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

Percentage Accurate: 61.2% → 96.1%

Time: 16.7s

Alternatives: 15

Speedup: 1.1×

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: 61.2% 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: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(a + z \cdot \left(\frac{x}{t\_1} + \frac{y}{t\_1}\right)\right) - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 4e+290)))
     (- (+ a (* z (+ (/ x t_1) (/ y t_1)))) (* y (/ b (+ x (+ y t)))))
     (/ (+ (* t a) (+ (* x z) (* y (- (+ z a) b)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 4e+290)) {
		tmp = (a + (z * ((x / t_1) + (y / t_1)))) - (y * (b / (x + (y + t))));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 4e+290)) {
		tmp = (a + (z * ((x / t_1) + (y / t_1)))) - (y * (b / (x + (y + t))));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = y + (x + t)
	t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 4e+290):
		tmp = (a + (z * ((x / t_1) + (y / t_1)))) - (y * (b / (x + (y + t))))
	else:
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 4e+290))
		tmp = Float64(Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1)))) - Float64(y * Float64(b / Float64(x + Float64(y + t)))));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * Float64(Float64(z + a) - b)))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = y + (x + t);
	t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 4e+290)))
		tmp = (a + (z * ((x / t_1) + (y / t_1)))) - (y * (b / (x + (y + t))));
	else
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 4e+290]], $MachinePrecision]], N[(N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.00000000000000025e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in z around 0 37.2%

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

      1. associate-/l* 53.3%

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

      2. add-sqr-sqrt 26.5%

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

      3. sqrt-unprod 31.5%

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

      4. sqr-neg 31.5%

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

      5. sqrt-unprod 18.3%

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

      6. add-sqr-sqrt 38.1%

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

      7. associate-+r+ 38.1%

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

      8. clear-num 38.1%

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

      9. inv-pow 38.1%

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

      10. associate-+r+ 38.1%

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

      11. +-commutative 38.1%

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

      12. add-sqr-sqrt 18.3%

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

      13. sqrt-unprod 31.5%

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

      14. sqr-neg 31.5%

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

      15. sqrt-unprod 26.5%

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

      16. add-sqr-sqrt 53.2%

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

   5. Applied egg-rr 53.2%

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

   6. Taylor expanded in b around 0 37.2%

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

      1. associate-/l* 53.3%

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

      2. +-commutative 53.3%

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

      3. associate-/r/ 53.3%

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

      4. associate-+r+ 53.3%

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

      5. +-commutative 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in t around inf 92.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000025e290

   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. Taylor expanded in y around 0 99.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(a + z \cdot \left(\frac{x}{\left(x + y\right) + t} + \frac{y}{\left(x + y\right) + t}\right)\right) - y \cdot \frac{b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 5 \cdot 10^{+295}\right):\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}} + \left(x + y\right) \cdot \frac{z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 5e+295)))
     (+ (/ a (/ t_1 (+ y t))) (* (+ x y) (/ z t_1)))
     (/ (+ (* t a) (+ (* x z) (* y (- (+ z a) b)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 5e+295)) {
		tmp = (a / (t_1 / (y + t))) + ((x + y) * (z / t_1));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y + (x + t);
	double t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 5e+295)) {
		tmp = (a / (t_1 / (y + t))) + ((x + y) * (z / t_1));
	} else {
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + t
	t_2 = y + (x + t)
	t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 5e+295):
		tmp = (a / (t_1 / (y + t))) + ((x + y) * (z / t_1))
	else:
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 5e+295))
		tmp = Float64(Float64(a / Float64(t_1 / Float64(y + t))) + Float64(Float64(x + y) * Float64(z / t_1)));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * Float64(Float64(z + a) - b)))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + t;
	t_2 = y + (x + t);
	t_3 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 5e+295)))
		tmp = (a / (t_1 / (y + t))) + ((x + y) * (z / t_1));
	else
		tmp = ((t * a) + ((x * z) + (y * ((z + a) - b)))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 5e+295]], $MachinePrecision]], N[(N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.99999999999999991e295 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.7%

