2))))
     (if (<= t_1 5e+274) t_1 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (x + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	} else if (t_1 <= 5e+274) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = t + (x + y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	} else if (t_1 <= 5e+274) {
		tmp = t_1;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = t + (x + y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z + (a * ((y / t_2) + (t / t_2)))
	elif t_1 <= 5e+274:
		tmp = t_1
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z + Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))));
	elseif (t_1 <= 5e+274)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = t + (x + y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z + (a * ((y / t_2) + (t / t_2)));
	elseif (t_1 <= 5e+274)
		tmp = t_1;
	else
		tmp = (z + a) - b;
	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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z + N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], t$95$1, 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)) < -inf.0

   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. Taylor expanded in a around 0 39.2%

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

      1. associate--l+ 39.2%

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

      2. +-commutative 39.2%

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

      3. +-commutative 39.2%

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

      4. +-commutative 39.2%

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

      5. div-sub 39.2%

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

      6. +-commutative 39.2%

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

      7. *-commutative 39.2%

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

      8. +-commutative 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in x around inf 82.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999998e274

   1. Initial program 99.7%

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

   if 4.9999999999999998e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.9%

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

   2. Taylor expanded in y around inf 77.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 3: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -475:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-38}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-114}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* a (+ y t)) (* y b)) (+ y (+ x t)))) (t_2 (- (+ z a) b)))
   (if (<= y -6.5e+130)
     t_2
     (if (<= y -475.0)
       t_1
       (if (<= y -5.1e-38)
         (+ z (/ a (/ (+ x y) y)))
         (if (<= y -1.2e-119)
           t_1
           (if (<= y 2.65e-245)
             (/ (+ (* t a) (* x z)) (+ x t))
             (if (<= y 6e-114) (+ z a) (if (<= y 1.65e-67) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a * (y + t)) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+130) {
		tmp = t_2;
	} else if (y <= -475.0) {
		tmp = t_1;
	} else if (y <= -5.1e-38) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= -1.2e-119) {
		tmp = t_1;
	} else if (y <= 2.65e-245) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6e-114) {
		tmp = z + a;
	} else if (y <= 1.65e-67) {
		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 * (y + t)) - (y * b)) / (y + (x + t))
    t_2 = (z + a) - b
    if (y <= (-6.5d+130)) then
        tmp = t_2
    else if (y <= (-475.0d0)) then
        tmp = t_1
    else if (y <= (-5.1d-38)) then
        tmp = z + (a / ((x + y) / y))
    else if (y <= (-1.2d-119)) then
        tmp = t_1
    else if (y <= 2.65d-245) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 6d-114) then
        tmp = z + a
    else if (y <= 1.65d-67) 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 * (y + t)) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+130) {
		tmp = t_2;
	} else if (y <= -475.0) {
		tmp = t_1;
	} else if (y <= -5.1e-38) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= -1.2e-119) {
		tmp = t_1;
	} else if (y <= 2.65e-245) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6e-114) {
		tmp = z + a;
	} else if (y <= 1.65e-67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a * (y + t)) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -6.5e+130:
		tmp = t_2
	elif y <= -475.0:
		tmp = t_1
	elif y <= -5.1e-38:
		tmp = z + (a / ((x + y) / y))
	elif y <= -1.2e-119:
		tmp = t_1
	elif y <= 2.65e-245:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 6e-114:
		tmp = z + a
	elif y <= 1.65e-67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.5e+130)
		tmp = t_2;
	elseif (y <= -475.0)
		tmp = t_1;
	elseif (y <= -5.1e-38)
		tmp = Float64(z + Float64(a / Float64(Float64(x + y) / y)));
	elseif (y <= -1.2e-119)
		tmp = t_1;
	elseif (y <= 2.65e-245)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 6e-114)
		tmp = Float64(z + a);
	elseif (y <= 1.65e-67)
		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 * (y + t)) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.5e+130)
		tmp = t_2;
	elseif (y <= -475.0)
		tmp = t_1;
	elseif (y <= -5.1e-38)
		tmp = z + (a / ((x + y) / y));
	elseif (y <= -1.2e-119)
		tmp = t_1;
	elseif (y <= 2.65e-245)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 6e-114)
		tmp = z + a;
	elseif (y <= 1.65e-67)
		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[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.5e+130], t$95$2, If[LessEqual[y, -475.0], t$95$1, If[LessEqual[y, -5.1e-38], N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-119], t$95$1, If[LessEqual[y, 2.65e-245], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-114], N[(z + a), $MachinePrecision], If[LessEqual[y, 1.65e-67], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.5e130 or 1.6500000000000001e-67 < y

   1. Initial program 49.8%

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

   2. Taylor expanded in y around inf 76.7%

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

   if -6.5e130 < y < -475 or -5.10000000000000028e-38 < y < -1.20000000000000004e-119 or 6.0000000000000003e-114 < y < 1.6500000000000001e-67

