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

Percentage Accurate: 61.0% → 97.5%

Time: 14.6s

Alternatives: 15

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := a \cdot \frac{y + t}{t\_1} + z \cdot \frac{y + x}{t\_1}\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+43} \lor \neg \left(b \leq 10^{-9}\right):\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{t\_2}{b}, \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b \cdot y}{t\_1}, t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x))
        (t_2 (+ (* a (/ (+ y t) t_1)) (* z (/ (+ y x) t_1)))))
   (if (or (<= b -2.9e+43) (not (<= b 1e-9)))
     (* (- b) (fma -1.0 (/ t_2 b) (/ y t_1)))
     (fma -1.0 (/ (* b y) 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 * ((y + t) / t_1)) + (z * ((y + x) / t_1));
	double tmp;
	if ((b <= -2.9e+43) || !(b <= 1e-9)) {
		tmp = -b * fma(-1.0, (t_2 / b), (y / t_1));
	} else {
		tmp = fma(-1.0, ((b * y) / t_1), 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 * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(y + x) / t_1)))
	tmp = 0.0
	if ((b <= -2.9e+43) || !(b <= 1e-9))
		tmp = Float64(Float64(-b) * fma(-1.0, Float64(t_2 / b), Float64(y / t_1)));
	else
		tmp = fma(-1.0, Float64(Float64(b * y) / t_1), t_2);
	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[(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]}, If[Or[LessEqual[b, -2.9e+43], N[Not[LessEqual[b, 1e-9]], $MachinePrecision]], N[((-b) * N[(-1.0 * N[(t$95$2 / b), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.9000000000000002e43 or 1.00000000000000006e-9 < b

   1. Initial program 49.4%

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

   3. Taylor expanded in b around -inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. neg-mul-1 56.2%

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

      3. fma-define 56.2%

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

   5. Simplified 97.4%

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

   if -2.9000000000000002e43 < b < 1.00000000000000006e-9

   1. Initial program 62.4%

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

   3. Taylor expanded in b around 0 62.5%

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

      1. fma-define 62.5%

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

      2. *-commutative 62.5%

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

      3. +-commutative 62.5%

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

      4. associate-+r+ 62.5%

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

      5. associate-/l* 80.7%

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

      6. +-commutative 80.7%

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

      7. +-commutative 80.7%

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

      8. associate-+r+ 80.7%

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

      9. associate-/l* 98.9%

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

      10. +-commutative 98.9%

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

      11. +-commutative 98.9%

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

      12. associate-+r+ 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+43} \lor \neg \left(b \leq 10^{-9}\right):\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b \cdot y}{\left(y + t\right) + x}, a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \frac{y + t}{t\_1}\\ t_3 := \frac{y}{t\_1}\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - t\_3\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b \cdot y}{t\_1}, a \cdot t\_2 + z \cdot \frac{y + x}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(z, \frac{y + x}{b \cdot t\_1}, t\_2 \cdot \frac{a}{b}\right) - t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (/ (+ y t) t_1)) (t_3 (/ y t_1)))
   (if (<= b -5.6e+114)
     (* b (- (+ (/ a b) (/ z b)) t_3))
     (if (<= b 3.1e+137)
       (fma -1.0 (/ (* b y) t_1) (+ (* a t_2) (* z (/ (+ y x) t_1))))
       (* b (- (fma z (/ (+ y x) (* b t_1)) (* t_2 (/ a b))) t_3))))))

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) / t_1;
	double t_3 = y / t_1;
	double tmp;
	if (b <= -5.6e+114) {
		tmp = b * (((a / b) + (z / b)) - t_3);
	} else if (b <= 3.1e+137) {
		tmp = fma(-1.0, ((b * y) / t_1), ((a * t_2) + (z * ((y + x) / t_1))));
	} else {
		tmp = b * (fma(z, ((y + x) / (b * t_1)), (t_2 * (a / b))) - t_3);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(Float64(y + t) / t_1)
	t_3 = Float64(y / t_1)
	tmp = 0.0
	if (b <= -5.6e+114)
		tmp = Float64(b * Float64(Float64(Float64(a / b) + Float64(z / b)) - t_3));
	elseif (b <= 3.1e+137)
		tmp = fma(-1.0, Float64(Float64(b * y) / t_1), Float64(Float64(a * t_2) + Float64(z * Float64(Float64(y + x) / t_1))));
	else
		tmp = Float64(b * Float64(fma(z, Float64(Float64(y + x) / Float64(b * t_1)), Float64(t_2 * Float64(a / b))) - t_3));
	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[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[b, -5.6e+114], N[(b * N[(N[(N[(a / b), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e+137], N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(a * t$95$2), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(z * N[(N[(y + x), $MachinePrecision] / N[(b * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.6000000000000001e114