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

   3. Taylor expanded in b around 0 5.2%

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

   4. Taylor expanded in a around inf 5.2%

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

      1. associate-/l* 36.9%

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

      2. +-commutative 36.9%

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

      3. +-commutative 36.9%

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

      4. +-commutative 36.9%

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

      5. associate-/l* 81.1%

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

      6. +-commutative 81.1%

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

      7. +-commutative 81.1%

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

      8. associate-/r/ 81.1%

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

      9. +-commutative 81.1%

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

      10. +-commutative 81.1%

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

      11. +-commutative 81.1%

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

   6. Simplified 81.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999991e295

   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. Taylor expanded in y around 0 99.2%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+295}\right):\\ \;\;\;\;\frac{a}{\frac{\left(x + y\right) + t}{y + t}} + \left(x + y\right) \cdot \frac{z}{\left(x + y\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_3\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 4e+290)))
     t_3
     (/ (+ (* t a) (+ (* x z) (* y t_3))) t_1))))

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) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 4e+290)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 4e+290)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (z + a) - b
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 4e+290):
		tmp = t_3
	else:
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1
	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(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 4e+290))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_3))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (z + a) - b;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 4e+290)))
		tmp = t_3;
	else
		tmp = ((t * a) + ((x * z) + (y * t_3))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 4e+290]], $MachinePrecision]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.00000000000000025e290 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in y around inf 70.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000025e290

   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. Taylor expanded in y around 0 99.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+290}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-150}:\\ \;\;\;\;\frac{\left(t \cdot a + y \cdot a\right) + \left(x + y\right) \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y)))) (t_2 (- (+ z a) b)))
   (if (<= y -1.15e+135)
     t_2
     (if (<= y -1.45e-124)
       t_1
       (if (<= y 1.55e-150)
         (/ (+ (+ (* t a) (* y a)) (* (+ x y) z)) (+ y (+ x t)))
         (if (<= y 1.8e+78) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.15e+135) {
		tmp = t_2;
	} else if (y <= -1.45e-124) {
		tmp = t_1;
	} else if (y <= 1.55e-150) {
		tmp = (((t * a) + (y * a)) + ((x + y) * z)) / (y + (x + t));
	} else if (y <= 1.8e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    if (y <= (-1.15d+135)) then
        tmp = t_2
    else if (y <= (-1.45d-124)) then
        tmp = t_1
    else if (y <= 1.55d-150) then
        tmp = (((t * a) + (y * a)) + ((x + y) * z)) / (y + (x + t))
    else if (y <= 1.8d+78) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.15e+135) {
		tmp = t_2;
	} else if (y <= -1.45e-124) {
		tmp = t_1;
	} else if (y <= 1.55e-150) {
		tmp = (((t * a) + (y * a)) + ((x + y) * z)) / (y + (x + t));
	} else if (y <= 1.8e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.15e+135:
		tmp = t_2
	elif y <= -1.45e-124:
		tmp = t_1
	elif y <= 1.55e-150:
		tmp = (((t * a) + (y * a)) + ((x + y) * z)) / (y + (x + t))
	elif y <= 1.8e+78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.15e+135)
		tmp = t_2;
	elseif (y <= -1.45e-124)
		tmp = t_1;
	elseif (y <= 1.55e-150)
		tmp = Float64(Float64(Float64(Float64(t * a) + Float64(y * a)) + Float64(Float64(x + y) * z)) / Float64(y + Float64(x + t)));
	elseif (y <= 1.8e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.15e+135)
		tmp = t_2;
	elseif (y <= -1.45e-124)
		tmp = t_1;
	elseif (y <= 1.55e-150)
		tmp = (((t * a) + (y * a)) + ((x + y) * z)) / (y + (x + t));
	elseif (y <= 1.8e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.15e+135], t$95$2, If[LessEqual[y, -1.45e-124], t$95$1, If[LessEqual[y, 1.55e-150], N[(N[(N[(N[(t * a), $MachinePrecision] + N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+78], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1500000000000001e135 or 1.8000000000000001e78 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 79.1%

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

   if -1.1500000000000001e135 < y < -1.4500000000000001e-124 or 1.54999999999999999e-150 < y < 1.8000000000000001e78