   1. Initial program 78.0%

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

   2. Taylor expanded in z around 0 64.1%

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

   if -475 < y < -5.10000000000000028e-38

   1. Initial program 52.9%

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

   2. Taylor expanded in a around 0 62.5%

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

      1. associate--l+ 62.5%

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

      2. +-commutative 62.5%

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

      3. +-commutative 62.5%

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

      4. +-commutative 62.5%

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

      5. div-sub 62.5%

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

      6. +-commutative 62.5%

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

      7. *-commutative 62.5%

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

      8. +-commutative 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in x around inf 87.6%

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

   6. Taylor expanded in t around 0 87.6%

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

      1. associate-/l* 87.6%

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

      2. +-commutative 87.6%

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

   8. Simplified 87.6%

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

   if -1.20000000000000004e-119 < y < 2.64999999999999998e-245

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 77.2%

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

   if 2.64999999999999998e-245 < y < 6.0000000000000003e-114

   1. Initial program 66.0%

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

   2. Taylor expanded in a around 0 84.6%

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

      1. associate--l+ 84.6%

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

      2. +-commutative 84.6%

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

      3. +-commutative 84.6%

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

      4. +-commutative 84.6%

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

      5. div-sub 84.6%

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

      6. +-commutative 84.6%

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

      7. *-commutative 84.6%

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

      8. +-commutative 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 79.1%

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

   6. Taylor expanded in y around inf 63.6%

      \[\leadsto \color{blue}{a} + z \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -475:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-38}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-114}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-67}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 4: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{t_1 - y \cdot b}{t_2}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -42:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-38}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + t_1}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- t_1 (* y b)) t_2))
        (t_4 (- (+ z a) b)))
   (if (<= y -6.5e+130)
     t_4
     (if (<= y -42.0)
       t_3
       (if (<= y -5.6e-38)
         (+ z (/ a (/ (+ x y) y)))
         (if (<= y -6.2e-119)
           t_3
           (if (<= y 4e-32) (/ (+ (* z (+ x y)) t_1) t_2) t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (t_1 - (y * b)) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+130) {
		tmp = t_4;
	} else if (y <= -42.0) {
		tmp = t_3;
	} else if (y <= -5.6e-38) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= -6.2e-119) {
		tmp = t_3;
	} else if (y <= 4e-32) {
		tmp = ((z * (x + y)) + 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 = a * (y + t)
    t_2 = y + (x + t)
    t_3 = (t_1 - (y * b)) / t_2
    t_4 = (z + a) - b
    if (y <= (-6.5d+130)) then
        tmp = t_4
    else if (y <= (-42.0d0)) then
        tmp = t_3
    else if (y <= (-5.6d-38)) then
        tmp = z + (a / ((x + y) / y))
    else if (y <= (-6.2d-119)) then
        tmp = t_3
    else if (y <= 4d-32) then
        tmp = ((z * (x + y)) + 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 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (t_1 - (y * b)) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (y <= -6.5e+130) {
		tmp = t_4;
	} else if (y <= -42.0) {
		tmp = t_3;
	} else if (y <= -5.6e-38) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= -6.2e-119) {
		tmp = t_3;
	} else if (y <= 4e-32) {
		tmp = ((z * (x + y)) + t_1) / t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = (t_1 - (y * b)) / t_2
	t_4 = (z + a) - b
	tmp = 0
	if y <= -6.5e+130:
		tmp = t_4
	elif y <= -42.0:
		tmp = t_3
	elif y <= -5.6e-38:
		tmp = z + (a / ((x + y) / y))
	elif y <= -6.2e-119:
		tmp = t_3
	elif y <= 4e-32:
		tmp = ((z * (x + y)) + t_1) / t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(t_1 - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.5e+130)
		tmp = t_4;
	elseif (y <= -42.0)
		tmp = t_3;
	elseif (y <= -5.6e-38)
		tmp = Float64(z + Float64(a / Float64(Float64(x + y) / y)));
	elseif (y <= -6.2e-119)
		tmp = t_3;
	elseif (y <= 4e-32)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) + 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 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = (t_1 - (y * b)) / t_2;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.5e+130)
		tmp = t_4;
	elseif (y <= -42.0)
		tmp = t_3;
	elseif (y <= -5.6e-38)
		tmp = z + (a / ((x + y) / y));
	elseif (y <= -6.2e-119)
		tmp = t_3;
	elseif (y <= 4e-32)
		tmp = ((z * (x + y)) + 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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.5e+130], t$95$4, If[LessEqual[y, -42.0], t$95$3, If[LessEqual[y, -5.6e-38], N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-119], t$95$3, If[LessEqual[y, 4e-32], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5e130 or 4.00000000000000022e-32 < y

