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

Percentage Accurate: 60.2% → 88.7%

Time: 15.1s

Alternatives: 17

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.2% 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: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \left(y + t\right) + x\\ t_3 := \left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{t\_2} + z \cdot \frac{y + x}{t\_2}}{b}, \frac{y}{t\_2}\right)\\ t_4 := z \cdot \left(y + x\right)\\ t_5 := \frac{\left(t\_4 + t\_1\right) - b \cdot y}{y + \left(t + x\right)}\\ t_6 := t + \left(y + x\right)\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\left(\frac{t\_1}{t\_6} + \frac{t\_4}{t\_6}\right) - \frac{b \cdot y}{t\_6}\\ \mathbf{elif}\;t\_5 \leq \infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ (+ y t) x))
        (t_3
         (*
          (- b)
          (fma
           -1.0
           (/ (+ (* a (/ (+ y t) t_2)) (* z (/ (+ y x) t_2))) b)
           (/ y t_2))))
        (t_4 (* z (+ y x)))
        (t_5 (/ (- (+ t_4 t_1) (* b y)) (+ y (+ t x))))
        (t_6 (+ t (+ y x))))
   (if (<= t_5 (- INFINITY))
     t_3
     (if (<= t_5 2e+288)
       (- (+ (/ t_1 t_6) (/ t_4 t_6)) (/ (* b y) t_6))
       (if (<= t_5 INFINITY) (- (+ a z) b) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = (y + t) + x;
	double t_3 = -b * fma(-1.0, (((a * ((y + t) / t_2)) + (z * ((y + x) / t_2))) / b), (y / t_2));
	double t_4 = z * (y + x);
	double t_5 = ((t_4 + t_1) - (b * y)) / (y + (t + x));
	double t_6 = t + (y + x);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_5 <= 2e+288) {
		tmp = ((t_1 / t_6) + (t_4 / t_6)) - ((b * y) / t_6);
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(y + t) + x)
	t_3 = Float64(Float64(-b) * fma(-1.0, Float64(Float64(Float64(a * Float64(Float64(y + t) / t_2)) + Float64(z * Float64(Float64(y + x) / t_2))) / b), Float64(y / t_2)))
	t_4 = Float64(z * Float64(y + x))
	t_5 = Float64(Float64(Float64(t_4 + t_1) - Float64(b * y)) / Float64(y + Float64(t + x)))
	t_6 = Float64(t + Float64(y + x))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_5 <= 2e+288)
		tmp = Float64(Float64(Float64(t_1 / t_6) + Float64(t_4 / t_6)) - Float64(Float64(b * y) / t_6));
	elseif (t_5 <= Inf)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$3 = N[((-b) * N[(-1.0 * N[(N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$3, If[LessEqual[t$95$5, 2e+288], N[(N[(N[(t$95$1 / t$95$6), $MachinePrecision] + N[(t$95$4 / t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 4.4%

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

   3. Taylor expanded in b around -inf 21.7%

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

      1. associate-*r* 21.7%

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

      2. neg-mul-1 21.7%

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

      3. fma-define 21.7%

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

   5. Simplified 81.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e288

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 99.8%

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

   if 2e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < +inf.0

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 78.9%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\left(\frac{a \cdot \left(y + t\right)}{t + \left(y + x\right)} + \frac{z \cdot \left(y + x\right)}{t + \left(y + x\right)}\right) - \frac{b \cdot y}{t + \left(y + x\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq \infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := t + \left(y + x\right)\\ t_3 := z \cdot \left(y + x\right)\\ t_4 := \frac{\left(t\_3 + t\_1\right) - b \cdot y}{y + \left(t + x\right)}\\ t_5 := \left(y + t\right) + x\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(z, \frac{y + x}{b \cdot t\_5}, \frac{y + t}{t\_5} \cdot \frac{a}{b}\right) - \frac{y}{t\_5}\right)\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\left(\frac{t\_1}{t\_2} + \frac{t\_3}{t\_2}\right) - \frac{b \cdot y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ t (+ y x)))
        (t_3 (* z (+ y x)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) (+ y (+ t x))))
        (t_5 (+ (+ y t) x)))
   (if (<= t_4 (- INFINITY))
     (*
      b
      (- (fma z (/ (+ y x) (* b t_5)) (* (/ (+ y t) t_5) (/ a b))) (/ y t_5)))
     (if (<= t_4 2e+288)
       (- (+ (/ t_1 t_2) (/ t_3 t_2)) (/ (* b y) t_2))
       (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = t + (y + x);
	double t_3 = z * (y + x);
	double t_4 = ((t_3 + t_1) - (b * y)) / (y + (t + x));
	double t_5 = (y + t) + x;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = b * (fma(z, ((y + x) / (b * t_5)), (((y + t) / t_5) * (a / b))) - (y / t_5));
	} else if (t_4 <= 2e+288) {
		tmp = ((t_1 / t_2) + (t_3 / t_2)) - ((b * y) / t_2);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(t + Float64(y + x))
	t_3 = Float64(z * Float64(y + x))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / Float64(y + Float64(t + x)))
	t_5 = Float64(Float64(y + t) + x)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(b * Float64(fma(z, Float64(Float64(y + x) / Float64(b * t_5)), Float64(Float64(Float64(y + t) / t_5) * Float64(a / b))) - Float64(y / t_5)));
	elseif (t_4 <= 2e+288)
		tmp = Float64(Float64(Float64(t_1 / t_2) + Float64(t_3 / t_2)) - Float64(Float64(b * y) / t_2));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(b * N[(N[(z * N[(N[(y + x), $MachinePrecision] / N[(b * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] / t$95$5), $MachinePrecision] * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+288], N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] + N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.2%