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 24.6%

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

      1. +-commutative 24.6%

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

      2. mul-1-neg 24.6%

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

      3. unsub-neg 24.6%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in y around inf 83.6%

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

   if -5.6000000000000001e114 < b < 3.0999999999999999e137

   1. Initial program 63.8%

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

   3. Taylor expanded in b around 0 63.8%

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

      1. fma-define 63.8%

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

      2. *-commutative 63.8%

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

      3. +-commutative 63.8%

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

      4. associate-+r+ 63.8%

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

      5. associate-/l* 79.2%

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

      6. +-commutative 79.2%

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

      7. +-commutative 79.2%

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

      8. associate-+r+ 79.2%

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

      9. associate-/l* 96.5%

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

      10. +-commutative 96.5%

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

      11. +-commutative 96.5%

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

      12. associate-+r+ 96.5%

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

   5. Simplified 96.5%

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

   if 3.0999999999999999e137 < b

   1. Initial program 40.5%

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

   3. Taylor expanded in b around inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

   5. Simplified 94.2%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b \cdot y}{\left(y + t\right) + x}, a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(z, \frac{y + x}{b \cdot \left(\left(y + t\right) + x\right)}, \frac{y + t}{\left(y + t\right) + x} \cdot \frac{a}{b}\right) - \frac{y}{\left(y + t\right) + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+115} \lor \neg \left(b \leq 3.1 \cdot 10^{+159}\right):\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b \cdot y}{t\_1}, a \cdot \frac{y + t}{t\_1} + z \cdot \frac{y + x}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)))
   (if (or (<= b -1.2e+115) (not (<= b 3.1e+159)))
     (* b (- (+ (/ a b) (/ z b)) (/ y t_1)))
     (fma
      -1.0
      (/ (* b y) t_1)
      (+ (* a (/ (+ y t) t_1)) (* z (/ (+ y x) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double tmp;
	if ((b <= -1.2e+115) || !(b <= 3.1e+159)) {
		tmp = b * (((a / b) + (z / b)) - (y / t_1));
	} else {
		tmp = fma(-1.0, ((b * y) / t_1), ((a * ((y + t) / t_1)) + (z * ((y + x) / t_1))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	tmp = 0.0
	if ((b <= -1.2e+115) || !(b <= 3.1e+159))
		tmp = Float64(b * Float64(Float64(Float64(a / b) + Float64(z / b)) - Float64(y / t_1)));
	else
		tmp = fma(-1.0, Float64(Float64(b * y) / t_1), Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(y + x) / 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]}, If[Or[LessEqual[b, -1.2e+115], N[Not[LessEqual[b, 3.1e+159]], $MachinePrecision]], N[(b * N[(N[(N[(a / b), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$1), $MachinePrecision] + 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]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e115 or 3.0999999999999998e159 < b

   1. Initial program 33.3%

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

   3. Taylor expanded in b around inf 34.8%

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

      1. +-commutative 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around inf 84.4%

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

   if -1.2e115 < b < 3.0999999999999998e159

   1. Initial program 64.0%

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

   3. Taylor expanded in b around 0 64.0%

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

      1. fma-define 64.0%

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

      2. *-commutative 64.0%

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

      3. +-commutative 64.0%

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

      4. associate-+r+ 64.0%

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

      5. associate-/l* 79.2%

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

      6. +-commutative 79.2%

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

      7. +-commutative 79.2%

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

      8. associate-+r+ 79.2%

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

      9. associate-/l* 96.2%

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

      10. +-commutative 96.2%

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

      11. +-commutative 96.2%

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

      12. associate-+r+ 96.2%

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

   5. Simplified 96.2%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+115} \lor \neg \left(b \leq 3.1 \cdot 10^{+159}\right):\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{b \cdot y}{\left(y + t\right) + x}, a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+222}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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+222))) (- (+ 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+222)) {
		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+222)) {
		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+222):
		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+222))
		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+222)))
		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+222]], $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 2.0000000000000001e222 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.7%

