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

Percentage Accurate: 61.0% → 89.3%

Time: 43.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{t\_1}, \frac{y}{t\_1}\right) - \frac{b}{t\_1} \cdot \frac{y}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_2 2e+282)
       t_2
       (*
        z
        (+
         (/ x t_1)
         (-
          (fma (/ a z) (/ (+ y t) t_1) (/ y t_1))
          (* (/ b t_1) (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_2 <= 2e+282) {
		tmp = t_2;
	} else {
		tmp = z * ((x / t_1) + (fma((a / z), ((y + t) / t_1), (y / t_1)) - ((b / t_1) * (y / z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_2 <= 2e+282)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(fma(Float64(a / z), Float64(Float64(y + t) / t_1), Float64(y / t_1)) - Float64(Float64(b / t_1) * Float64(y / z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 2e+282], t$95$2, N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(N[(a / z), $MachinePrecision] * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(b / t$95$1), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 73.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000007e282

   1. Initial program 99.1%

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

   if 2.00000000000000007e282 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.1%

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

   3. Taylor expanded in z around inf 32.9%

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

      1. associate--l+ 32.9%

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

      2. associate-+r+ 32.9%

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

      3. +-commutative 32.9%

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

      4. times-frac 60.4%

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

      5. fma-define 60.4%

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

      6. associate-+r+ 60.4%

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

      7. associate-+r+ 60.4%

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

      8. *-commutative 60.4%

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

   5. Simplified 81.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{y + \left(x + t\right)}, \frac{y}{y + \left(x + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x + y}\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + y} + \left(t\_1 + \left(\frac{a}{z} \cdot t\_1 - t\_1 \cdot \frac{b}{z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (+ x y)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (<= t_2 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_2 5e+246)
       t_2
       (* z (+ (/ x (+ x y)) (+ t_1 (- (* (/ a z) t_1) (* t_1 (/ b z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (x + y);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_2 <= 5e+246) {
		tmp = t_2;
	} else {
		tmp = z * ((x / (x + y)) + (t_1 + (((a / z) * t_1) - (t_1 * (b / z)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (x + y);
	double t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + a) - b;
	} else if (t_2 <= 5e+246) {
		tmp = t_2;
	} else {
		tmp = z * ((x / (x + y)) + (t_1 + (((a / z) * t_1) - (t_1 * (b / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y / (x + y)
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z + a) - b
	elif t_2 <= 5e+246:
		tmp = t_2
	else:
		tmp = z * ((x / (x + y)) + (t_1 + (((a / z) * t_1) - (t_1 * (b / z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(x + y))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_2 <= 5e+246)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(Float64(x / Float64(x + y)) + Float64(t_1 + Float64(Float64(Float64(a / z) * t_1) - Float64(t_1 * Float64(b / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y / (x + y);
	t_2 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z + a) - b;
	elseif (t_2 <= 5e+246)
		tmp = t_2;
	else
		tmp = z * ((x / (x + y)) + (t_1 + (((a / z) * t_1) - (t_1 * (b / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 5e+246], t$95$2, N[(z * N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(N[(N[(a / z), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(t$95$1 * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   3. Taylor expanded in y around inf 73.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999976e246

   1. Initial program 99.1%

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

   if 4.99999999999999976e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.2%

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

   3. Taylor expanded in z around inf 36.4%

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

      1. associate--l+ 36.4%

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

      2. associate-+r+ 36.4%

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

      3. +-commutative 36.4%

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

      4. times-frac 62.4%

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

      5. fma-define 62.4%

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

      6. associate-+r+ 62.4%

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

      7. associate-+r+ 62.4%

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

      8. *-commutative 62.4%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 40.0%

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

      1. associate--l+ 40.0%

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

      2. associate--l+ 40.0%

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

      3. times-frac 53.8%

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

      4. times-frac 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+246}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + y} + \left(\frac{y}{x + y} + \left(\frac{a}{z} \cdot \frac{y}{x + y} - \frac{y}{x + y} \cdot \frac{b}{z}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+245}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+245))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+245)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+245)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+245):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+245))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+245)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+245]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000004e245 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.8%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000004e245