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

   3. Taylor expanded in b around inf 28.6%

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

      1. +-commutative 28.6%

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

      2. mul-1-neg 28.6%

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

      3. unsub-neg 28.6%

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

   5. Simplified 65.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e288

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 99.8%

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

   if 2e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 74.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(z, \frac{y + x}{b \cdot \left(\left(y + t\right) + x\right)}, \frac{y + t}{\left(y + t\right) + x} \cdot \frac{a}{b}\right) - \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\left(\frac{a \cdot \left(y + t\right)}{t + \left(y + x\right)} + \frac{z \cdot \left(y + x\right)}{t + \left(y + x\right)}\right) - \frac{b \cdot y}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \frac{y}{t\_1}\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{-57} \lor \neg \left(b \leq 1.25 \cdot 10^{-114}\right):\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{t\_1} + z \cdot \frac{y + x}{t\_1}}{b}, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\mathsf{fma}\left(z, \frac{y + x}{a \cdot t\_1}, t\_2\right) - \frac{\frac{b \cdot y}{a}}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (/ y t_1)))
   (if (or (<= b -4.4e-57) (not (<= b 1.25e-114)))
     (*
      (- b)
      (fma -1.0 (/ (+ (* a (/ (+ y t) t_1)) (* z (/ (+ y x) t_1))) b) t_2))
     (*
      a
      (+
       (/ t t_1)
       (- (fma z (/ (+ y x) (* a t_1)) t_2) (/ (/ (* b y) a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = y / t_1;
	double tmp;
	if ((b <= -4.4e-57) || !(b <= 1.25e-114)) {
		tmp = -b * fma(-1.0, (((a * ((y + t) / t_1)) + (z * ((y + x) / t_1))) / b), t_2);
	} else {
		tmp = a * ((t / t_1) + (fma(z, ((y + x) / (a * t_1)), t_2) - (((b * y) / a) / t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if ((b <= -4.4e-57) || !(b <= 1.25e-114))
		tmp = Float64(Float64(-b) * fma(-1.0, Float64(Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(y + x) / t_1))) / b), t_2));
	else
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(fma(z, Float64(Float64(y + x) / Float64(a * t_1)), t_2) - Float64(Float64(Float64(b * y) / a) / t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[b, -4.4e-57], N[Not[LessEqual[b, 1.25e-114]], $MachinePrecision]], N[((-b) * N[(-1.0 * N[(N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(z * N[(N[(y + x), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(N[(N[(b * y), $MachinePrecision] / a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.39999999999999997e-57 or 1.24999999999999997e-114 < b