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

   3. Taylor expanded in y around inf 72.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e222

   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 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 2 \cdot 10^{+222}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+25} \lor \neg \left(b \leq 3.8 \cdot 10^{-63}\right):\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e+25) (not (<= b 3.8e-63)))
   (* b (- (+ (/ a b) (/ z b)) (/ y (+ (+ y t) x))))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+25) || !(b <= 3.8e-63)) {
		tmp = b * (((a / b) + (z / b)) - (y / ((y + 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 ((b <= (-6.5d+25)) .or. (.not. (b <= 3.8d-63))) then
        tmp = b * (((a / b) + (z / b)) - (y / ((y + 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 ((b <= -6.5e+25) || !(b <= 3.8e-63)) {
		tmp = b * (((a / b) + (z / b)) - (y / ((y + t) + x)));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.5e+25) or not (b <= 3.8e-63):
		tmp = b * (((a / b) + (z / b)) - (y / ((y + t) + x)))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.5e+25) || !(b <= 3.8e-63))
		tmp = Float64(b * Float64(Float64(Float64(a / b) + Float64(z / b)) - Float64(y / Float64(Float64(y + 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 ((b <= -6.5e+25) || ~((b <= 3.8e-63)))
		tmp = b * (((a / b) + (z / b)) - (y / ((y + t) + x)));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.5e+25], N[Not[LessEqual[b, 3.8e-63]], $MachinePrecision]], N[(b * N[(N[(N[(a / b), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.50000000000000005e25 or 3.80000000000000017e-63 < b

   1. Initial program 53.7%

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

   3. Taylor expanded in b around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in y around inf 77.1%

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

   if -6.50000000000000005e25 < b < 3.80000000000000017e-63

   1. Initial program 59.6%

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

   3. Taylor expanded in y around inf 66.4%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+25} \lor \neg \left(b \leq 3.8 \cdot 10^{-63}\right):\\ \;\;\;\;b \cdot \left(\left(\frac{a}{b} + \frac{z}{b}\right) - \frac{y}{\left(y + t\right) + x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-69} \lor \neg \left(y \leq 1.1 \cdot 10^{-145}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t + x} + \frac{x \cdot z}{a \cdot \left(t + x\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e-69) (not (<= y 1.1e-145)))
   (- (+ a z) b)
   (* a (+ (/ t (+ t x)) (/ (* x z) (* a (+ t x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e-69) || !(y <= 1.1e-145)) {
		tmp = (a + z) - b;
	} else {
		tmp = a * ((t / (t + x)) + ((x * z) / (a * (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 <= (-3.2d-69)) .or. (.not. (y <= 1.1d-145))) then
        tmp = (a + z) - b
    else
        tmp = a * ((t / (t + x)) + ((x * z) / (a * (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 <= -3.2e-69) || !(y <= 1.1e-145)) {
		tmp = (a + z) - b;
	} else {
		tmp = a * ((t / (t + x)) + ((x * z) / (a * (t + x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e-69) or not (y <= 1.1e-145):
		tmp = (a + z) - b
	else:
		tmp = a * ((t / (t + x)) + ((x * z) / (a * (t + x))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e-69) || !(y <= 1.1e-145))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a * Float64(Float64(t / Float64(t + x)) + Float64(Float64(x * z) / Float64(a * Float64(t + x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e-69) || ~((y <= 1.1e-145)))
		tmp = (a + z) - b;
	else
		tmp = a * ((t / (t + x)) + ((x * z) / (a * (t + x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e-69], N[Not[LessEqual[y, 1.1e-145]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(a * N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999999e-69 or 1.1e-145 < y

