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

Percentage Accurate: 61.6% → 92.9%

Time: 9.4s

Alternatives: 16

Speedup: 0.4×

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: 61.6% 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: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(y + x\right) + t\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_3 \leq -\infty \lor \neg \left(t\_3 \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t\_2} + \frac{x}{t\_2}, z, \frac{\mathsf{fma}\left(-b, y, t\_1\right)}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ y x) t))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 5e+301)))
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     (fma (+ (/ y t_2) (/ x t_2)) z (/ (fma (- b) y t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (y + x) + t;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 5e+301)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma(((y / t_2) + (x / t_2)), z, (fma(-b, y, t_1) / t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(y + x) + t)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 5e+301))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = fma(Float64(Float64(y / t_2) + Float64(x / t_2)), z, Float64(fma(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[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 5e+301]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / t$95$2), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-b) * y + t$95$1), $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 5.0000000000000004e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 24.9%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 86.2

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

   7. Applied rewrites 86.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e301

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \frac{\mathsf{fma}\left(-b, y, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+99}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2))
        (t_4 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_3 -5e+99)
     t_4
     (if (<= t_3 -5e-178)
       (/ (fma z x (* y (- z b))) t_2)
       (if (<= t_3 5e+301) (/ (fma (+ y x) z t_1) (+ (+ y x) t)) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double t_4 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_3 <= -5e+99) {
		tmp = t_4;
	} else if (t_3 <= -5e-178) {
		tmp = fma(z, x, (y * (z - b))) / t_2;
	} else if (t_3 <= 5e+301) {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_3 <= -5e+99)
		tmp = t_4;
	elseif (t_3 <= -5e-178)
		tmp = Float64(fma(z, x, Float64(y * Float64(z - b))) / t_2);
	elseif (t_3 <= 5e+301)
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+99], t$95$4, If[LessEqual[t$95$3, -5e-178], N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 5e+301], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]

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)) < -5.00000000000000008e99 or 5.0000000000000004e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 21.9%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 37.4%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 85.0

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

   7. Applied rewrites 85.0%

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

   if -5.00000000000000008e99 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999976e-178

   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 a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-out-- N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 82.8

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

   5. Applied rewrites 82.8%

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

   if -4.99999999999999976e-178 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e301

   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

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 84.9

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

   5. Applied rewrites 84.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+99}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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_1))
        (t_3 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_2 -5e+99)
     t_3
     (if (<= t_2 -5e-178)
       (/ (fma z x (* y (- z b))) t_1)
       (if (<= t_2 5e-49) (/ (fma a t (* z x)) (+ t x)) t_3)))))

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)) / t_1;
	double t_3 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_2 <= -5e+99) {
		tmp = t_3;
	} else if (t_2 <= -5e-178) {
		tmp = fma(z, x, (y * (z - b))) / t_1;
	} else if (t_2 <= 5e-49) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_2 <= -5e+99)
		tmp = t_3;
	elseif (t_2 <= -5e-178)
		tmp = Float64(fma(z, x, Float64(y * Float64(z - b))) / t_1);
	elseif (t_2 <= 5e-49)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_3;
	end
	return 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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+99], t$95$3, If[LessEqual[t$95$2, -5e-178], N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e-49], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $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)) < -5.00000000000000008e99 or 4.9999999999999999e-49 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 52.7%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 78.5

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

   7. Applied rewrites 78.5%

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

   if -5.00000000000000008e99 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999976e-178

   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 a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-out-- N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 82.8

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

   5. Applied rewrites 82.8%

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

   if -4.99999999999999976e-178 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 81.8

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

   5. Applied rewrites 81.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+99}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{-178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+99}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+36}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x + y}\\ \end{array} \end{array} \]

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_1)))
   (if (<= t_2 -5e+99)
     (- (+ z a) (* y (/ b (+ y t))))
     (if (<= t_2 -2e+36)
       (/ (* (- (+ a z) b) y) t_1)
       (if (<= t_2 2e+157)
         (/ (fma a t (* z x)) (+ t x))
         (- (+ z a) (* y (/ b (+ x y)))))))))

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)) / t_1;
	double tmp;
	if (t_2 <= -5e+99) {
		tmp = (z + a) - (y * (b / (y + t)));
	} else if (t_2 <= -2e+36) {
		tmp = (((a + z) - b) * y) / t_1;
	} else if (t_2 <= 2e+157) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = (z + a) - (y * (b / (x + y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= -5e+99)
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(y + t))));
	elseif (t_2 <= -2e+36)
		tmp = Float64(Float64(Float64(Float64(a + z) - b) * y) / t_1);
	elseif (t_2 <= 2e+157)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(x + y))));
	end
	return 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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+99], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+36], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+157], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.00000000000000008e99