   1. Initial program 47.0%

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

   2. Taylor expanded in y around inf 77.7%

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

   if -6.5e130 < y < -42 or -5.6e-38 < y < -6.19999999999999956e-119

   1. Initial program 77.3%

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

   2. Taylor expanded in z around 0 64.7%

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

   if -42 < y < -5.6e-38

   1. Initial program 52.9%

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

   2. Taylor expanded in a around 0 62.5%

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

      1. associate--l+ 62.5%

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

      2. +-commutative 62.5%

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

      3. +-commutative 62.5%

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

      4. +-commutative 62.5%

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

      5. div-sub 62.5%

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

      6. +-commutative 62.5%

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

      7. *-commutative 62.5%

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

      8. +-commutative 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in x around inf 87.6%

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

   6. Taylor expanded in t around 0 87.6%

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

      1. associate-/l* 87.6%

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

      2. +-commutative 87.6%

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

   8. Simplified 87.6%

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

   if -6.19999999999999956e-119 < y < 4.00000000000000022e-32

   1. Initial program 81.1%

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

   2. Taylor expanded in b around 0 69.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -42:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-38}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + a \cdot \left(y + t\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 5: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_2}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (+ z (* a (+ (/ y t_1) (/ t t_1))))))
   (if (<= a -2.3e-61)
     t_3
     (if (<= a -1.65e-192)
       (- (+ z a) b)
       (if (<= a 1.8e-87)
         (/ (- (* z (+ x y)) (* y b)) t_2)
         (if (<= a 2.5e+77) (/ (- (* a (+ y t)) (* y b)) t_2) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = z + (a * ((y / t_1) + (t / t_1)));
	double tmp;
	if (a <= -2.3e-61) {
		tmp = t_3;
	} else if (a <= -1.65e-192) {
		tmp = (z + a) - b;
	} else if (a <= 1.8e-87) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else if (a <= 2.5e+77) {
		tmp = ((a * (y + t)) - (y * b)) / 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 = t + (x + y)
    t_2 = y + (x + t)
    t_3 = z + (a * ((y / t_1) + (t / t_1)))
    if (a <= (-2.3d-61)) then
        tmp = t_3
    else if (a <= (-1.65d-192)) then
        tmp = (z + a) - b
    else if (a <= 1.8d-87) then
        tmp = ((z * (x + y)) - (y * b)) / t_2
    else if (a <= 2.5d+77) then
        tmp = ((a * (y + t)) - (y * b)) / 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 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = z + (a * ((y / t_1) + (t / t_1)));
	double tmp;
	if (a <= -2.3e-61) {
		tmp = t_3;
	} else if (a <= -1.65e-192) {
		tmp = (z + a) - b;
	} else if (a <= 1.8e-87) {
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	} else if (a <= 2.5e+77) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = y + (x + t)
	t_3 = z + (a * ((y / t_1) + (t / t_1)))
	tmp = 0
	if a <= -2.3e-61:
		tmp = t_3
	elif a <= -1.65e-192:
		tmp = (z + a) - b
	elif a <= 1.8e-87:
		tmp = ((z * (x + y)) - (y * b)) / t_2
	elif a <= 2.5e+77:
		tmp = ((a * (y + t)) - (y * b)) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))))
	tmp = 0.0
	if (a <= -2.3e-61)
		tmp = t_3;
	elseif (a <= -1.65e-192)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 1.8e-87)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / t_2);
	elseif (a <= 2.5e+77)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = y + (x + t);
	t_3 = z + (a * ((y / t_1) + (t / t_1)));
	tmp = 0.0;
	if (a <= -2.3e-61)
		tmp = t_3;
	elseif (a <= -1.65e-192)
		tmp = (z + a) - b;
	elseif (a <= 1.8e-87)
		tmp = ((z * (x + y)) - (y * b)) / t_2;
	elseif (a <= 2.5e+77)
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + 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, -2.3e-61], t$95$3, If[LessEqual[a, -1.65e-192], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 1.8e-87], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 2.5e+77], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.29999999999999992e-61 or 2.50000000000000002e77 < a

   1. Initial program 55.3%

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

   2. Taylor expanded in a around 0 79.6%

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

      1. associate--l+ 79.6%

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

      2. +-commutative 79.6%

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

      3. +-commutative 79.6%

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

      4. +-commutative 79.6%

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

      5. div-sub 79.6%

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

      6. +-commutative 79.6%

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

      7. *-commutative 79.6%

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

      8. +-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in x around inf 85.7%

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

   if -2.29999999999999992e-61 < a < -1.64999999999999995e-192

   1. Initial program 69.5%

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

   2. Taylor expanded in y around inf 81.2%

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

   if -1.64999999999999995e-192 < a < 1.79999999999999996e-87

   1. Initial program 73.5%

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

   2. Taylor expanded in a around 0 67.7%

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

      1. +-commutative 67.7%

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

      2. *-commutative 67.7%

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

   4. Simplified 67.7%

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

   if 1.79999999999999996e-87 < a < 2.50000000000000002e77

   1. Initial program 77.0%

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

   2. Taylor expanded in z around 0 60.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-192}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(\frac{y}{t + \left(x + y\right)} + \frac{t}{t + \left(x + y\right)}\right)\\ \end{array} \]