   1. Initial program 60.2%

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

   3. Taylor expanded in b around -inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. neg-mul-1 67.3%

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

      3. fma-define 67.3%

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

   5. Simplified 95.2%

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

   if -4.39999999999999997e-57 < b < 1.24999999999999997e-114

   1. Initial program 63.5%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. associate--l+ 75.0%

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

      2. +-commutative 75.0%

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

      3. associate-+r+ 75.0%

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

   5. Simplified 85.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-57} \lor \neg \left(b \leq 1.25 \cdot 10^{-114}\right):\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{\left(y + t\right) + x} + \left(\mathsf{fma}\left(z, \frac{y + x}{a \cdot \left(\left(y + t\right) + x\right)}, \frac{y}{\left(y + t\right) + x}\right) - \frac{\frac{b \cdot y}{a}}{\left(y + t\right) + x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := t + \left(y + x\right)\\ t_3 := z \cdot \left(y + x\right)\\ t_4 := \frac{\left(t\_3 + t\_1\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_4 \leq -\infty \lor \neg \left(t\_4 \leq 2 \cdot 10^{+288}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t\_1}{t\_2} + \frac{t\_3}{t\_2}\right) - \frac{b \cdot y}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ t (+ y x)))
        (t_3 (* z (+ y x)))
        (t_4 (/ (- (+ t_3 t_1) (* b y)) (+ y (+ t x)))))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 2e+288)))
     (- (+ a z) b)
     (- (+ (/ t_1 t_2) (/ t_3 t_2)) (/ (* b y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = t + (y + x);
	double t_3 = z * (y + x);
	double t_4 = ((t_3 + t_1) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 2e+288)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((t_1 / t_2) + (t_3 / t_2)) - ((b * y) / t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = t + (y + x);
	double t_3 = z * (y + x);
	double t_4 = ((t_3 + t_1) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 2e+288)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((t_1 / t_2) + (t_3 / t_2)) - ((b * y) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = t + (y + x)
	t_3 = z * (y + x)
	t_4 = ((t_3 + t_1) - (b * y)) / (y + (t + x))
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 2e+288):
		tmp = (a + z) - b
	else:
		tmp = ((t_1 / t_2) + (t_3 / t_2)) - ((b * y) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(t + Float64(y + x))
	t_3 = Float64(z * Float64(y + x))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(b * y)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 2e+288))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(t_1 / t_2) + Float64(t_3 / t_2)) - Float64(Float64(b * y) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = t + (y + x);
	t_3 = z * (y + x);
	t_4 = ((t_3 + t_1) - (b * y)) / (y + (t + x));
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 2e+288)))
		tmp = (a + z) - b;
	else
		tmp = ((t_1 / t_2) + (t_3 / t_2)) - ((b * y) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 2e+288]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] + N[(t$95$3 / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / t$95$2), $MachinePrecision]), $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 2e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.3%

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

   3. Taylor expanded in y around inf 67.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e288

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 99.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot y}{t + \left(x + y\right)} + \left(\frac{a \cdot \left(t + y\right)}{t + \left(x + y\right)} + \frac{z \cdot \left(x + y\right)}{t + \left(x + y\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+288}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a \cdot \left(y + t\right)}{t + \left(y + x\right)} + \frac{z \cdot \left(y + x\right)}{t + \left(y + x\right)}\right) - \frac{b \cdot y}{t + \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := z \cdot \left(y + x\right)\\ t_3 := \frac{\left(t\_2 + t\_1\right) - b \cdot y}{y + \left(t + x\right)}\\ t_4 := t + \left(y + x\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_4} + \left(\left(\frac{y}{t\_4} + a \cdot \frac{y + t}{z \cdot t\_4}\right) - \frac{b \cdot \frac{y}{z}}{t\_4}\right)\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\left(\frac{t\_1}{t\_4} + \frac{t\_2}{t\_4}\right) - \frac{b \cdot y}{t\_4}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (* z (+ y x)))
        (t_3 (/ (- (+ t_2 t_1) (* b y)) (+ y (+ t x))))
        (t_4 (+ t (+ y x))))
   (if (<= t_3 (- INFINITY))
     (*
      z
      (+
       (/ x t_4)
       (- (+ (/ y t_4) (* a (/ (+ y t) (* z t_4)))) (/ (* b (/ y z)) t_4))))
     (if (<= t_3 2e+288)
       (- (+ (/ t_1 t_4) (/ t_2 t_4)) (/ (* b y) t_4))
       (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = z * (y + x);
	double t_3 = ((t_2 + t_1) - (b * y)) / (y + (t + x));
	double t_4 = t + (y + x);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = z * ((x / t_4) + (((y / t_4) + (a * ((y + t) / (z * t_4)))) - ((b * (y / z)) / t_4)));
	} else if (t_3 <= 2e+288) {
		tmp = ((t_1 / t_4) + (t_2 / t_4)) - ((b * y) / t_4);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = z * (y + x);
	double t_3 = ((t_2 + t_1) - (b * y)) / (y + (t + x));
	double t_4 = t + (y + x);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / t_4) + (((y / t_4) + (a * ((y + t) / (z * t_4)))) - ((b * (y / z)) / t_4)));
	} else if (t_3 <= 2e+288) {
		tmp = ((t_1 / t_4) + (t_2 / t_4)) - ((b * y) / t_4);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = z * (y + x)
	t_3 = ((t_2 + t_1) - (b * y)) / (y + (t + x))
	t_4 = t + (y + x)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = z * ((x / t_4) + (((y / t_4) + (a * ((y + t) / (z * t_4)))) - ((b * (y / z)) / t_4)))
	elif t_3 <= 2e+288:
		tmp = ((t_1 / t_4) + (t_2 / t_4)) - ((b * y) / t_4)
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(z * Float64(y + x))
	t_3 = Float64(Float64(Float64(t_2 + t_1) - Float64(b * y)) / Float64(y + Float64(t + x)))
	t_4 = Float64(t + Float64(y + x))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / t_4) + Float64(Float64(Float64(y / t_4) + Float64(a * Float64(Float64(y + t) / Float64(z * t_4)))) - Float64(Float64(b * Float64(y / z)) / t_4))));
	elseif (t_3 <= 2e+288)
		tmp = Float64(Float64(Float64(t_1 / t_4) + Float64(t_2 / t_4)) - Float64(Float64(b * y) / t_4));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = z * (y + x);
	t_3 = ((t_2 + t_1) - (b * y)) / (y + (t + x));
	t_4 = t + (y + x);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = z * ((x / t_4) + (((y / t_4) + (a * ((y + t) / (z * t_4)))) - ((b * (y / z)) / t_4)));
	elseif (t_3 <= 2e+288)
		tmp = ((t_1 / t_4) + (t_2 / t_4)) - ((b * y) / t_4);
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(z * N[(N[(x / t$95$4), $MachinePrecision] + N[(N[(N[(y / t$95$4), $MachinePrecision] + N[(a * N[(N[(y + t), $MachinePrecision] / N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(y / z), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+288], N[(N[(N[(t$95$1 / t$95$4), $MachinePrecision] + N[(t$95$2 / t$95$4), $MachinePrecision]), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.2%