   1. Initial program 72.8%

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

   3. Taylor expanded in t around 0 57.4%

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

      1. associate--l+ 57.4%

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

      2. cancel-sign-sub-inv 57.4%

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

      3. *-commutative 57.4%

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

      4. *-commutative 57.4%

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

      5. +-commutative 57.4%

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

      6. associate-+r+ 57.4%

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

      7. *-commutative 57.4%

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

      8. distribute-rgt-in 57.4%

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

      9. sub-neg 57.4%

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

      10. *-commutative 57.4%

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

      11. +-commutative 57.4%

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

      12. +-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in z around 0 68.3%

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

   if -1.4500000000000001e-124 < y < 1.54999999999999999e-150

   1. Initial program 78.7%

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

   3. Taylor expanded in b around 0 68.7%

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

      1. distribute-rgt-in 68.7%

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

   5. Applied egg-rr 68.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-124}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-150}:\\ \;\;\;\;\frac{\left(t \cdot a + y \cdot a\right) + \left(x + y\right) \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+78}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-152}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + a \cdot \left(y + t\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y)))) (t_2 (- (+ z a) b)))
   (if (<= y -3.1e+134)
     t_2
     (if (<= y -1.9e-125)
       t_1
       (if (<= y 3.9e-152)
         (/ (+ (* (+ x y) z) (* a (+ y t))) (+ y (+ x t)))
         (if (<= y 1.55e+78) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -3.1e+134) {
		tmp = t_2;
	} else if (y <= -1.9e-125) {
		tmp = t_1;
	} else if (y <= 3.9e-152) {
		tmp = (((x + y) * z) + (a * (y + t))) / (y + (x + t));
	} else if (y <= 1.55e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    if (y <= (-3.1d+134)) then
        tmp = t_2
    else if (y <= (-1.9d-125)) then
        tmp = t_1
    else if (y <= 3.9d-152) then
        tmp = (((x + y) * z) + (a * (y + t))) / (y + (x + t))
    else if (y <= 1.55d+78) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -3.1e+134) {
		tmp = t_2;
	} else if (y <= -1.9e-125) {
		tmp = t_1;
	} else if (y <= 3.9e-152) {
		tmp = (((x + y) * z) + (a * (y + t))) / (y + (x + t));
	} else if (y <= 1.55e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -3.1e+134:
		tmp = t_2
	elif y <= -1.9e-125:
		tmp = t_1
	elif y <= 3.9e-152:
		tmp = (((x + y) * z) + (a * (y + t))) / (y + (x + t))
	elif y <= 1.55e+78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.1e+134)
		tmp = t_2;
	elseif (y <= -1.9e-125)
		tmp = t_1;
	elseif (y <= 3.9e-152)
		tmp = Float64(Float64(Float64(Float64(x + y) * z) + Float64(a * Float64(y + t))) / Float64(y + Float64(x + t)));
	elseif (y <= 1.55e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.1e+134)
		tmp = t_2;
	elseif (y <= -1.9e-125)
		tmp = t_1;
	elseif (y <= 3.9e-152)
		tmp = (((x + y) * z) + (a * (y + t))) / (y + (x + t));
	elseif (y <= 1.55e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.1e+134], t$95$2, If[LessEqual[y, -1.9e-125], t$95$1, If[LessEqual[y, 3.9e-152], N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+78], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999982e134 or 1.55e78 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 79.1%

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

   if -3.09999999999999982e134 < y < -1.9000000000000001e-125 or 3.9000000000000004e-152 < y < 1.55e78