   1. Initial program 99.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+245}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.4e-21)
     t_1
     (if (<= y 3.5e-86)
       (* z (+ (/ x (+ x t)) (* (/ a z) (/ t (+ x t)))))
       (if (<= y 4e+31)
         (/ (+ (* (+ x y) z) (* (+ y t) a)) (+ y (+ 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 <= -1.4e-21) {
		tmp = t_1;
	} else if (y <= 3.5e-86) {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	} else if (y <= 4e+31) {
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (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 <= (-1.4d-21)) then
        tmp = t_1
    else if (y <= 3.5d-86) then
        tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
    else if (y <= 4d+31) then
        tmp = (((x + y) * z) + ((y + t) * a)) / (y + (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 <= -1.4e-21) {
		tmp = t_1;
	} else if (y <= 3.5e-86) {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	} else if (y <= 4e+31) {
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (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 <= -1.4e-21:
		tmp = t_1
	elif y <= 3.5e-86:
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
	elif y <= 4e+31:
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (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 <= -1.4e-21)
		tmp = t_1;
	elseif (y <= 3.5e-86)
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(a / z) * Float64(t / Float64(x + t)))));
	elseif (y <= 4e+31)
		tmp = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(y + t) * a)) / Float64(y + 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 <= -1.4e-21)
		tmp = t_1;
	elseif (y <= 3.5e-86)
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	elseif (y <= 4e+31)
		tmp = (((x + y) * z) + ((y + t) * a)) / (y + (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, -1.4e-21], t$95$1, If[LessEqual[y, 3.5e-86], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+31], N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.40000000000000002e-21 or 3.9999999999999999e31 < y

   1. Initial program 39.2%

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

   3. Taylor expanded in y around inf 78.3%

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

   if -1.40000000000000002e-21 < y < 3.50000000000000021e-86

   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. Add Preprocessing

   3. Taylor expanded in z around inf 76.7%

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

      1. associate--l+ 76.7%

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

      2. associate-+r+ 76.7%

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

      3. +-commutative 76.7%

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

      4. times-frac 85.5%

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

      5. fma-define 85.5%

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

      6. associate-+r+ 85.5%

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

      7. associate-+r+ 85.5%

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

      8. *-commutative 85.5%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in y around 0 64.7%

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

      1. times-frac 76.1%

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

   8. Simplified 76.1%

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

   if 3.50000000000000021e-86 < y < 3.9999999999999999e31

   1. Initial program 90.3%

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

   3. Taylor expanded in b around 0 77.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-24} \lor \neg \left(y \leq 2.5 \cdot 10^{+47}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e-24) (not (<= y 2.5e+47)))
   (- (+ z a) b)
   (* z (+ (/ x (+ x t)) (* (/ a z) (/ t (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-24) || !(y <= 2.5e+47)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d-24)) .or. (.not. (y <= 2.5d+47))) then
        tmp = (z + a) - b
    else
        tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-24) || !(y <= 2.5e+47)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e-24) or not (y <= 2.5e+47):
		tmp = (z + a) - b
	else:
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e-24) || !(y <= 2.5e+47))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(a / z) * Float64(t / Float64(x + t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e-24) || ~((y <= 2.5e+47)))
		tmp = (z + a) - b;
	else
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e-24], N[Not[LessEqual[y, 2.5e+47]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000003e-24 or 2.50000000000000011e47 < y

   1. Initial program 39.5%

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

   3. Taylor expanded in y around inf 78.9%

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

   if -1.35000000000000003e-24 < y < 2.50000000000000011e47

   1. Initial program 79.2%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. associate--l+ 80.3%

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

      2. associate-+r+ 80.3%

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

      3. +-commutative 80.3%

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

      4. times-frac 87.3%

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

      5. fma-define 87.3%

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

      6. associate-+r+ 87.3%

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

      7. associate-+r+ 87.3%

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

      8. *-commutative 87.3%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in y around 0 60.9%

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

      1. times-frac 70.5%

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

   8. Simplified 70.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-24} \lor \neg \left(y \leq 2.5 \cdot 10^{+47}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-28} \lor \neg \left(y \leq 4.25 \cdot 10^{-91}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e-28) (not (<= y 4.25e-91)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e-28) || !(y <= 4.25e-91)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.3d-28)) .or. (.not. (y <= 4.25d-91))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (x * z)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e-28) || !(y <= 4.25e-91)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e-28) or not (y <= 4.25e-91):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e-28) || !(y <= 4.25e-91))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e-28) || ~((y <= 4.25e-91)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e-28], N[Not[LessEqual[y, 4.25e-91]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-28 or 4.24999999999999992e-91 < y

   1. Initial program 49.0%

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

   3. Taylor expanded in y around inf 71.5%

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

   if -1.3e-28 < y < 4.24999999999999992e-91

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 62.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-28} \lor \neg \left(y \leq 4.25 \cdot 10^{-91}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-13} \lor \neg \left(y \leq 4.15 \cdot 10^{+46}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.8e-13) (not (<= y 4.15e+46)))
   (- (+ z a) b)
   (* z (/ (+ x y) (+ y (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e-13) || !(y <= 4.15e+46)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (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) :: tmp
    if ((y <= (-6.8d-13)) .or. (.not. (y <= 4.15d+46))) then
        tmp = (z + a) - b
    else
        tmp = z * ((x + y) / (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 tmp;
	if ((y <= -6.8e-13) || !(y <= 4.15e+46)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.8e-13) or not (y <= 4.15e+46):
		tmp = (z + a) - b
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.8e-13) || !(y <= 4.15e+46))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.8e-13) || ~((y <= 4.15e+46)))
		tmp = (z + a) - b;
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.8e-13], N[Not[LessEqual[y, 4.15e+46]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.80000000000000031e-13 or 4.14999999999999976e46 < y