Alternative 6: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+109}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ a (/ (+ x y) y)))))
   (if (<= x -1.45e+79)
     t_1
     (if (<= x 1.5e+109)
       (- (+ z a) b)
       (if (<= x 2.9e+166) t_1 (/ (- (* z (+ x y)) (* y b)) (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((x + y) / y));
	double tmp;
	if (x <= -1.45e+79) {
		tmp = t_1;
	} else if (x <= 1.5e+109) {
		tmp = (z + a) - b;
	} else if (x <= 2.9e+166) {
		tmp = t_1;
	} else {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a / ((x + y) / y))
    if (x <= (-1.45d+79)) then
        tmp = t_1
    else if (x <= 1.5d+109) then
        tmp = (z + a) - b
    else if (x <= 2.9d+166) then
        tmp = t_1
    else
        tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((x + y) / y));
	double tmp;
	if (x <= -1.45e+79) {
		tmp = t_1;
	} else if (x <= 1.5e+109) {
		tmp = (z + a) - b;
	} else if (x <= 2.9e+166) {
		tmp = t_1;
	} else {
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a / ((x + y) / y))
	tmp = 0
	if x <= -1.45e+79:
		tmp = t_1
	elif x <= 1.5e+109:
		tmp = (z + a) - b
	elif x <= 2.9e+166:
		tmp = t_1
	else:
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a / Float64(Float64(x + y) / y)))
	tmp = 0.0
	if (x <= -1.45e+79)
		tmp = t_1;
	elseif (x <= 1.5e+109)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 2.9e+166)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(z * Float64(x + y)) - Float64(y * b)) / Float64(y + Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a / ((x + y) / y));
	tmp = 0.0;
	if (x <= -1.45e+79)
		tmp = t_1;
	elseif (x <= 1.5e+109)
		tmp = (z + a) - b;
	elseif (x <= 2.9e+166)
		tmp = t_1;
	else
		tmp = ((z * (x + y)) - (y * b)) / (y + (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+79], t$95$1, If[LessEqual[x, 1.5e+109], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 2.9e+166], t$95$1, N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999996e79 or 1.50000000000000008e109 < x < 2.9000000000000001e166

   1. Initial program 56.4%

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

   2. Taylor expanded in a around 0 64.3%

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

      1. associate--l+ 64.3%

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

      2. +-commutative 64.3%

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

      3. +-commutative 64.3%

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

      4. +-commutative 64.3%

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

      5. div-sub 64.3%

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

      6. +-commutative 64.3%

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

      7. *-commutative 64.3%

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

      8. +-commutative 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in x around inf 79.6%