   1. Initial program 72.8%

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

   3. Taylor expanded in t around 0 57.4%

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

      1. associate--l+ 57.4%

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

      2. cancel-sign-sub-inv 57.4%

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

      3. *-commutative 57.4%

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

      4. *-commutative 57.4%

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

      5. +-commutative 57.4%

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

      6. associate-+r+ 57.4%

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

      7. *-commutative 57.4%

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

      8. distribute-rgt-in 57.4%

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

      9. sub-neg 57.4%

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

      10. *-commutative 57.4%

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

      11. +-commutative 57.4%

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

      12. +-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in z around 0 68.3%

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

   if -1.9000000000000001e-125 < y < 3.9000000000000004e-152

   1. Initial program 78.7%

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

   3. Taylor expanded in b around 0 68.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-125}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-152}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + a \cdot \left(y + t\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+78}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (/ (* y (- a b)) (+ x y)))) (t_2 (- (+ z a) b)))
   (if (<= y -5.8e+136)
     t_2
     (if (<= y -6.5e-127)
       t_1
       (if (<= y 9.5e-158)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 1.65e+78) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -5.8e+136) {
		tmp = t_2;
	} else if (y <= -6.5e-127) {
		tmp = t_1;
	} else if (y <= 9.5e-158) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.65e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + ((y * (a - b)) / (x + y))
    t_2 = (z + a) - b
    if (y <= (-5.8d+136)) then
        tmp = t_2
    else if (y <= (-6.5d-127)) then
        tmp = t_1
    else if (y <= 9.5d-158) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 1.65d+78) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + ((y * (a - b)) / (x + y));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -5.8e+136) {
		tmp = t_2;
	} else if (y <= -6.5e-127) {
		tmp = t_1;
	} else if (y <= 9.5e-158) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 1.65e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + ((y * (a - b)) / (x + y))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -5.8e+136:
		tmp = t_2
	elif y <= -6.5e-127:
		tmp = t_1
	elif y <= 9.5e-158:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 1.65e+78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5.8e+136)
		tmp = t_2;
	elseif (y <= -6.5e-127)
		tmp = t_1;
	elseif (y <= 9.5e-158)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 1.65e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + ((y * (a - b)) / (x + y));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5.8e+136)
		tmp = t_2;
	elseif (y <= -6.5e-127)
		tmp = t_1;
	elseif (y <= 9.5e-158)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 1.65e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5.8e+136], t$95$2, If[LessEqual[y, -6.5e-127], t$95$1, If[LessEqual[y, 9.5e-158], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+78], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999949e136 or 1.65e78 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 79.1%

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

   if -5.79999999999999949e136 < y < -6.49999999999999998e-127 or 9.50000000000000051e-158 < y < 1.65e78

   1. Initial program 72.8%

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

   3. Taylor expanded in t around 0 57.4%

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

      1. associate--l+ 57.4%

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

      2. cancel-sign-sub-inv 57.4%

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

      3. *-commutative 57.4%

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

      4. *-commutative 57.4%

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

      5. +-commutative 57.4%

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

      6. associate-+r+ 57.4%

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

      7. *-commutative 57.4%

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

      8. distribute-rgt-in 57.4%

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

      9. sub-neg 57.4%

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

      10. *-commutative 57.4%

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

      11. +-commutative 57.4%

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

      12. +-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in z around 0 68.3%

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

   if -6.49999999999999998e-127 < y < 9.50000000000000051e-158

   1. Initial program 78.7%

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

   3. Taylor expanded in y around 0 61.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-127}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+78}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{\frac{x}{t} + 1}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;z - \frac{z \cdot t}{x}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ a (+ (/ x t) 1.0))))
   (if (<= t -2e+64)
     t_2
     (if (<= t 1.25e-184)
       t_1
       (if (<= t 1.3e-130)
         (- z (/ (* z t) x))
         (if (<= t 1.22e+202) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a / ((x / t) + 1.0);
	double tmp;
	if (t <= -2e+64) {
		tmp = t_2;
	} else if (t <= 1.25e-184) {
		tmp = t_1;
	} else if (t <= 1.3e-130) {
		tmp = z - ((z * t) / x);
	} else if (t <= 1.22e+202) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a / ((x / t) + 1.0d0)
    if (t <= (-2d+64)) then
        tmp = t_2
    else if (t <= 1.25d-184) then
        tmp = t_1
    else if (t <= 1.3d-130) then
        tmp = z - ((z * t) / x)
    else if (t <= 1.22d+202) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a / ((x / t) + 1.0);
	double tmp;
	if (t <= -2e+64) {
		tmp = t_2;
	} else if (t <= 1.25e-184) {
		tmp = t_1;
	} else if (t <= 1.3e-130) {
		tmp = z - ((z * t) / x);
	} else if (t <= 1.22e+202) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a / ((x / t) + 1.0)
	tmp = 0
	if t <= -2e+64:
		tmp = t_2
	elif t <= 1.25e-184:
		tmp = t_1
	elif t <= 1.3e-130:
		tmp = z - ((z * t) / x)
	elif t <= 1.22e+202:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a / Float64(Float64(x / t) + 1.0))
	tmp = 0.0
	if (t <= -2e+64)
		tmp = t_2;
	elseif (t <= 1.25e-184)
		tmp = t_1;
	elseif (t <= 1.3e-130)
		tmp = Float64(z - Float64(Float64(z * t) / x));
	elseif (t <= 1.22e+202)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a / ((x / t) + 1.0);
	tmp = 0.0;
	if (t <= -2e+64)
		tmp = t_2;
	elseif (t <= 1.25e-184)
		tmp = t_1;
	elseif (t <= 1.3e-130)
		tmp = z - ((z * t) / x);
	elseif (t <= 1.22e+202)
		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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(N[(x / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+64], t$95$2, If[LessEqual[t, 1.25e-184], t$95$1, If[LessEqual[t, 1.3e-130], N[(z - N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+202], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.00000000000000004e64 or 1.22e202 < t