   1. Initial program 38.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 82.6

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

   7. Applied rewrites 82.6%

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

   8. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 78.2

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

   10. Applied rewrites 78.2%

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

   if -5.00000000000000008e99 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000008e36

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -2.00000000000000008e36 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e157

   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 y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 65.4

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

   5. Applied rewrites 65.4%

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

   if 1.99999999999999997e157 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 18.5%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 36.9%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 85.8

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

   7. Applied rewrites 85.8%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 80.6

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

   10. Applied rewrites 80.6%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+99}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+36}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{t\_1}\\ \end{array} \end{array} \]

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_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+301)))
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     (/ (fma (- (+ a z) b) y (fma a t (* z x))) t_1))))

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)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+301)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma(((a + z) - b), y, fma(a, t, (z * x))) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+301))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = Float64(fma(Float64(Float64(a + z) - b), y, fma(a, t, Float64(z * x))) / t_1);
	end
	return 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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+301]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y + N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.0000000000000004e301 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 24.9%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 86.2

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

   7. Applied rewrites 86.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000004e301

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 99.7

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

   5. Applied rewrites 99.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-138} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -2e-138) (not (<= t_1 5e-49)))
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -2e-138) || !(t_1 <= 5e-49)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -2e-138) || !(t_1 <= 5e-49))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-138], N[Not[LessEqual[t$95$1, 5e-49]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $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)) < -2.00000000000000013e-138 or 4.9999999999999999e-49 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 53.5%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.5

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

   7. Applied rewrites 76.5%

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

   if -2.00000000000000013e-138 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{-138} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+51} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -4e+51) (not (<= t_1 2e+157)))
     (- (+ z a) (* y (/ b (+ x y))))
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -4e+51) || !(t_1 <= 2e+157)) {
		tmp = (z + a) - (y * (b / (x + y)));
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -4e+51) || !(t_1 <= 2e+157))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(x + y))));
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+51], N[Not[LessEqual[t$95$1, 2e+157]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $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)) < -4e51 or 1.99999999999999997e157 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 32.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 45.0%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 83.3

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

   7. Applied rewrites 83.3%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 77.6

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

   10. Applied rewrites 77.6%

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

   if -4e51 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e157

   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 y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 64.0

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

   5. Applied rewrites 64.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -4 \cdot 10^{+51} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+47} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+47) (not (<= t_1 2e+157)))
     (- (+ a z) b)
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+47) || !(t_1 <= 2e+157)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+47) || !(t_1 <= 2e+157))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+47], N[Not[LessEqual[t$95$1, 2e+157]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $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)) < -5.00000000000000022e47 or 1.99999999999999997e157 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 32.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 70.3

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

   5. Applied rewrites 70.3%

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

   if -5.00000000000000022e47 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e157

   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 y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 64.6

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

   5. Applied rewrites 64.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+47} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+36}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 -2e+36)
     (- (+ z a) (* y (/ b (+ y t))))
     (if (<= t_1 2e+157)
       (/ (fma a t (* z x)) (+ t x))
       (- (+ z a) (* y (/ b (+ x y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -2e+36) {
		tmp = (z + a) - (y * (b / (y + t)));
	} else if (t_1 <= 2e+157) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = (z + a) - (y * (b / (x + y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= -2e+36)
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(y + t))));
	elseif (t_1 <= 2e+157)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(x + y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+36], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+157], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000008e36

   1. Initial program 48.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 55.1%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.5

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 73.5

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

   10. Applied rewrites 73.5%

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

   if -2.00000000000000008e36 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999997e157

   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 y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 65.4

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

   5. Applied rewrites 65.4%

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

   if 1.99999999999999997e157 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 18.5%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 36.9%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 85.8

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

   7. Applied rewrites 85.8%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 80.6

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

   10. Applied rewrites 80.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+36}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{y + t}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+20} \lor \neg \left(x \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-b}{x}, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.3e+20) (not (<= x 1.25e+183)))
   (fma (/ (- b) x) y z)
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.3e+20) || !(x <= 1.25e+183)) {
		tmp = fma((-b / x), y, z);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.3e+20) || !(x <= 1.25e+183))
		tmp = fma(Float64(Float64(-b) / x), y, z);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.3e+20], N[Not[LessEqual[x, 1.25e+183]], $MachinePrecision]], N[(N[((-b) / x), $MachinePrecision] * y + z), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e20 or 1.25000000000000002e183 < x

   1. Initial program 61.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. distribute-rgt-in N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-out-- N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 47.1