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

   6. Taylor expanded in t around 0 65.8%

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

      1. associate-/l* 75.1%

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

      2. +-commutative 75.1%

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

   8. Simplified 75.1%

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

   if -1.44999999999999996e79 < x < 1.50000000000000008e109

   1. Initial program 68.3%

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

   2. Taylor expanded in y around inf 67.4%

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

   if 2.9000000000000001e166 < x

   1. Initial program 61.3%

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

   2. Taylor expanded in a around 0 54.1%

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

      1. +-commutative 54.1%

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

      2. *-commutative 54.1%

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

   4. Simplified 54.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+109}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+166}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7: 61.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3:\\ \;\;\;\;\frac{y \cdot t_1}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-83}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -6.8e+92)
     t_1
     (if (<= y -3.0)
       (/ (* y t_1) (+ y (+ x t)))
       (if (<= y -4.1e-83)
         (+ z (/ a (/ (+ x y) y)))
         (if (<= y 2.65e-245) (/ (+ (* t a) (* x z)) (+ x t)) 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 <= -6.8e+92) {
		tmp = t_1;
	} else if (y <= -3.0) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= -4.1e-83) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= 2.65e-245) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-6.8d+92)) then
        tmp = t_1
    else if (y <= (-3.0d0)) then
        tmp = (y * t_1) / (y + (x + t))
    else if (y <= (-4.1d-83)) then
        tmp = z + (a / ((x + y) / y))
    else if (y <= 2.65d-245) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -6.8e+92) {
		tmp = t_1;
	} else if (y <= -3.0) {
		tmp = (y * t_1) / (y + (x + t));
	} else if (y <= -4.1e-83) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= 2.65e-245) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -6.8e+92:
		tmp = t_1
	elif y <= -3.0:
		tmp = (y * t_1) / (y + (x + t))
	elif y <= -4.1e-83:
		tmp = z + (a / ((x + y) / y))
	elif y <= 2.65e-245:
		tmp = ((t * a) + (x * z)) / (x + t)
	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 <= -6.8e+92)
		tmp = t_1;
	elseif (y <= -3.0)
		tmp = Float64(Float64(y * t_1) / Float64(y + Float64(x + t)));
	elseif (y <= -4.1e-83)
		tmp = Float64(z + Float64(a / Float64(Float64(x + y) / y)));
	elseif (y <= 2.65e-245)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.8e+92)
		tmp = t_1;
	elseif (y <= -3.0)
		tmp = (y * t_1) / (y + (x + t));
	elseif (y <= -4.1e-83)
		tmp = z + (a / ((x + y) / y));
	elseif (y <= 2.65e-245)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.8e+92], t$95$1, If[LessEqual[y, -3.0], N[(N[(y * t$95$1), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-83], N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-245], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.7999999999999996e92 or 2.64999999999999998e-245 < y

   1. Initial program 55.6%

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

   2. Taylor expanded in y around inf 69.9%

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

   if -6.7999999999999996e92 < y < -3

   1. Initial program 70.3%

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

   2. Taylor expanded in y around inf 55.3%

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

   if -3 < y < -4.1e-83

   1. Initial program 68.4%

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

   2. Taylor expanded in a around 0 76.4%

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

      1. associate--l+ 76.4%

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

      2. +-commutative 76.4%

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

      3. +-commutative 76.4%

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

      4. +-commutative 76.4%

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

      5. div-sub 76.4%

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

      6. +-commutative 76.4%

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

      7. *-commutative 76.4%

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

      8. +-commutative 76.4%

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

   4. Simplified 76.4%

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

   5. Taylor expanded in x around inf 74.8%

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

   6. Taylor expanded in t around 0 70.9%

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

      1. associate-/l* 70.9%

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

      2. +-commutative 70.9%

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

   8. Simplified 70.9%

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

   if -4.1e-83 < y < 2.64999999999999998e-245

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 75.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-83}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 57.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{1 + \frac{t}{x}}\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+301}:\\ \;\;\;\;a \cdot \frac{1}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (+ 1.0 (/ t x)))))
   (if (<= x -1.05e+137)
     t_1
     (if (<= x 6.2e+122)
       (- (+ z a) b)
       (if (<= x 1.4e+245)
         t_1
         (if (<= x 3.9e+301) (* a (/ 1.0 (/ (+ x t) t))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (1.0 + (t / x));
	double tmp;
	if (x <= -1.05e+137) {
		tmp = t_1;
	} else if (x <= 6.2e+122) {
		tmp = (z + a) - b;
	} else if (x <= 1.4e+245) {
		tmp = t_1;
	} else if (x <= 3.9e+301) {
		tmp = a * (1.0 / ((x + t) / t));
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (1.0d0 + (t / x))
    if (x <= (-1.05d+137)) then
        tmp = t_1
    else if (x <= 6.2d+122) then
        tmp = (z + a) - b
    else if (x <= 1.4d+245) then
        tmp = t_1
    else if (x <= 3.9d+301) then
        tmp = a * (1.0d0 / ((x + t) / t))
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (1.0 + (t / x));
	double tmp;
	if (x <= -1.05e+137) {
		tmp = t_1;
	} else if (x <= 6.2e+122) {
		tmp = (z + a) - b;
	} else if (x <= 1.4e+245) {
		tmp = t_1;
	} else if (x <= 3.9e+301) {
		tmp = a * (1.0 / ((x + t) / t));
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / (1.0 + (t / x))
	tmp = 0
	if x <= -1.05e+137:
		tmp = t_1
	elif x <= 6.2e+122:
		tmp = (z + a) - b
	elif x <= 1.4e+245:
		tmp = t_1
	elif x <= 3.9e+301:
		tmp = a * (1.0 / ((x + t) / t))
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(1.0 + Float64(t / x)))
	tmp = 0.0
	if (x <= -1.05e+137)
		tmp = t_1;
	elseif (x <= 6.2e+122)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 1.4e+245)
		tmp = t_1;
	elseif (x <= 3.9e+301)
		tmp = Float64(a * Float64(1.0 / Float64(Float64(x + t) / t)));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z / (1.0 + (t / x));
	tmp = 0.0;
	if (x <= -1.05e+137)
		tmp = t_1;
	elseif (x <= 6.2e+122)
		tmp = (z + a) - b;
	elseif (x <= 1.4e+245)
		tmp = t_1;
	elseif (x <= 3.9e+301)
		tmp = a * (1.0 / ((x + t) / t));
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(1.0 + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+137], t$95$1, If[LessEqual[x, 6.2e+122], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 1.4e+245], t$95$1, If[LessEqual[x, 3.9e+301], N[(a * N[(1.0 / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], z]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.05e137 or 6.19999999999999998e122 < x < 1.39999999999999989e245