   1. Initial program 45.4%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 68.2%

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

      2. associate-+r+ 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in t around inf 68.2%

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

   if -2.00000000000000004e64 < t < 1.25000000000000001e-184 or 1.3e-130 < t < 1.22e202

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 56.9%

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

   if 1.25000000000000001e-184 < t < 1.3e-130

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

      3. associate-/l* 63.1%

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

      4. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in y around 0 69.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+64}:\\ \;\;\;\;\frac{a}{\frac{x}{t} + 1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-184}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;z - \frac{z \cdot t}{x}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+202}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x}{t} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{\frac{x}{t} + 1}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x + y}\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (/ a (+ (/ x t) 1.0))))
   (if (<= t -5.6e+63)
     t_2
     (if (<= t 1.08e-184)
       t_1
       (if (<= t 2.5e-124)
         (* z (- 1.0 (/ t (+ x y))))
         (if (<= t 1.22e+202) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a / ((x / t) + 1.0);
	double tmp;
	if (t <= -5.6e+63) {
		tmp = t_2;
	} else if (t <= 1.08e-184) {
		tmp = t_1;
	} else if (t <= 2.5e-124) {
		tmp = z * (1.0 - (t / (x + y)));
	} else if (t <= 1.22e+202) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a / ((x / t) + 1.0d0)
    if (t <= (-5.6d+63)) then
        tmp = t_2
    else if (t <= 1.08d-184) then
        tmp = t_1
    else if (t <= 2.5d-124) then
        tmp = z * (1.0d0 - (t / (x + y)))
    else if (t <= 1.22d+202) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a / ((x / t) + 1.0);
	double tmp;
	if (t <= -5.6e+63) {
		tmp = t_2;
	} else if (t <= 1.08e-184) {
		tmp = t_1;
	} else if (t <= 2.5e-124) {
		tmp = z * (1.0 - (t / (x + y)));
	} else if (t <= 1.22e+202) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a / ((x / t) + 1.0)
	tmp = 0
	if t <= -5.6e+63:
		tmp = t_2
	elif t <= 1.08e-184:
		tmp = t_1
	elif t <= 2.5e-124:
		tmp = z * (1.0 - (t / (x + y)))
	elif t <= 1.22e+202:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a / Float64(Float64(x / t) + 1.0))
	tmp = 0.0
	if (t <= -5.6e+63)
		tmp = t_2;
	elseif (t <= 1.08e-184)
		tmp = t_1;
	elseif (t <= 2.5e-124)
		tmp = Float64(z * Float64(1.0 - Float64(t / Float64(x + y))));
	elseif (t <= 1.22e+202)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a / ((x / t) + 1.0);
	tmp = 0.0;
	if (t <= -5.6e+63)
		tmp = t_2;
	elseif (t <= 1.08e-184)
		tmp = t_1;
	elseif (t <= 2.5e-124)
		tmp = z * (1.0 - (t / (x + y)));
	elseif (t <= 1.22e+202)
		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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(N[(x / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+63], t$95$2, If[LessEqual[t, 1.08e-184], t$95$1, If[LessEqual[t, 2.5e-124], N[(z * N[(1.0 - N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+202], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.59999999999999974e63 or 1.22e202 < t

   1. Initial program 45.4%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-/l* 68.2%

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

      2. associate-+r+ 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in t around inf 68.2%