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

      1. fma-define 6.2%

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

      2. +-commutative 6.2%

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

      3. associate-+l+ 6.2%

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

      4. +-commutative 6.2%

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

   3. Simplified 6.2%

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

   5. Taylor expanded in z around inf 5.9%

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

   6. Taylor expanded in z around inf 44.0%

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

      1. associate--l+ 44.0%

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

      2. +-commutative 44.0%

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

      3. +-commutative 44.0%

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

      4. associate-/l* 60.0%

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

      5. +-commutative 60.0%

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

      6. +-commutative 60.0%

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

      7. associate-/r* 55.3%

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

      8. associate-/l* 63.1%

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

      9. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e288

   1. Initial program 99.7%

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

   3. Taylor expanded in b around 0 99.8%

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

   if 2e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

   3. Taylor expanded in y around inf 74.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{t + \left(y + x\right)} + \left(\left(\frac{y}{t + \left(y + x\right)} + a \cdot \frac{y + t}{z \cdot \left(t + \left(y + x\right)\right)}\right) - \frac{b \cdot \frac{y}{z}}{t + \left(y + x\right)}\right)\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\left(\frac{a \cdot \left(y + t\right)}{t + \left(y + x\right)} + \frac{z \cdot \left(y + x\right)}{t + \left(y + x\right)}\right) - \frac{b \cdot y}{t + \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+288}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* b y)) (+ y (+ t x)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+288))) (- (+ a z) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+288)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+288)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / (y + (t + x))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+288):
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(b * y)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+288))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (y + x)) + (a * (y + t))) - (b * y)) / (y + (t + x));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+288)))
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+288]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.3%

