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

Percentage Accurate: 60.1% → 90.6%

Time: 9.2s

Alternatives: 14

Speedup: 1.4×

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: 60.1% 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: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+175} \lor \neg \left(t\_1 \leq 10^{+307}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1e+175) (not (<= t_1 1e+307)))
     (- (+ a z) (* y (/ b (+ (+ t x) y))))
     t_1)))

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 <= -1e+175) || !(t_1 <= 1e+307)) {
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
    if ((t_1 <= (-1d+175)) .or. (.not. (t_1 <= 1d+307))) then
        tmp = (a + z) - (y * (b / ((t + x) + y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -1e+175) || !(t_1 <= 1e+307)) {
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if (t_1 <= -1e+175) or not (t_1 <= 1e+307):
		tmp = (a + z) - (y * (b / ((t + x) + y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -1e+175) || !(t_1 <= 1e+307))
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if ((t_1 <= -1e+175) || ~((t_1 <= 1e+307)))
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(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, -1e+175], N[Not[LessEqual[t$95$1, 1e+307]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e174 or 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 26.9%

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

   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. lower-+.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -9.9999999999999994e174 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+175} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+307}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+175} \lor \neg \left(t\_2 \leq 10^{+307}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{t\_1}\\ \end{array} \end{array} \]

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 -1e+175) (not (<= t_2 1e+307)))
     (- (+ a z) (* 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 <= -1e+175) || !(t_2 <= 1e+307)) {
		tmp = (a + z) - (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 <= -1e+175) || !(t_2 <= 1e+307))
		tmp = Float64(Float64(a + z) - 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, -1e+175], N[Not[LessEqual[t$95$2, 1e+307]], $MachinePrecision]], N[(N[(a + z), $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)) < -9.9999999999999994e174 or 9.99999999999999986e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 26.9%

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

   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. lower-+.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -9.9999999999999994e174 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{a \cdot t + \left(x \cdot z + y \cdot \left(\left(a + z\right) - b\right)\right)}}{\left(x + t\right) + y} \]
   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 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+175} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+307}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+162} \lor \neg \left(t\_2 \leq 10^{+107}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_2 -2e+162) (not (<= t_2 1e+107)))
     (- (+ a z) (* y (/ b (+ (+ t x) y))))
     (/ (fma (+ y x) z t_1) (+ (+ y x) t)))))

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 + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_2 <= -2e+162) || !(t_2 <= 1e+107)) {
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_2 <= -2e+162) || !(t_2 <= 1e+107))
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	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[(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$2, -2e+162], N[Not[LessEqual[t$95$2, 1e+107]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $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)) < -1.9999999999999999e162 or 9.9999999999999997e106 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 28.3%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 37.2%

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

   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. lower-+.f64 84.1

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

   7. Applied rewrites 84.1%

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

   if -1.9999999999999999e162 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999997e106

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{t + \left(x + y\right)}} \]
   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 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+162} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+107}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;x \leq -1.28 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right)}{y + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) (* y (/ b (+ (+ t x) y))))))
   (if (<= x -1.28e-42)
     t_1
     (if (<= x 4.3e+32)
       (fma y (/ (- z b) (+ t y)) a)
       (if (<= x 2.3e+235) t_1 (/ (fma (+ x y) z (* (+ y t) a)) (+ y x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - (y * (b / ((t + x) + y)));
	double tmp;
	if (x <= -1.28e-42) {
		tmp = t_1;
	} else if (x <= 4.3e+32) {
		tmp = fma(y, ((z - b) / (t + y)), a);
	} else if (x <= 2.3e+235) {
		tmp = t_1;
	} else {
		tmp = fma((x + y), z, ((y + t) * a)) / (y + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (x <= -1.28e-42)
		tmp = t_1;
	elseif (x <= 4.3e+32)
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	elseif (x <= 2.3e+235)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(x + y), z, Float64(Float64(y + t) * a)) / Float64(y + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.28e-42], t$95$1, If[LessEqual[x, 4.3e+32], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[x, 2.3e+235], t$95$1, N[(N[(N[(x + y), $MachinePrecision] * z + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.27999999999999994e-42 or 4.2999999999999997e32 < x < 2.3e235

   1. Initial program 54.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 59.2%

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

   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. lower-+.f64 70.5

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

   7. Applied rewrites 70.5%

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

   if -1.27999999999999994e-42 < x < 4.2999999999999997e32

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 60.5

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 85.5%

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

   if 2.3e235 < x

   1. Initial program 73.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 10.4

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

   5. Applied rewrites 10.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 10.4

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

   8. Applied rewrites 10.4%

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

   9. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-+.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. +-commutative N/A

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

       8. lower-+.f64 61.8

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

   11. Applied rewrites 61.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-42}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+235}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right)}{y + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-42} \lor \neg \left(x \leq 4.3 \cdot 10^{+32}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.28e-42) (not (<= x 4.3e+32)))
   (- (+ a z) (* y (/ b (+ (+ t x) y))))
   (fma y (/ (- z b) (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.28e-42) || !(x <= 4.3e+32)) {
		tmp = (a + z) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma(y, ((z - b) / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.28e-42) || !(x <= 4.3e+32))
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.28e-42], N[Not[LessEqual[x, 4.3e+32]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.27999999999999994e-42 or 4.2999999999999997e32 < x