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

   if -5.59999999999999974e63 < t < 1.07999999999999995e-184 or 2.5000000000000001e-124 < t < 1.22e202

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 57.3%

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

   if 1.07999999999999995e-184 < t < 2.5000000000000001e-124

   1. Initial program 75.5%

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

   3. Taylor expanded in z around inf 49.3%

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

      1. +-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in t around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

      3. associate-/l* 58.8%

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

      4. +-commutative 58.8%

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

   8. Simplified 58.8%

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

   9. Taylor expanded in z around 0 64.1%

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

       1. +-commutative 64.1%

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

   11. Simplified 64.1%

       \[\leadsto \color{blue}{z \cdot \left(1 - \frac{t}{y + x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{a}{\frac{x}{t} + 1}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-184}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x + y}\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+202}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x}{t} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-124}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -5.6e+77)
     a
     (if (<= t 2.8e-184)
       t_1
       (if (<= t 2.35e-124) z (if (<= t 4.2e+203) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -5.6e+77) {
		tmp = a;
	} else if (t <= 2.8e-184) {
		tmp = t_1;
	} else if (t <= 2.35e-124) {
		tmp = z;
	} else if (t <= 4.2e+203) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-5.6d+77)) then
        tmp = a
    else if (t <= 2.8d-184) then
        tmp = t_1
    else if (t <= 2.35d-124) then
        tmp = z
    else if (t <= 4.2d+203) then
        tmp = t_1
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -5.6e+77) {
		tmp = a;
	} else if (t <= 2.8e-184) {
		tmp = t_1;
	} else if (t <= 2.35e-124) {
		tmp = z;
	} else if (t <= 4.2e+203) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -5.6e+77:
		tmp = a
	elif t <= 2.8e-184:
		tmp = t_1
	elif t <= 2.35e-124:
		tmp = z
	elif t <= 4.2e+203:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -5.6e+77)
		tmp = a;
	elseif (t <= 2.8e-184)
		tmp = t_1;
	elseif (t <= 2.35e-124)
		tmp = z;
	elseif (t <= 4.2e+203)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -5.6e+77)
		tmp = a;
	elseif (t <= 2.8e-184)
		tmp = t_1;
	elseif (t <= 2.35e-124)
		tmp = z;
	elseif (t <= 4.2e+203)
		tmp = t_1;
	else
		tmp = a;
	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[t, -5.6e+77], a, If[LessEqual[t, 2.8e-184], t$95$1, If[LessEqual[t, 2.35e-124], z, If[LessEqual[t, 4.2e+203], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.60000000000000001e77 or 4.19999999999999967e203 < t

   1. Initial program 45.0%

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

   3. Taylor expanded in t around inf 65.9%

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

   if -5.60000000000000001e77 < t < 2.7999999999999998e-184 or 2.35000000000000002e-124 < t < 4.19999999999999967e203

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 56.9%

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

   if 2.7999999999999998e-184 < t < 2.35000000000000002e-124

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 62.7%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-184}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-124}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+203}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+78}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;z - \frac{z \cdot t}{x}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= t -3.9e+78)
     a
     (if (<= t 1.95e-184)
       t_1
       (if (<= t 1.5e-130) (- z (/ (* z t) x)) (if (<= t 3.6e+204) t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -3.9e+78) {
		tmp = a;
	} else if (t <= 1.95e-184) {
		tmp = t_1;
	} else if (t <= 1.5e-130) {
		tmp = z - ((z * t) / x);
	} else if (t <= 3.6e+204) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (t <= (-3.9d+78)) then
        tmp = a
    else if (t <= 1.95d-184) then
        tmp = t_1
    else if (t <= 1.5d-130) then
        tmp = z - ((z * t) / x)
    else if (t <= 3.6d+204) then
        tmp = t_1
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (t <= -3.9e+78) {
		tmp = a;
	} else if (t <= 1.95e-184) {
		tmp = t_1;
	} else if (t <= 1.5e-130) {
		tmp = z - ((z * t) / x);
	} else if (t <= 3.6e+204) {
		tmp = t_1;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if t <= -3.9e+78:
		tmp = a
	elif t <= 1.95e-184:
		tmp = t_1
	elif t <= 1.5e-130:
		tmp = z - ((z * t) / x)
	elif t <= 3.6e+204:
		tmp = t_1
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t <= -3.9e+78)
		tmp = a;
	elseif (t <= 1.95e-184)
		tmp = t_1;
	elseif (t <= 1.5e-130)
		tmp = Float64(z - Float64(Float64(z * t) / x));
	elseif (t <= 3.6e+204)
		tmp = t_1;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (t <= -3.9e+78)
		tmp = a;
	elseif (t <= 1.95e-184)
		tmp = t_1;
	elseif (t <= 1.5e-130)
		tmp = z - ((z * t) / x);
	elseif (t <= 3.6e+204)
		tmp = t_1;
	else
		tmp = a;
	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[t, -3.9e+78], a, If[LessEqual[t, 1.95e-184], t$95$1, If[LessEqual[t, 1.5e-130], N[(z - N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+204], t$95$1, a]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9000000000000004e78 or 3.6000000000000002e204 < t