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

   3. Taylor expanded in y around inf 67.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e288

   1. Initial program 99.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+288}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -2 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{a \cdot t + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (- (+ a z) b)))
   (if (<= y -2e-42)
     t_2
     (if (<= y -3.4e-201)
       (* z (/ (+ y x) t_1))
       (if (<= y 1.5e-146)
         (/ (+ (* a t) (* x z)) (+ t x))
         (if (<= y 2.15e-50) (* a (/ (+ y t) t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -2e-42) {
		tmp = t_2;
	} else if (y <= -3.4e-201) {
		tmp = z * ((y + x) / t_1);
	} else if (y <= 1.5e-146) {
		tmp = ((a * t) + (x * z)) / (t + x);
	} else if (y <= 2.15e-50) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + t) + x
    t_2 = (a + z) - b
    if (y <= (-2d-42)) then
        tmp = t_2
    else if (y <= (-3.4d-201)) then
        tmp = z * ((y + x) / t_1)
    else if (y <= 1.5d-146) then
        tmp = ((a * t) + (x * z)) / (t + x)
    else if (y <= 2.15d-50) then
        tmp = a * ((y + t) / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -2e-42) {
		tmp = t_2;
	} else if (y <= -3.4e-201) {
		tmp = z * ((y + x) / t_1);
	} else if (y <= 1.5e-146) {
		tmp = ((a * t) + (x * z)) / (t + x);
	} else if (y <= 2.15e-50) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) + x
	t_2 = (a + z) - b
	tmp = 0
	if y <= -2e-42:
		tmp = t_2
	elif y <= -3.4e-201:
		tmp = z * ((y + x) / t_1)
	elif y <= 1.5e-146:
		tmp = ((a * t) + (x * z)) / (t + x)
	elif y <= 2.15e-50:
		tmp = a * ((y + t) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -2e-42)
		tmp = t_2;
	elseif (y <= -3.4e-201)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif (y <= 1.5e-146)
		tmp = Float64(Float64(Float64(a * t) + Float64(x * z)) / Float64(t + x));
	elseif (y <= 2.15e-50)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) + x;
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (y <= -2e-42)
		tmp = t_2;
	elseif (y <= -3.4e-201)
		tmp = z * ((y + x) / t_1);
	elseif (y <= 1.5e-146)
		tmp = ((a * t) + (x * z)) / (t + x);
	elseif (y <= 2.15e-50)
		tmp = a * ((y + t) / 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[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2e-42], t$95$2, If[LessEqual[y, -3.4e-201], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-146], N[(N[(N[(a * t), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-50], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000008e-42 or 2.14999999999999999e-50 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in y around inf 65.2%

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

   if -2.00000000000000008e-42 < y < -3.39999999999999985e-201

   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 z around inf 49.6%

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

      1. associate-/l* 65.6%

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

      2. +-commutative 65.6%

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

      3. +-commutative 65.6%

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

      4. associate-+r+ 65.6%

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

   5. Simplified 65.6%

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

   if -3.39999999999999985e-201 < y < 1.50000000000000009e-146

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0 74.2%

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

   if 1.50000000000000009e-146 < y < 2.14999999999999999e-50

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 56.4%

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

      1. associate-/l* 71.4%

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

      2. +-commutative 71.4%

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

      3. +-commutative 71.4%

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

      4. associate-+r+ 71.4%

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

   5. Simplified 71.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-42}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \frac{y + x}{\left(y + t\right) + x}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{a \cdot t + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(y + t\right) + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right)}{t\_1} - \frac{b \cdot y}{t\_1}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{z}{t + x} + a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))) (t_2 (- (+ a z) b)))
   (if (<= y -8.2e+102)
     t_2
     (if (<= y -7.5e-41)
       (- (/ (* a (+ y t)) t_1) (/ (* b y) t_1))
       (if (<= y 1.06e+91) (+ (* x (/ z (+ t x))) (* a (/ t (+ t x)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -8.2e+102) {
		tmp = t_2;
	} else if (y <= -7.5e-41) {
		tmp = ((a * (y + t)) / t_1) - ((b * y) / t_1);
	} else if (y <= 1.06e+91) {
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	} 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 = t + (y + x)
    t_2 = (a + z) - b
    if (y <= (-8.2d+102)) then
        tmp = t_2
    else if (y <= (-7.5d-41)) then
        tmp = ((a * (y + t)) / t_1) - ((b * y) / t_1)
    else if (y <= 1.06d+91) then
        tmp = (x * (z / (t + x))) + (a * (t / (t + x)))
    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 = t + (y + x);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -8.2e+102) {
		tmp = t_2;
	} else if (y <= -7.5e-41) {
		tmp = ((a * (y + t)) / t_1) - ((b * y) / t_1);
	} else if (y <= 1.06e+91) {
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = (a + z) - b
	tmp = 0
	if y <= -8.2e+102:
		tmp = t_2
	elif y <= -7.5e-41:
		tmp = ((a * (y + t)) / t_1) - ((b * y) / t_1)
	elif y <= 1.06e+91:
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -8.2e+102)
		tmp = t_2;
	elseif (y <= -7.5e-41)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) / t_1) - Float64(Float64(b * y) / t_1));
	elseif (y <= 1.06e+91)
		tmp = Float64(Float64(x * Float64(z / Float64(t + x))) + Float64(a * Float64(t / Float64(t + x))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (y <= -8.2e+102)
		tmp = t_2;
	elseif (y <= -7.5e-41)
		tmp = ((a * (y + t)) / t_1) - ((b * y) / t_1);
	elseif (y <= 1.06e+91)
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.2e+102], t$95$2, If[LessEqual[y, -7.5e-41], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(b * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+91], N[(N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999999e102 or 1.05999999999999996e91 < y