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

   5. Applied rewrites 47.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.4%

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

   9. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(-1 \cdot \frac{b}{x}, y, z\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 61.9%

       \[\leadsto \mathsf{fma}\left(\frac{-b}{x}, y, z\right) \]

   if -1.3e20 < x < 1.25000000000000002e183

   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

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 64.9

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

   5. Applied rewrites 64.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+20} \lor \neg \left(x \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-b}{x}, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+20} \lor \neg \left(x \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.3e+20) (not (<= x 1.25e+183)))
   (- z (/ (* b y) x))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.3e+20) || !(x <= 1.25e+183)) {
		tmp = z - ((b * y) / 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 <= (-1.3d+20)) .or. (.not. (x <= 1.25d+183))) then
        tmp = z - ((b * y) / 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 <= -1.3e+20) || !(x <= 1.25e+183)) {
		tmp = z - ((b * y) / x);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.3e+20) or not (x <= 1.25e+183):
		tmp = z - ((b * y) / x)
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.3e+20) || !(x <= 1.25e+183))
		tmp = Float64(z - Float64(Float64(b * y) / 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 <= -1.3e+20) || ~((x <= 1.25e+183)))
		tmp = z - ((b * y) / x);
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.3e+20], N[Not[LessEqual[x, 1.25e+183]], $MachinePrecision]], N[(z - N[(N[(b * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e20 or 1.25000000000000002e183 < x

   1. Initial program 61.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. distribute-rgt-in N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-out-- N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 47.1

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

   5. Applied rewrites 47.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.4%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 58.5%

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

   if -1.3e20 < x < 1.25000000000000002e183

   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

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 64.9

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

   5. Applied rewrites 64.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+20} \lor \neg \left(x \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{x}, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.3e+20) (fma a (/ y x) z) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.3e+20) {
		tmp = fma(a, (y / x), z);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.3e+20)
		tmp = fma(a, Float64(y / x), z);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.3e+20], N[(a * N[(y / x), $MachinePrecision] + z), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e20

   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 t around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. distribute-rgt-in N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-out-- N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 48.8

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

   5. Applied rewrites 48.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 60.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.6%

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

   if -1.3e20 < x

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 62.6

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

   5. Applied rewrites 62.6%

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

Alternative 13: 48.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+101} \lor \neg \left(a \leq 6.5 \cdot 10^{+65}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.15e+101) (not (<= a 6.5e+65))) (- a b) (- z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e+101) || !(a <= 6.5e+65)) {
		tmp = a - b;
	} else {
		tmp = 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 ((a <= (-2.15d+101)) .or. (.not. (a <= 6.5d+65))) then
        tmp = a - b
    else
        tmp = 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 ((a <= -2.15e+101) || !(a <= 6.5e+65)) {
		tmp = a - b;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.15e+101) or not (a <= 6.5e+65):
		tmp = a - b
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.15e+101) || !(a <= 6.5e+65))
		tmp = Float64(a - b);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.15e+101) || ~((a <= 6.5e+65)))
		tmp = a - b;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.15e+101], N[Not[LessEqual[a, 6.5e+65]], $MachinePrecision]], N[(a - b), $MachinePrecision], N[(z - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.15e101 or 6.5000000000000003e65 < a

   1. Initial program 49.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 61.9

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

   5. Applied rewrites 61.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.7%

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

   if -2.15e101 < a < 6.5000000000000003e65

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 52.0

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

   5. Applied rewrites 52.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 51.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+101} \lor \neg \left(a \leq 6.5 \cdot 10^{+65}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.3e+20) (- z b) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.3e+20) {
		tmp = z - b;
	} 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 <= (-1.3d+20)) then
        tmp = z - b
    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 <= -1.3e+20) {
		tmp = z - b;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.3e+20:
		tmp = z - b
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.3e+20)
		tmp = Float64(z - b);
	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 <= -1.3e+20)
		tmp = z - b;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.3e+20], N[(z - b), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e20

   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 y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 41.7%

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

   if -1.3e20 < x

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 62.6

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

   5. Applied rewrites 62.6%

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

Alternative 15: 37.4% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

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 - b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.9%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. lower-+.f64 55.5

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

5. Applied rewrites 55.5%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 37.4%

   \[\leadsto a - \color{blue}{b} \]
9. Add Preprocessing

Alternative 16: 12.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -b \end{array} \]

FPCore

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

C

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

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 = -b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := (-b)

Derivation

1. Initial program 59.9%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. lower-+.f64 55.5

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

5. Applied rewrites 55.5%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 17.4%

   \[\leadsto -b \]
9. Add Preprocessing

Developer Target 1: 82.8% 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 2024296 
(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)))