   1. Initial program 48.4%

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

   3. Taylor expanded in y around inf 69.9%

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

   if -3.19999999999999999e-69 < y < 1.1e-145

   1. Initial program 75.8%

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

   3. Taylor expanded in b around 0 75.8%

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

      1. fma-define 75.8%

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

      2. *-commutative 75.8%

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

      3. +-commutative 75.8%

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

      4. associate-+r+ 75.8%

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

      5. associate-/l* 90.5%

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

      6. +-commutative 90.5%

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

      7. +-commutative 90.5%

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

      8. associate-+r+ 90.5%

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

      9. associate-/l* 98.0%

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

      10. +-commutative 98.0%

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

      11. +-commutative 98.0%

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

      12. associate-+r+ 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in a around inf 77.2%

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

      1. fma-define 77.2%

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

      2. times-frac 71.0%

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

      3. times-frac 79.0%

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

   8. Simplified 79.0%

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

   9. Taylor expanded in y around 0 66.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-69} \lor \neg \left(y \leq 1.1 \cdot 10^{-145}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{t}{t + x} + \frac{x \cdot z}{a \cdot \left(t + x\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-227}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-166}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -7.6e+38)
     t_1
     (if (<= y -4.9e-227)
       (/ (- (* a (+ y t)) (* b y)) (+ y (+ t x)))
       (if (<= y 9.2e-166) (/ (+ (* x z) (* 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 <= -7.6e+38) {
		tmp = t_1;
	} else if (y <= -4.9e-227) {
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x));
	} else if (y <= 9.2e-166) {
		tmp = ((x * z) + (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 <= (-7.6d+38)) then
        tmp = t_1
    else if (y <= (-4.9d-227)) then
        tmp = ((a * (y + t)) - (b * y)) / (y + (t + x))
    else if (y <= 9.2d-166) then
        tmp = ((x * z) + (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 <= -7.6e+38) {
		tmp = t_1;
	} else if (y <= -4.9e-227) {
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x));
	} else if (y <= 9.2e-166) {
		tmp = ((x * z) + (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 <= -7.6e+38:
		tmp = t_1
	elif y <= -4.9e-227:
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x))
	elif y <= 9.2e-166:
		tmp = ((x * z) + (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 <= -7.6e+38)
		tmp = t_1;
	elseif (y <= -4.9e-227)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(b * y)) / Float64(y + Float64(t + x)));
	elseif (y <= 9.2e-166)
		tmp = Float64(Float64(Float64(x * z) + Float64(a * 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 <= -7.6e+38)
		tmp = t_1;
	elseif (y <= -4.9e-227)
		tmp = ((a * (y + t)) - (b * y)) / (y + (t + x));
	elseif (y <= 9.2e-166)
		tmp = ((x * z) + (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, -7.6e+38], t$95$1, If[LessEqual[y, -4.9e-227], 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, 9.2e-166], N[(N[(N[(x * z), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999996e38 or 9.19999999999999995e-166 < y

   1. Initial program 43.8%

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

   3. Taylor expanded in y around inf 71.4%

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

   if -7.5999999999999996e38 < y < -4.9000000000000002e-227

   1. Initial program 77.5%

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

   3. Taylor expanded in z around 0 58.4%

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

      1. +-commutative 58.4%

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

      2. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   if -4.9000000000000002e-227 < y < 9.19999999999999995e-166

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0 78.4%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+38}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-227}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-166}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-105} \lor \neg \left(y \leq 2.8 \cdot 10^{-153}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e-105) (not (<= y 2.8e-153)))
   (- (+ a z) b)
   (/ (+ (* x z) (* a t)) (+ t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e-105) || !(y <= 2.8e-153)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((x * z) + (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 <= (-1.3d-105)) .or. (.not. (y <= 2.8d-153))) then
        tmp = (a + z) - b
    else
        tmp = ((x * z) + (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 <= -1.3e-105) || !(y <= 2.8e-153)) {
		tmp = (a + z) - b;
	} else {
		tmp = ((x * z) + (a * t)) / (t + x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e-105) or not (y <= 2.8e-153):
		tmp = (a + z) - b
	else:
		tmp = ((x * z) + (a * t)) / (t + x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e-105) || !(y <= 2.8e-153))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(Float64(x * z) + Float64(a * t)) / Float64(t + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e-105) || ~((y <= 2.8e-153)))
		tmp = (a + z) - b;
	else
		tmp = ((x * z) + (a * t)) / (t + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e-105], N[Not[LessEqual[y, 2.8e-153]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(x * z), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e-105 or 2.8000000000000001e-153 < y