   1. Initial program 36.0%

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

   3. Taylor expanded in y around inf 81.6%

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

   if -8.1999999999999999e102 < y < -7.50000000000000049e-41

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. +-commutative 65.1%

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

      3. associate-+r+ 65.1%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in z around 0 56.4%

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

   if -7.50000000000000049e-41 < y < 1.05999999999999996e91

   1. Initial program 77.4%

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

   3. Taylor expanded in b around -inf 66.7%

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

      1. associate-*r* 66.7%

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

      2. neg-mul-1 66.7%

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

      3. fma-define 66.7%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around 0 53.5%

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

      1. +-commutative 53.5%

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

      2. associate-/l* 58.6%

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

      3. +-commutative 58.6%

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

   8. Simplified 58.6%

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

      1. associate-/l* 70.1%

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

   10. Applied egg-rr 70.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+102}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right)}{t + \left(y + x\right)} - \frac{b \cdot y}{t + \left(y + x\right)}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{z}{t + x} + a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{z}{t + x} + a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -8.2e+102)
     t_1
     (if (<= y -1.05e-40)
       (/ (- (* a (+ y t)) (* b y)) (+ y (+ t x)))
       (if (<= y 7.5e+93) (+ (* x (/ z (+ t x))) (* a (/ t (+ t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -8.2e+102) {
		tmp = t_1;
	} else if (y <= -1.05e-40) {
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x));
	} else if (y <= 7.5e+93) {
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	} 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 + z) - b
    if (y <= (-8.2d+102)) then
        tmp = t_1
    else if (y <= (-1.05d-40)) then
        tmp = ((a * (y + t)) - (b * y)) / (y + (t + x))
    else if (y <= 7.5d+93) then
        tmp = (x * (z / (t + x))) + (a * (t / (t + x)))
    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 + z) - b;
	double tmp;
	if (y <= -8.2e+102) {
		tmp = t_1;
	} else if (y <= -1.05e-40) {
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x));
	} else if (y <= 7.5e+93) {
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -8.2e+102:
		tmp = t_1
	elif y <= -1.05e-40:
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x))
	elif y <= 7.5e+93:
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -8.2e+102)
		tmp = t_1;
	elseif (y <= -1.05e-40)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(b * y)) / Float64(y + Float64(t + x)));
	elseif (y <= 7.5e+93)
		tmp = Float64(Float64(x * Float64(z / Float64(t + x))) + Float64(a * Float64(t / Float64(t + x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -8.2e+102)
		tmp = t_1;
	elseif (y <= -1.05e-40)
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x));
	elseif (y <= 7.5e+93)
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.2e+102], t$95$1, If[LessEqual[y, -1.05e-40], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+93], N[(N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999999e102 or 7.5000000000000002e93 < y

   1. Initial program 36.0%

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

   3. Taylor expanded in y around inf 81.6%

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

   if -8.1999999999999999e102 < y < -1.05000000000000009e-40

   1. Initial program 65.9%

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

   3. Taylor expanded in z around 0 56.3%

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

      1. +-commutative 56.3%

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

      2. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   if -1.05000000000000009e-40 < y < 7.5000000000000002e93

   1. Initial program 77.4%

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

   3. Taylor expanded in b around -inf 66.7%

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

      1. associate-*r* 66.7%

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

      2. neg-mul-1 66.7%

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

      3. fma-define 66.7%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around 0 53.5%

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

      1. +-commutative 53.5%

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

      2. associate-/l* 58.6%

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

      3. +-commutative 58.6%

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

   8. Simplified 58.6%

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

      1. associate-/l* 70.1%

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

   10. Applied egg-rr 70.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+102}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{z}{t + x} + a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+67} \lor \neg \left(y \leq 4 \cdot 10^{+91}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t + x} + a \cdot \frac{t}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e+67) (not (<= y 4e+91)))
   (- (+ a z) b)
   (+ (* x (/ z (+ t x))) (* a (/ t (+ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e+67) || !(y <= 4e+91)) {
		tmp = (a + z) - b;
	} else {
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.4d+67)) .or. (.not. (y <= 4d+91))) then
        tmp = (a + z) - b
    else
        tmp = (x * (z / (t + x))) + (a * (t / (t + x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e+67) || !(y <= 4e+91)) {
		tmp = (a + z) - b;
	} else {
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.4e+67) or not (y <= 4e+91):
		tmp = (a + z) - b
	else:
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.4e+67) || !(y <= 4e+91))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(x * Float64(z / Float64(t + x))) + Float64(a * Float64(t / Float64(t + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.4e+67) || ~((y <= 4e+91)))
		tmp = (a + z) - b;
	else
		tmp = (x * (z / (t + x))) + (a * (t / (t + x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.4e+67], N[Not[LessEqual[y, 4e+91]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000002e67 or 4.00000000000000032e91 < y