   1. Initial program 60.2%

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

   2. Taylor expanded in z around inf 40.3%

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

      1. associate-/l* 66.9%

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

      2. +-commutative 66.9%

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

      3. +-commutative 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -1.05e137 < x < 6.19999999999999998e122

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 67.5%

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

   if 1.39999999999999989e245 < x < 3.9000000000000001e301

   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. Taylor expanded in a around inf 16.7%

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

   3. Taylor expanded in y around 0 16.8%

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

      1. associate-/l* 64.0%

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

   5. Simplified 64.0%

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

      1. div-inv 64.2%

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

      2. +-commutative 64.2%

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

   7. Applied egg-rr 64.2%

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

   if 3.9000000000000001e301 < x

   1. Initial program 68.8%

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

   2. Taylor expanded in x around inf 81.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+137}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+245}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+301}:\\ \;\;\;\;a \cdot \frac{1}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 9: 58.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{if}\;x \leq -8 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+104}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+301}:\\ \;\;\;\;a \cdot \frac{1}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ a (/ (+ x y) y)))))
   (if (<= x -8e+86)
     t_1
     (if (<= x 2.85e+104)
       (- (+ z a) b)
       (if (<= x 1.2e+241)
         t_1
         (if (<= x 3.9e+301) (* a (/ 1.0 (/ (+ x t) t))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((x + y) / y));
	double tmp;
	if (x <= -8e+86) {
		tmp = t_1;
	} else if (x <= 2.85e+104) {
		tmp = (z + a) - b;
	} else if (x <= 1.2e+241) {
		tmp = t_1;
	} else if (x <= 3.9e+301) {
		tmp = a * (1.0 / ((x + t) / t));
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (a / ((x + y) / y))
    if (x <= (-8d+86)) then
        tmp = t_1
    else if (x <= 2.85d+104) then
        tmp = (z + a) - b
    else if (x <= 1.2d+241) then
        tmp = t_1
    else if (x <= 3.9d+301) then
        tmp = a * (1.0d0 / ((x + t) / t))
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a / ((x + y) / y));
	double tmp;
	if (x <= -8e+86) {
		tmp = t_1;
	} else if (x <= 2.85e+104) {
		tmp = (z + a) - b;
	} else if (x <= 1.2e+241) {
		tmp = t_1;
	} else if (x <= 3.9e+301) {
		tmp = a * (1.0 / ((x + t) / t));
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a / ((x + y) / y))
	tmp = 0
	if x <= -8e+86:
		tmp = t_1
	elif x <= 2.85e+104:
		tmp = (z + a) - b
	elif x <= 1.2e+241:
		tmp = t_1
	elif x <= 3.9e+301:
		tmp = a * (1.0 / ((x + t) / t))
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a / Float64(Float64(x + y) / y)))
	tmp = 0.0
	if (x <= -8e+86)
		tmp = t_1;
	elseif (x <= 2.85e+104)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 1.2e+241)
		tmp = t_1;
	elseif (x <= 3.9e+301)
		tmp = Float64(a * Float64(1.0 / Float64(Float64(x + t) / t)));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a / ((x + y) / y));
	tmp = 0.0;
	if (x <= -8e+86)
		tmp = t_1;
	elseif (x <= 2.85e+104)
		tmp = (z + a) - b;
	elseif (x <= 1.2e+241)
		tmp = t_1;
	elseif (x <= 3.9e+301)
		tmp = a * (1.0 / ((x + t) / t));
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+86], t$95$1, If[LessEqual[x, 2.85e+104], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 1.2e+241], t$95$1, If[LessEqual[x, 3.9e+301], N[(a * N[(1.0 / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], z]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.0000000000000001e86 or 2.84999999999999993e104 < x < 1.1999999999999999e241

   1. Initial program 57.5%

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

   2. Taylor expanded in a around 0 65.1%

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

      1. associate--l+ 65.1%

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

      2. +-commutative 65.1%

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

      3. +-commutative 65.1%

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

      4. +-commutative 65.1%

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

      5. div-sub 65.1%

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

      6. +-commutative 65.1%

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

      7. *-commutative 65.1%

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

      8. +-commutative 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in x around inf 77.2%