   1. Initial program 48.9%

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

   3. Taylor expanded in y around inf 68.4%

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

   if -1.2999999999999999e-105 < y < 2.8000000000000001e-153

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 67.2%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-105} \lor \neg \left(y \leq 2.8 \cdot 10^{-153}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+146} \lor \neg \left(t \leq 2.8 \cdot 10^{+156}\right):\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.6e+146) (not (<= t 2.8e+156)))
   (+ a (* y (/ (- z b) t)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.6e+146) || !(t <= 2.8e+156)) {
		tmp = a + (y * ((z - b) / t));
	} 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 <= (-3.6d+146)) .or. (.not. (t <= 2.8d+156))) then
        tmp = a + (y * ((z - b) / t))
    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 <= -3.6e+146) || !(t <= 2.8e+156)) {
		tmp = a + (y * ((z - b) / t));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.6e+146) or not (t <= 2.8e+156):
		tmp = a + (y * ((z - b) / t))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.6e+146) || !(t <= 2.8e+156))
		tmp = Float64(a + Float64(y * Float64(Float64(z - b) / t)));
	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 <= -3.6e+146) || ~((t <= 2.8e+156)))
		tmp = a + (y * ((z - b) / t));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.6e+146], N[Not[LessEqual[t, 2.8e+156]], $MachinePrecision]], N[(a + N[(y * N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5999999999999998e146 or 2.79999999999999988e156 < t

   1. Initial program 47.7%

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

   3. Taylor expanded in x around 0 38.3%

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

   4. Taylor expanded in y around 0 75.9%

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

   5. Taylor expanded in t around 0 75.9%

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

   if -3.5999999999999998e146 < t < 2.79999999999999988e156

   1. Initial program 59.3%

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

   3. Taylor expanded in y around inf 64.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+146} \lor \neg \left(t \leq 2.8 \cdot 10^{+156}\right):\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+145} \lor \neg \left(t \leq 3.9 \cdot 10^{+156}\right):\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e+145) (not (<= t 3.9e+156)))
   (+ a (* y (/ z t)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e+145) || !(t <= 3.9e+156)) {
		tmp = a + (y * (z / t));
	} 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 <= (-1.4d+145)) .or. (.not. (t <= 3.9d+156))) then
        tmp = a + (y * (z / t))
    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 <= -1.4e+145) || !(t <= 3.9e+156)) {
		tmp = a + (y * (z / t));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e+145) or not (t <= 3.9e+156):
		tmp = a + (y * (z / t))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e+145) || !(t <= 3.9e+156))
		tmp = Float64(a + Float64(y * Float64(z / t)));
	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 <= -1.4e+145) || ~((t <= 3.9e+156)))
		tmp = a + (y * (z / t));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e+145], N[Not[LessEqual[t, 3.9e+156]], $MachinePrecision]], N[(a + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e145 or 3.8999999999999997e156 < t

   1. Initial program 47.7%

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

   3. Taylor expanded in x around 0 38.3%

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

   4. Taylor expanded in y around 0 75.9%

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

   5. Taylor expanded in b around 0 61.9%

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

      1. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -1.3999999999999999e145 < t < 3.8999999999999997e156

   1. Initial program 59.3%

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

   3. Taylor expanded in y around inf 64.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+145} \lor \neg \left(t \leq 3.9 \cdot 10^{+156}\right):\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-110} \lor \neg \left(y \leq 2.5 \cdot 10^{-147}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.05e-110) (not (<= y 2.5e-147)))
   (- (+ a z) b)
   (* z (/ x (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e-110) || !(y <= 2.5e-147)) {
		tmp = (a + z) - b;
	} else {
		tmp = z * (x / (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 <= (-2.05d-110)) .or. (.not. (y <= 2.5d-147))) then
        tmp = (a + z) - b
    else
        tmp = z * (x / (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 <= -2.05e-110) || !(y <= 2.5e-147)) {
		tmp = (a + z) - b;
	} else {
		tmp = z * (x / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.05e-110) or not (y <= 2.5e-147):
		tmp = (a + z) - b
	else:
		tmp = z * (x / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.05e-110) || !(y <= 2.5e-147))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z * Float64(x / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.05e-110) || ~((y <= 2.5e-147)))
		tmp = (a + z) - b;
	else
		tmp = z * (x / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.05e-110], N[Not[LessEqual[y, 2.5e-147]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.04999999999999991e-110 or 2.50000000000000007e-147 < y