   1. Initial program 45.0%

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

   3. Taylor expanded in t around inf 65.9%

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

   if -3.9000000000000004e78 < t < 1.94999999999999997e-184 or 1.49999999999999993e-130 < t < 3.6000000000000002e204

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 56.6%

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

   if 1.94999999999999997e-184 < t < 1.49999999999999993e-130

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

      3. associate-/l* 63.1%

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

      4. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in y around 0 69.3%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+78}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-184}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;z - \frac{z \cdot t}{x}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+204}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{x}{t} + 1}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 27500:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+201}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (+ (/ x t) 1.0))))
   (if (<= t -3.8e+79)
     t_1
     (if (<= t 27500.0)
       (+ z (/ (* y (- a b)) (+ x y)))
       (if (<= t 9.5e+201) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((x / t) + 1.0);
	double tmp;
	if (t <= -3.8e+79) {
		tmp = t_1;
	} else if (t <= 27500.0) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (t <= 9.5e+201) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / ((x / t) + 1.0d0)
    if (t <= (-3.8d+79)) then
        tmp = t_1
    else if (t <= 27500.0d0) then
        tmp = z + ((y * (a - b)) / (x + y))
    else if (t <= 9.5d+201) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((x / t) + 1.0);
	double tmp;
	if (t <= -3.8e+79) {
		tmp = t_1;
	} else if (t <= 27500.0) {
		tmp = z + ((y * (a - b)) / (x + y));
	} else if (t <= 9.5e+201) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / ((x / t) + 1.0)
	tmp = 0
	if t <= -3.8e+79:
		tmp = t_1
	elif t <= 27500.0:
		tmp = z + ((y * (a - b)) / (x + y))
	elif t <= 9.5e+201:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(Float64(x / t) + 1.0))
	tmp = 0.0
	if (t <= -3.8e+79)
		tmp = t_1;
	elseif (t <= 27500.0)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / Float64(x + y)));
	elseif (t <= 9.5e+201)
		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 = a / ((x / t) + 1.0);
	tmp = 0.0;
	if (t <= -3.8e+79)
		tmp = t_1;
	elseif (t <= 27500.0)
		tmp = z + ((y * (a - b)) / (x + y));
	elseif (t <= 9.5e+201)
		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[(a / N[(N[(x / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+79], t$95$1, If[LessEqual[t, 27500.0], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+201], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e79 or 9.5000000000000002e201 < t

   1. Initial program 44.2%

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

   3. Taylor expanded in a around inf 32.1%

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

      1. associate-/l* 68.3%

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

      2. associate-+r+ 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around inf 68.3%