   1. Initial program 37.9%

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

   3. Taylor expanded in y around inf 77.1%

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

   if -2.40000000000000002e67 < y < 4.00000000000000032e91

   1. Initial program 76.7%

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

   3. Taylor expanded in b around -inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. neg-mul-1 66.9%

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

      3. fma-define 66.9%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around 0 50.2%

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

      1. +-commutative 50.2%

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

      2. associate-/l* 54.5%

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

      3. +-commutative 54.5%

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

   8. Simplified 54.5%

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

      1. associate-/l* 66.0%

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

   10. Applied egg-rr 66.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+67} \lor \neg \left(y \leq 4 \cdot 10^{+91}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t + x} + a \cdot \frac{t}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+177} \lor \neg \left(x \leq 3.8 \cdot 10^{+45}\right):\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.9e+177) (not (<= x 3.8e+45)))
   (* z (/ x (+ t x)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.9e+177) || !(x <= 3.8e+45)) {
		tmp = z * (x / (t + x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-2.9d+177)) .or. (.not. (x <= 3.8d+45))) then
        tmp = z * (x / (t + x))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.9e+177) || !(x <= 3.8e+45)) {
		tmp = z * (x / (t + x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.9e+177) or not (x <= 3.8e+45):
		tmp = z * (x / (t + x))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.9e+177) || !(x <= 3.8e+45))
		tmp = Float64(z * Float64(x / Float64(t + x)));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.9e+177) || ~((x <= 3.8e+45)))
		tmp = z * (x / (t + x));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.9e+177], N[Not[LessEqual[x, 3.8e+45]], $MachinePrecision]], N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000013e177 or 3.8000000000000002e45 < x

   1. Initial program 46.7%

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

   3. Taylor expanded in z around inf 23.5%

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

      1. associate-/l* 57.2%

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

      2. +-commutative 57.2%

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

      3. +-commutative 57.2%

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

      4. associate-+r+ 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in y around 0 57.2%

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

   if -2.90000000000000013e177 < x < 3.8000000000000002e45

   1. Initial program 66.9%

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

   3. Taylor expanded in y around inf 65.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+177} \lor \neg \left(x \leq 3.8 \cdot 10^{+45}\right):\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+83} \lor \neg \left(t \leq 3.1 \cdot 10^{+84}\right):\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.9e+83) (not (<= t 3.1e+84)))
   (* a (/ t (+ t x)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.9e+83) || !(t <= 3.1e+84)) {
		tmp = a * (t / (t + x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.9d+83)) .or. (.not. (t <= 3.1d+84))) then
        tmp = a * (t / (t + x))
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.9e+83) || !(t <= 3.1e+84)) {
		tmp = a * (t / (t + x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.9e+83) or not (t <= 3.1e+84):
		tmp = a * (t / (t + x))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.9e+83) || !(t <= 3.1e+84))
		tmp = Float64(a * Float64(t / Float64(t + x)));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.9e+83) || ~((t <= 3.1e+84)))
		tmp = a * (t / (t + x));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.9e+83], N[Not[LessEqual[t, 3.1e+84]], $MachinePrecision]], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9000000000000001e83 or 3.10000000000000003e84 < t