   1. Initial program 49.4%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -2.04999999999999991e-110 < y < 2.50000000000000007e-147

   1. Initial program 76.8%

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

   3. Taylor expanded in z around inf 43.7%

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

      1. associate-/l* 52.2%

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

      2. +-commutative 52.2%

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

      3. +-commutative 52.2%

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

      4. associate-+r+ 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in y around 0 50.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-110} \lor \neg \left(y \leq 2.5 \cdot 10^{-147}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+156}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+162)
   (- a (* y (/ b t)))
   (if (<= t 2e+156) (- (+ a z) b) (+ a (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+162) {
		tmp = a - (y * (b / t));
	} else if (t <= 2e+156) {
		tmp = (a + z) - b;
	} else {
		tmp = a + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.2d+162)) then
        tmp = a - (y * (b / t))
    else if (t <= 2d+156) then
        tmp = (a + z) - b
    else
        tmp = a + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+162) {
		tmp = a - (y * (b / t));
	} else if (t <= 2e+156) {
		tmp = (a + z) - b;
	} else {
		tmp = a + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+162:
		tmp = a - (y * (b / t))
	elif t <= 2e+156:
		tmp = (a + z) - b
	else:
		tmp = a + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+162)
		tmp = Float64(a - Float64(y * Float64(b / t)));
	elseif (t <= 2e+156)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+162)
		tmp = a - (y * (b / t));
	elseif (t <= 2e+156)
		tmp = (a + z) - b;
	else
		tmp = a + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+162], N[(a - N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+156], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999987e162

   1. Initial program 42.4%

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

   3. Taylor expanded in x around 0 29.4%

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

   4. Taylor expanded in y around 0 74.3%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. neg-mul-1 71.3%

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

      2. distribute-neg-frac 71.3%

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

   7. Simplified 71.3%

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

   if -7.19999999999999987e162 < t < 2e156

   1. Initial program 59.4%

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

   3. Taylor expanded in y around inf 64.5%

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

   if 2e156 < t

   1. Initial program 50.6%

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

   3. Taylor expanded in x around 0 43.4%

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

   4. Taylor expanded in y around 0 76.6%

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

   5. Taylor expanded in b around 0 62.3%

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

      1. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;a - y \cdot \frac{b}{t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+156}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-45}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.5e+86) z (if (<= z 3.4e-45) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+86) {
		tmp = z;
	} else if (z <= 3.4e-45) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.5d+86)) then
        tmp = z
    else if (z <= 3.4d-45) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+86) {
		tmp = z;
	} else if (z <= 3.4e-45) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.5e+86:
		tmp = z
	elif z <= 3.4e-45:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.5e+86)
		tmp = z;
	elseif (z <= 3.4e-45)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.5e+86)
		tmp = z;
	elseif (z <= 3.4e-45)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.5e+86], z, If[LessEqual[z, 3.4e-45], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e86 or 3.40000000000000004e-45 < z

   1. Initial program 44.4%

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

   3. Taylor expanded in x around inf 49.0%

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

   if -5.5000000000000002e86 < z < 3.40000000000000004e-45

   1. Initial program 66.4%

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

   3. Taylor expanded in t around inf 49.8%

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

Alternative 14: 56.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+160}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e+160) a (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+160) {
		tmp = a;
	} 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 <= (-1.2d+160)) then
        tmp = a
    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 <= -1.2e+160) {
		tmp = a;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e+160:
		tmp = a
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e+160)
		tmp = a;
	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 <= -1.2e+160)
		tmp = a;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e+160], a, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2000000000000001e160

   1. Initial program 42.4%

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

   3. Taylor expanded in t around inf 64.9%

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

   if -1.2000000000000001e160 < t

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 61.1%

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

Alternative 15: 32.1% 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 56.5%

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

3. Taylor expanded in t around inf 36.0%

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

Developer Target 1: 82.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024182 
(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)))