   1. Initial program 38.9%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -6.80000000000000031e-13 < y < 4.14999999999999976e46

   1. Initial program 79.4%

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

   3. Taylor expanded in z around inf 38.4%

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

      1. associate-/l* 49.6%

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

      2. +-commutative 49.6%

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

      3. associate-+r+ 49.6%

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

   5. Simplified 49.6%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-13} \lor \neg \left(y \leq 4.15 \cdot 10^{+46}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+183} \lor \neg \left(x \leq 6.8 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -9e+183) (not (<= x 6.8e+105)))
   (* z (/ x (+ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9e+183) || !(x <= 6.8e+105)) {
		tmp = z * (x / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-9d+183)) .or. (.not. (x <= 6.8d+105))) then
        tmp = z * (x / (x + t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9e+183) || !(x <= 6.8e+105)) {
		tmp = z * (x / (x + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -9e+183) or not (x <= 6.8e+105):
		tmp = z * (x / (x + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -9e+183) || !(x <= 6.8e+105))
		tmp = Float64(z * Float64(x / Float64(x + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -9e+183) || ~((x <= 6.8e+105)))
		tmp = z * (x / (x + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -9e+183], N[Not[LessEqual[x, 6.8e+105]], $MachinePrecision]], N[(z * N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.00000000000000034e183 or 6.7999999999999999e105 < x

   1. Initial program 51.5%

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

   3. Taylor expanded in z around inf 77.4%

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

      1. associate--l+ 77.4%

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

      2. associate-+r+ 77.4%

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

      3. +-commutative 77.4%

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

      4. times-frac 82.1%

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

      5. fma-define 82.1%

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

      6. associate-+r+ 82.1%

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

      7. associate-+r+ 82.1%

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

      8. *-commutative 82.1%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in y around 0 73.0%

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

      1. times-frac 78.9%

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

   8. Simplified 78.9%

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

   9. Taylor expanded in a around 0 69.0%

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

   if -9.00000000000000034e183 < x < 6.7999999999999999e105

   1. Initial program 65.2%

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

   3. Taylor expanded in y around inf 59.4%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+183} \lor \neg \left(x \leq 6.8 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+191}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.2e+191) z (if (<= x 3.2e+105) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+191) {
		tmp = z;
	} else if (x <= 3.2e+105) {
		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 <= (-9.2d+191)) then
        tmp = z
    else if (x <= 3.2d+105) 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 <= -9.2e+191) {
		tmp = z;
	} else if (x <= 3.2e+105) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.2e+191:
		tmp = z
	elif x <= 3.2e+105:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.2e+191)
		tmp = z;
	elseif (x <= 3.2e+105)
		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 <= -9.2e+191)
		tmp = z;
	elseif (x <= 3.2e+105)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.2e+191], z, If[LessEqual[x, 3.2e+105], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -9.1999999999999997e191 or 3.2e105 < x

   1. Initial program 51.5%

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

   3. Taylor expanded in x around inf 66.0%

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

   if -9.1999999999999997e191 < x < 3.2e105

   1. Initial program 65.2%

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

   3. Taylor expanded in y around inf 59.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+191}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 0.006:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.5e-130) z (if (<= z 0.006) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e-130) {
		tmp = z;
	} else if (z <= 0.006) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.5d-130)) then
        tmp = z
    else if (z <= 0.006d0) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e-130) {
		tmp = z;
	} else if (z <= 0.006) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.5e-130:
		tmp = z
	elif z <= 0.006:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.5e-130)
		tmp = z;
	elseif (z <= 0.006)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.5e-130)
		tmp = z;
	elseif (z <= 0.006)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.5e-130], z, If[LessEqual[z, 0.006], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999998e-130 or 0.0060000000000000001 < z

   1. Initial program 59.0%

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

   3. Taylor expanded in x around inf 54.3%

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

   if -2.4999999999999998e-130 < z < 0.0060000000000000001

   1. Initial program 66.6%

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

   3. Taylor expanded in t around inf 48.8%

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

Alternative 11: 32.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.7%

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

3. Taylor expanded in t around inf 30.6%

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

Developer Target 1: 83.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

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