   1. Initial program 56.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
   3. 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 61.3%

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

   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. lower-+.f64 66.3

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

   7. Applied rewrites 66.3%

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

   if -1.27999999999999994e-42 < x < 4.2999999999999997e32

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 60.5

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 85.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-42} \lor \neg \left(x \leq 4.3 \cdot 10^{+32}\right):\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{\left(y + x\right) + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.7e-42)
   (- (+ a z) (* y (/ b (+ x y))))
   (if (<= x 1.05e+54)
     (fma y (/ (- z b) (+ t y)) a)
     (* (+ y x) (/ z (+ (+ y x) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.7e-42) {
		tmp = (a + z) - (y * (b / (x + y)));
	} else if (x <= 1.05e+54) {
		tmp = fma(y, ((z - b) / (t + y)), a);
	} else {
		tmp = (y + x) * (z / ((y + x) + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.7e-42)
		tmp = Float64(Float64(a + z) - Float64(y * Float64(b / Float64(x + y))));
	elseif (x <= 1.05e+54)
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	else
		tmp = Float64(Float64(y + x) * Float64(z / Float64(Float64(y + x) + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.7e-42], N[(N[(a + z), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+54], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(y + x), $MachinePrecision] * N[(z / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7000000000000002e-42

   1. Initial program 50.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 54.3%

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

   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. lower-+.f64 74.1

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

   7. Applied rewrites 74.1%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 71.2

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

   10. Applied rewrites 71.2%

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

   if -3.7000000000000002e-42 < x < 1.04999999999999993e54

   1. Initial program 71.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 59.7

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

   5. Applied rewrites 59.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 85.6%

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

   if 1.04999999999999993e54 < x

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 52.2

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

   5. Applied rewrites 52.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;\left(a + z\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{\left(y + x\right) + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+159}:\\ \;\;\;\;\left(-z\right) \cdot -1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{z}{\left(y + x\right) + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+159)
   (* (- z) -1.0)
   (if (<= x 1.05e+54)
     (fma y (/ (- z b) (+ t y)) a)
     (* (+ y x) (/ z (+ (+ y x) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+159) {
		tmp = -z * -1.0;
	} else if (x <= 1.05e+54) {
		tmp = fma(y, ((z - b) / (t + y)), a);
	} else {
		tmp = (y + x) * (z / ((y + x) + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+159)
		tmp = Float64(Float64(-z) * -1.0);
	elseif (x <= 1.05e+54)
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	else
		tmp = Float64(Float64(y + x) * Float64(z / Float64(Float64(y + x) + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+159], N[((-z) * -1.0), $MachinePrecision], If[LessEqual[x, 1.05e+54], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(y + x), $MachinePrecision] * N[(z / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000003e159

   1. Initial program 34.5%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 40.9%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 83.3%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(-z\right) \cdot -1 \]
   10. Step-by-step derivation

   11. Applied rewrites 67.8%

       \[\leadsto \left(-z\right) \cdot -1 \]

   if -9.5000000000000003e159 < x < 1.04999999999999993e54

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 52.8

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

   5. Applied rewrites 52.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 80.8%

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

   if 1.04999999999999993e54 < x

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 52.2

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

   5. Applied rewrites 52.2%

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

Alternative 8: 69.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+159} \lor \neg \left(x \leq 3.2 \cdot 10^{+183}\right):\\ \;\;\;\;\left(-z\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -9.5e+159) (not (<= x 3.2e+183)))
   (* (- z) -1.0)
   (fma y (/ (- z b) (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -9.5e+159) || !(x <= 3.2e+183)) {
		tmp = -z * -1.0;
	} else {
		tmp = fma(y, ((z - b) / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -9.5e+159) || !(x <= 3.2e+183))
		tmp = Float64(Float64(-z) * -1.0);
	else
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -9.5e+159], N[Not[LessEqual[x, 3.2e+183]], $MachinePrecision]], N[((-z) * -1.0), $MachinePrecision], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000003e159 or 3.2000000000000002e183 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 54.3%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 78.2%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(-z\right) \cdot -1 \]
   10. Step-by-step derivation

   11. Applied rewrites 58.8%

       \[\leadsto \left(-z\right) \cdot -1 \]

   if -9.5000000000000003e159 < x < 3.2000000000000002e183

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 49.4

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

   5. Applied rewrites 49.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 77.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+159} \lor \neg \left(x \leq 3.2 \cdot 10^{+183}\right):\\ \;\;\;\;\left(-z\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+157} \lor \neg \left(t \leq 1.45 \cdot 10^{+23}\right):\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4e+157) (not (<= t 1.45e+23)))
   (fma y (/ (- z b) t) a)
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+157) || !(t <= 1.45e+23)) {
		tmp = fma(y, ((z - b) / t), a);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4e+157) || !(t <= 1.45e+23))
		tmp = fma(y, Float64(Float64(z - b) / t), a);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4e+157], N[Not[LessEqual[t, 1.45e+23]], $MachinePrecision]], N[(y * N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision] + a), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999993e157 or 1.45000000000000006e23 < t