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

   if -3.8000000000000002e79 < t < 27500

   1. Initial program 68.7%

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

   3. Taylor expanded in t around 0 57.1%

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

      1. associate--l+ 57.1%

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

      2. cancel-sign-sub-inv 57.1%

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

      3. *-commutative 57.1%

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

      4. *-commutative 57.1%

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

      5. +-commutative 57.1%

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

      6. associate-+r+ 57.1%

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

      7. *-commutative 57.1%

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

      8. distribute-rgt-in 57.1%

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

      9. sub-neg 57.1%

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

      10. *-commutative 57.1%

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

      11. +-commutative 57.1%

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

      12. +-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in z around 0 71.8%

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

   if 27500 < t < 9.5000000000000002e201

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 55.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{a}{\frac{x}{t} + 1}\\ \mathbf{elif}\;t \leq 27500:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+201}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x}{t} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+36} \lor \neg \left(x \leq 1.12 \cdot 10^{+136}\right):\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -6e+36) (not (<= x 1.12e+136)))
   (+ z (/ y (/ x (- a b))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -6e+36) || !(x <= 1.12e+136)) {
		tmp = z + (y / (x / (a - b)));
	} 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 <= (-6d+36)) .or. (.not. (x <= 1.12d+136))) then
        tmp = z + (y / (x / (a - b)))
    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 <= -6e+36) || !(x <= 1.12e+136)) {
		tmp = z + (y / (x / (a - b)));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -6e+36) or not (x <= 1.12e+136):
		tmp = z + (y / (x / (a - b)))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -6e+36) || !(x <= 1.12e+136))
		tmp = Float64(z + Float64(y / Float64(x / Float64(a - b))));
	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 <= -6e+36) || ~((x <= 1.12e+136)))
		tmp = z + (y / (x / (a - b)));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -6e+36], N[Not[LessEqual[x, 1.12e+136]], $MachinePrecision]], N[(z + N[(y / N[(x / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6e36 or 1.12000000000000001e136 < x

   1. Initial program 59.9%

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

   3. Taylor expanded in t around 0 50.3%

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

      1. associate--l+ 50.3%

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

      2. cancel-sign-sub-inv 50.3%

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

      3. *-commutative 50.3%

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

      4. *-commutative 50.3%

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

      5. +-commutative 50.3%

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

      6. associate-+r+ 50.3%

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

      7. *-commutative 50.3%

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

      8. distribute-rgt-in 50.3%

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

      9. sub-neg 50.3%

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

      10. *-commutative 50.3%

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

      11. +-commutative 50.3%

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

      12. +-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around inf 62.7%

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

      1. associate-/l* 67.2%

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

   8. Simplified 67.2%

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

   if -6e36 < x < 1.12000000000000001e136

   1. Initial program 62.0%

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

   3. Taylor expanded in y around inf 62.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+36} \lor \neg \left(x \leq 1.12 \cdot 10^{+136}\right):\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.4e+68) a (if (<= t 3.2e+84) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+68) {
		tmp = a;
	} else if (t <= 3.2e+84) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.4d+68)) then
        tmp = a
    else if (t <= 3.2d+84) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+68) {
		tmp = a;
	} else if (t <= 3.2e+84) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.4e+68:
		tmp = a
	elif t <= 3.2e+84:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.4e+68)
		tmp = a;
	elseif (t <= 3.2e+84)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.4e+68)
		tmp = a;
	elseif (t <= 3.2e+84)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.4e+68], a, If[LessEqual[t, 3.2e+84], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e68 or 3.2000000000000001e84 < t

   1. Initial program 46.9%

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

   3. Taylor expanded in t around inf 57.2%

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

   if -1.4e68 < t < 3.2000000000000001e84

   1. Initial program 67.8%

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

   3. Taylor expanded in x around inf 45.0%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+84}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.55 \cdot 10^{+274}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 1.55e+274) (+ z a) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.55e+274) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.55d+274) then
        tmp = z + a
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.55e+274) {
		tmp = z + a;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.55e+274:
		tmp = z + a
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.55e+274)
		tmp = Float64(z + a);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.55e+274)
		tmp = z + a;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.55e+274], N[(z + a), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 1.55e274

   1. Initial program 62.5%

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

   3. Taylor expanded in b around 0 48.2%

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

   4. Taylor expanded in y around inf 50.3%

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

   if 1.55e274 < b

   1. Initial program 36.6%

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

   3. Taylor expanded in b around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. associate-/l* 84.8%

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

      3. distribute-neg-frac 84.8%

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

      4. associate-+r+ 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in y around inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot b} \]
   7. Step-by-step derivation

      1. mul-1-neg 55.3%

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

   8. Simplified 55.3%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.55 \cdot 10^{+274}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.0% 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 61.2%

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

3. Taylor expanded in t around inf 28.5%

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

4. Final simplification 28.5%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.4% 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 2024034 
(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)))