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

   6. Taylor expanded in t around 0 62.4%

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

      1. associate-/l* 70.0%

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

      2. +-commutative 70.0%

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

   8. Simplified 70.0%

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

   if -8.0000000000000001e86 < x < 2.84999999999999993e104

   1. Initial program 68.3%

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

   2. Taylor expanded in y around inf 67.4%

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

   if 1.1999999999999999e241 < x < 3.9000000000000001e301

   1. Initial program 57.9%

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

   2. Taylor expanded in a around inf 15.7%

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

   3. Taylor expanded in y around 0 15.7%

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

      1. associate-/l* 57.7%

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

   5. Simplified 57.7%

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

      1. div-inv 57.8%

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

      2. +-commutative 57.8%

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

   7. Applied egg-rr 57.8%

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

   if 3.9000000000000001e301 < x

   1. Initial program 68.8%

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

   2. Taylor expanded in x around inf 81.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+86}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+104}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+241}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+301}:\\ \;\;\;\;a \cdot \frac{1}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 10: 62.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-78}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.2e+80)
     t_1
     (if (<= y -7.4e-78)
       (+ z (/ a (/ (+ x y) y)))
       (if (<= y 2.65e-245) (/ (+ (* t a) (* x z)) (+ x t)) 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 <= -1.2e+80) {
		tmp = t_1;
	} else if (y <= -7.4e-78) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= 2.65e-245) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.2d+80)) then
        tmp = t_1
    else if (y <= (-7.4d-78)) then
        tmp = z + (a / ((x + y) / y))
    else if (y <= 2.65d-245) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.2e+80) {
		tmp = t_1;
	} else if (y <= -7.4e-78) {
		tmp = z + (a / ((x + y) / y));
	} else if (y <= 2.65e-245) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.2e+80:
		tmp = t_1
	elif y <= -7.4e-78:
		tmp = z + (a / ((x + y) / y))
	elif y <= 2.65e-245:
		tmp = ((t * a) + (x * z)) / (x + t)
	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 <= -1.2e+80)
		tmp = t_1;
	elseif (y <= -7.4e-78)
		tmp = Float64(z + Float64(a / Float64(Float64(x + y) / y)));
	elseif (y <= 2.65e-245)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.2e+80)
		tmp = t_1;
	elseif (y <= -7.4e-78)
		tmp = z + (a / ((x + y) / y));
	elseif (y <= 2.65e-245)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.2e+80], t$95$1, If[LessEqual[y, -7.4e-78], N[(z + N[(a / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-245], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1999999999999999e80 or 2.64999999999999998e-245 < y

   1. Initial program 55.6%

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

   2. Taylor expanded in y around inf 69.1%

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

   if -1.1999999999999999e80 < y < -7.40000000000000011e-78

   1. Initial program 70.1%

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

   2. Taylor expanded in a around 0 77.1%

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

      1. associate--l+ 77.1%

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

      2. +-commutative 77.1%

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

      3. +-commutative 77.1%

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

      4. +-commutative 77.1%

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

      5. div-sub 77.1%

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

      6. +-commutative 77.1%

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

      7. *-commutative 77.1%

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

      8. +-commutative 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in x around inf 63.5%

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

   6. Taylor expanded in t around 0 56.7%

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

      1. associate-/l* 56.7%

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

      2. +-commutative 56.7%

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

   8. Simplified 56.7%

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

   if -7.40000000000000011e-78 < y < 2.64999999999999998e-245

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 75.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+80}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-78}:\\ \;\;\;\;z + \frac{a}{\frac{x + y}{y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 57.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{1 + \frac{t}{x}}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+117}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+301}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (+ 1.0 (/ t x)))))
   (if (<= x -7.8e+134)
     t_1
     (if (<= x 3.2e+117)
       (- (+ z a) b)
       (if (<= x 1.4e+245)
         t_1
         (if (<= x 3.9e+301) (/ a (+ 1.0 (/ x t))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (1.0 + (t / x));
	double tmp;
	if (x <= -7.8e+134) {
		tmp = t_1;
	} else if (x <= 3.2e+117) {
		tmp = (z + a) - b;
	} else if (x <= 1.4e+245) {
		tmp = t_1;
	} else if (x <= 3.9e+301) {
		tmp = a / (1.0 + (x / t));
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (1.0d0 + (t / x))
    if (x <= (-7.8d+134)) then
        tmp = t_1
    else if (x <= 3.2d+117) then
        tmp = (z + a) - b
    else if (x <= 1.4d+245) then
        tmp = t_1
    else if (x <= 3.9d+301) then
        tmp = a / (1.0d0 + (x / t))
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (1.0 + (t / x));
	double tmp;
	if (x <= -7.8e+134) {
		tmp = t_1;
	} else if (x <= 3.2e+117) {
		tmp = (z + a) - b;
	} else if (x <= 1.4e+245) {
		tmp = t_1;
	} else if (x <= 3.9e+301) {
		tmp = a / (1.0 + (x / t));
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / (1.0 + (t / x))
	tmp = 0
	if x <= -7.8e+134:
		tmp = t_1
	elif x <= 3.2e+117:
		tmp = (z + a) - b
	elif x <= 1.4e+245:
		tmp = t_1
	elif x <= 3.9e+301:
		tmp = a / (1.0 + (x / t))
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(1.0 + Float64(t / x)))
	tmp = 0.0
	if (x <= -7.8e+134)
		tmp = t_1;
	elseif (x <= 3.2e+117)
		tmp = Float64(Float64(z + a) - b);
	elseif (x <= 1.4e+245)
		tmp = t_1;
	elseif (x <= 3.9e+301)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z / (1.0 + (t / x));
	tmp = 0.0;
	if (x <= -7.8e+134)
		tmp = t_1;
	elseif (x <= 3.2e+117)
		tmp = (z + a) - b;
	elseif (x <= 1.4e+245)
		tmp = t_1;
	elseif (x <= 3.9e+301)
		tmp = a / (1.0 + (x / t));
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(1.0 + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+134], t$95$1, If[LessEqual[x, 3.2e+117], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[x, 1.4e+245], t$95$1, If[LessEqual[x, 3.9e+301], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], z]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.79999999999999967e134 or 3.20000000000000005e117 < x < 1.39999999999999989e245