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 47.1

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

   5. Applied rewrites 47.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 63.8%

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

   if -3.99999999999999993e157 < t < 1.45000000000000006e23

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 65.5

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

   5. Applied rewrites 65.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+157} \lor \neg \left(t \leq 1.45 \cdot 10^{+23}\right):\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+161} \lor \neg \left(x \leq 8.6 \cdot 10^{+95}\right):\\ \;\;\;\;\left(-z\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -3.35e+161) (not (<= x 8.6e+95))) (* (- z) -1.0) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.35e+161) || !(x <= 8.6e+95)) {
		tmp = -z * -1.0;
	} 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 <= (-3.35d+161)) .or. (.not. (x <= 8.6d+95))) then
        tmp = -z * (-1.0d0)
    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 <= -3.35e+161) || !(x <= 8.6e+95)) {
		tmp = -z * -1.0;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -3.35e+161) or not (x <= 8.6e+95):
		tmp = -z * -1.0
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -3.35e+161) || !(x <= 8.6e+95))
		tmp = Float64(Float64(-z) * -1.0);
	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 <= -3.35e+161) || ~((x <= 8.6e+95)))
		tmp = -z * -1.0;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -3.35e+161], N[Not[LessEqual[x, 8.6e+95]], $MachinePrecision]], N[((-z) * -1.0), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.35e161 or 8.6e95 < x

   1. Initial program 52.8%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 78.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(-z\right) \cdot -1 \]
   10. Step-by-step derivation

   11. Applied rewrites 56.8%

       \[\leadsto \left(-z\right) \cdot -1 \]

   if -3.35e161 < x < 8.6e95

   1. Initial program 68.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 63.2

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

   5. Applied rewrites 63.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{+161} \lor \neg \left(x \leq 8.6 \cdot 10^{+95}\right):\\ \;\;\;\;\left(-z\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6500000000000 \lor \neg \left(y \leq 0.0074\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6500000000000.0) (not (<= y 0.0074))) (- (+ a z) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6500000000000.0) || !(y <= 0.0074)) {
		tmp = (a + z) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6500000000000.0d0)) .or. (.not. (y <= 0.0074d0))) then
        tmp = (a + z) - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6500000000000.0) || !(y <= 0.0074)) {
		tmp = (a + z) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6500000000000.0) or not (y <= 0.0074):
		tmp = (a + z) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6500000000000.0) || !(y <= 0.0074))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6500000000000.0) || ~((y <= 0.0074)))
		tmp = (a + z) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6500000000000.0], N[Not[LessEqual[y, 0.0074]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e12 or 0.0074000000000000003 < y

   1. Initial program 44.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 78.7

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

   5. Applied rewrites 78.7%

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

   if -6.5e12 < y < 0.0074000000000000003

   1. Initial program 83.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 33.4

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

   5. Applied rewrites 33.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 25.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 43.4%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6500000000000 \lor \neg \left(y \leq 0.0074\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-24} \lor \neg \left(x \leq 1.7 \cdot 10^{-7}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.08e-24) (not (<= x 1.7e-7))) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.08e-24) || !(x <= 1.7e-7)) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.08d-24)) .or. (.not. (x <= 1.7d-7))) then
        tmp = z + a
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.08e-24) || !(x <= 1.7e-7)) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.08e-24) or not (x <= 1.7e-7):
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.08e-24) || !(x <= 1.7e-7))
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.08e-24) || ~((x <= 1.7e-7)))
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.08e-24], N[Not[LessEqual[x, 1.7e-7]], $MachinePrecision]], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08000000000000006e-24 or 1.69999999999999987e-7 < x

   1. Initial program 58.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 48.1

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

   5. Applied rewrites 48.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 52.5%

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

   if -1.08000000000000006e-24 < x < 1.69999999999999987e-7

   1. Initial program 71.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 64.7

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 57.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-24} \lor \neg \left(x \leq 1.7 \cdot 10^{-7}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+126}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -1.4e+126) (- b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+126) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.4d+126)) then
        tmp = -b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+126) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e+126:
		tmp = -b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e+126)
		tmp = Float64(-b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e+126)
		tmp = -b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e+126], (-b), N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.40000000000000005e126

   1. Initial program 45.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 51.9

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 41.3%

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

   9. Taylor expanded in a around 0

      \[\leadsto -1 \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 36.7%

       \[\leadsto -b \]

   if -1.40000000000000005e126 < b

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 56.4

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 38.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 54.4%

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

Alternative 14: 13.4% 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 64.3%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 55.7

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

5. Applied rewrites 55.7%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 39.2%

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

9. Taylor expanded in a around 0

   \[\leadsto -1 \cdot b \]
10. Step-by-step derivation

11. Applied rewrites 16.7%

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

Developer Target 1: 82.2% 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 2024323 
(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)))