   1. Initial program 55.3%

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

   3. Taylor expanded in z around 0 42.6%

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

      1. +-commutative 42.6%

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

      2. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around 0 35.5%

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

      1. associate-/l* 56.0%

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

   8. Simplified 56.0%

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

   if -1.9000000000000001e83 < t < 3.10000000000000003e84

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf 67.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+83} \lor \neg \left(t \leq 3.1 \cdot 10^{+84}\right):\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(y + t\right) + x}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+84}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+83)
   (* a (/ (+ y t) (+ (+ y t) x)))
   (if (<= t 2.8e+84) (- (+ a z) b) (* a (/ t (+ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+83) {
		tmp = a * ((y + t) / ((y + t) + x));
	} else if (t <= 2.8e+84) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6d+83)) then
        tmp = a * ((y + t) / ((y + t) + x))
    else if (t <= 2.8d+84) then
        tmp = (a + z) - b
    else
        tmp = a * (t / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+83) {
		tmp = a * ((y + t) / ((y + t) + x));
	} else if (t <= 2.8e+84) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+83:
		tmp = a * ((y + t) / ((y + t) + x))
	elif t <= 2.8e+84:
		tmp = (a + z) - b
	else:
		tmp = a * (t / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+83)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(Float64(y + t) + x)));
	elseif (t <= 2.8e+84)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a * Float64(t / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6e+83)
		tmp = a * ((y + t) / ((y + t) + x));
	elseif (t <= 2.8e+84)
		tmp = (a + z) - b;
	else
		tmp = a * (t / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+83], N[(a * N[(N[(y + t), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+84], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.9999999999999999e83

   1. Initial program 56.7%

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

   3. Taylor expanded in a around inf 39.7%

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

      1. associate-/l* 62.9%

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

      2. +-commutative 62.9%

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

      3. +-commutative 62.9%

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

      4. associate-+r+ 62.9%

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

   5. Simplified 62.9%

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

   if -5.9999999999999999e83 < t < 2.79999999999999982e84

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf 67.4%

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

   if 2.79999999999999982e84 < t

   1. Initial program 53.6%

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

   3. Taylor expanded in z around 0 38.3%

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

      1. +-commutative 38.3%

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

      2. *-commutative 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in y around 0 30.3%

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

      1. associate-/l* 49.9%

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

   8. Simplified 49.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \frac{y + t}{\left(y + t\right) + x}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+84}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+83}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+97}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.16e+83) a (if (<= t 7.2e+97) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.16e+83) {
		tmp = a;
	} else if (t <= 7.2e+97) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.16d+83)) then
        tmp = a
    else if (t <= 7.2d+97) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.16e+83) {
		tmp = a;
	} else if (t <= 7.2e+97) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.16e+83:
		tmp = a
	elif t <= 7.2e+97:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.16e+83)
		tmp = a;
	elseif (t <= 7.2e+97)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.16e+83)
		tmp = a;
	elseif (t <= 7.2e+97)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.16e+83], a, If[LessEqual[t, 7.2e+97], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1600000000000001e83 or 7.19999999999999932e97 < t

   1. Initial program 55.9%

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

   3. Taylor expanded in t around inf 51.6%

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

   if -1.1600000000000001e83 < t < 7.19999999999999932e97

   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 66.8%

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

Alternative 15: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+85}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -165000.0) z (if (<= z 1.6e+85) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -165000.0) {
		tmp = z;
	} else if (z <= 1.6e+85) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-165000.0d0)) then
        tmp = z
    else if (z <= 1.6d+85) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -165000.0) {
		tmp = z;
	} else if (z <= 1.6e+85) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -165000.0:
		tmp = z
	elif z <= 1.6e+85:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -165000.0)
		tmp = z;
	elseif (z <= 1.6e+85)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -165000.0)
		tmp = z;
	elseif (z <= 1.6e+85)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -165000.0], z, If[LessEqual[z, 1.6e+85], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -165000 or 1.60000000000000009e85 < z

   1. Initial program 48.3%

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

   3. Taylor expanded in x around inf 56.2%

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

   if -165000 < z < 1.60000000000000009e85

   1. Initial program 70.5%

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

   3. Taylor expanded in z around 0 57.9%

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

      1. +-commutative 57.9%

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

      2. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in y around inf 50.7%

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

Alternative 16: 44.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1780000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1780000.0) z (if (<= z 3.3e-37) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1780000.0) {
		tmp = z;
	} else if (z <= 3.3e-37) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1780000.0d0)) then
        tmp = z
    else if (z <= 3.3d-37) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1780000.0) {
		tmp = z;
	} else if (z <= 3.3e-37) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1780000.0:
		tmp = z
	elif z <= 3.3e-37:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1780000.0)
		tmp = z;
	elseif (z <= 3.3e-37)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1780000.0)
		tmp = z;
	elseif (z <= 3.3e-37)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1780000.0], z, If[LessEqual[z, 3.3e-37], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.78e6 or 3.29999999999999982e-37 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in x around inf 52.3%

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

   if -1.78e6 < z < 3.29999999999999982e-37

   1. Initial program 70.3%

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

   3. Taylor expanded in t around inf 50.7%

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

Alternative 17: 31.9% 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 61.4%

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

3. Taylor expanded in t around inf 36.2%

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

Developer Target 1: 82.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024148 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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