   1. Initial program 60.2%

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

   2. Taylor expanded in z around inf 40.3%

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

      1. associate-/l* 66.9%

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

      2. +-commutative 66.9%

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

      3. +-commutative 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -7.79999999999999967e134 < x < 3.20000000000000005e117

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 67.5%

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

   if 1.39999999999999989e245 < x < 3.9000000000000001e301

   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. Taylor expanded in a around inf 16.7%

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

   3. Taylor expanded in y around 0 16.8%

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

      1. associate-/l* 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in t around 0 64.0%

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

      1. +-commutative 64.0%

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

   8. Simplified 64.0%

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

   if 3.9000000000000001e301 < x

   1. Initial program 68.8%

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

   2. Taylor expanded in x around inf 81.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+117}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+245}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+301}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 12: 58.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.9 \cdot 10^{+165}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+122}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.9e+165) z (if (<= x 4.2e+122) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.9e+165) {
		tmp = z;
	} else if (x <= 4.2e+122) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.9d+165)) then
        tmp = z
    else if (x <= 4.2d+122) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.9e+165) {
		tmp = z;
	} else if (x <= 4.2e+122) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.9e+165:
		tmp = z
	elif x <= 4.2e+122:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.9e+165)
		tmp = z;
	elseif (x <= 4.2e+122)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.9e+165)
		tmp = z;
	elseif (x <= 4.2e+122)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.9e+165], z, If[LessEqual[x, 4.2e+122], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -6.90000000000000006e165 or 4.20000000000000032e122 < x

   1. Initial program 57.7%

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

   2. Taylor expanded in x around inf 54.9%

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

   if -6.90000000000000006e165 < x < 4.20000000000000032e122

   1. Initial program 67.6%

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

   2. Taylor expanded in y around inf 66.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.9 \cdot 10^{+165}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+122}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13: 44.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+79) z (if (<= x 4e+45) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+79) {
		tmp = z;
	} else if (x <= 4e+45) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6d+79)) then
        tmp = z
    else if (x <= 4d+45) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+79) {
		tmp = z;
	} else if (x <= 4e+45) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+79:
		tmp = z
	elif x <= 4e+45:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+79)
		tmp = z;
	elseif (x <= 4e+45)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6e+79)
		tmp = z;
	elseif (x <= 4e+45)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+79], z, If[LessEqual[x, 4e+45], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999948e79 or 3.9999999999999997e45 < x

   1. Initial program 59.5%

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

   2. Taylor expanded in x around inf 49.1%

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

   if -5.99999999999999948e79 < x < 3.9999999999999997e45

   1. Initial program 68.2%

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

   2. Taylor expanded in t around inf 45.2%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 14: 51.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + 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 = z + a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 64.7%

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

2. Taylor expanded in a around 0 76.4%

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

   1. associate--l+ 76.4%

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

   2. +-commutative 76.4%

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

   3. +-commutative 76.4%

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

   4. +-commutative 76.4%

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

   5. div-sub 76.4%

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

   6. +-commutative 76.4%

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

   7. *-commutative 76.4%

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

   8. +-commutative 76.4%

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

4. Simplified 76.4%

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

5. Taylor expanded in x around inf 64.2%

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

6. Taylor expanded in y around inf 52.3%

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

7. Final simplification 52.3%

   \[\leadsto z + a \]

Alternative 15: 32.5% 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 64.7%

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

2. Taylor expanded in t around inf 32.8%

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

3. Final simplification 32.8%

   \[\leadsto a \]

Developer target: 82.2% 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 2023318 
(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)))