Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 79.6% → 79.6%

Time: 2.7s

Alternatives: 11

Speedup: 1.0×

• 36.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := \frac{t\_2}{z \cdot c}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-205}:\\ \;\;\;\;\frac{t\_1 + b}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot 9 - t\_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (* z 4.0) t) a))
        (t_2 (* (* x 9.0) y))
        (t_3 (/ t_2 (* z c))))
   (if (<= t_2 -2e+40)
     t_3
     (if (<= t_2 5e-205)
       (/ (+ t_1 b) (* z c))
       (if (<= t_2 2e-10) (/ (- (* x 9.0) t_1) (* z c)) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * 4.0) * t) * a;
	double t_2 = (x * 9.0) * y;
	double t_3 = t_2 / (z * c);
	double tmp;
	if (t_2 <= -2e+40) {
		tmp = t_3;
	} else if (t_2 <= 5e-205) {
		tmp = (t_1 + b) / (z * c);
	} else if (t_2 <= 2e-10) {
		tmp = ((x * 9.0) - t_1) / (z * c);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((z * 4.0d0) * t) * a
    t_2 = (x * 9.0d0) * y
    t_3 = t_2 / (z * c)
    if (t_2 <= (-2d+40)) then
        tmp = t_3
    else if (t_2 <= 5d-205) then
        tmp = (t_1 + b) / (z * c)
    else if (t_2 <= 2d-10) then
        tmp = ((x * 9.0d0) - t_1) / (z * c)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * 4.0) * t) * a;
	double t_2 = (x * 9.0) * y;
	double t_3 = t_2 / (z * c);
	double tmp;
	if (t_2 <= -2e+40) {
		tmp = t_3;
	} else if (t_2 <= 5e-205) {
		tmp = (t_1 + b) / (z * c);
	} else if (t_2 <= 2e-10) {
		tmp = ((x * 9.0) - t_1) / (z * c);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((z * 4.0) * t) * a
	t_2 = (x * 9.0) * y
	t_3 = t_2 / (z * c)
	tmp = 0
	if t_2 <= -2e+40:
		tmp = t_3
	elif t_2 <= 5e-205:
		tmp = (t_1 + b) / (z * c)
	elif t_2 <= 2e-10:
		tmp = ((x * 9.0) - t_1) / (z * c)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * 4.0) * t) * a)
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(t_2 / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -2e+40)
		tmp = t_3;
	elseif (t_2 <= 5e-205)
		tmp = Float64(Float64(t_1 + b) / Float64(z * c));
	elseif (t_2 <= 2e-10)
		tmp = Float64(Float64(Float64(x * 9.0) - t_1) / Float64(z * c));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * 4.0) * t) * a;
	t_2 = (x * 9.0) * y;
	t_3 = t_2 / (z * c);
	tmp = 0.0;
	if (t_2 <= -2e+40)
		tmp = t_3;
	elseif (t_2 <= 5e-205)
		tmp = (t_1 + b) / (z * c);
	elseif (t_2 <= 2e-10)
		tmp = ((x * 9.0) - t_1) / (z * c);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+40], t$95$3, If[LessEqual[t$95$2, 5e-205], N[(N[(t$95$1 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-10], N[(N[(N[(x * 9.0), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000006e40 or 2.00000000000000007e-10 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

   5. Applied rewrites 58.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} \]

   if -2.00000000000000006e40 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000001e-205

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} + b}{z \cdot c} \]

   5. Applied rewrites 47.5%

      \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} + b}{z \cdot c} \]

   if 5.00000000000000001e-205 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000007e-10

   1. Initial program 72.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

   5. Applied rewrites 51.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{9 \cdot \left(x \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a}{z \cdot c} \]

   8. Applied rewrites 37.9%

      \[\leadsto \frac{x \cdot 9 - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a}{z \cdot c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{t\_1}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (/ t_1 (* z c))))
   (if (<= t_1 -2e+40)
     t_2
     (if (<= t_1 2e-73) (/ (+ (* (* (* z 4.0) t) a) b) (* z c)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = t_1 / (z * c);
	double tmp;
	if (t_1 <= -2e+40) {
		tmp = t_2;
	} else if (t_1 <= 2e-73) {
		tmp = ((((z * 4.0) * t) * a) + b) / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = t_1 / (z * c)
    if (t_1 <= (-2d+40)) then
        tmp = t_2
    else if (t_1 <= 2d-73) then
        tmp = ((((z * 4.0d0) * t) * a) + b) / (z * c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = t_1 / (z * c);
	double tmp;
	if (t_1 <= -2e+40) {
		tmp = t_2;
	} else if (t_1 <= 2e-73) {
		tmp = ((((z * 4.0) * t) * a) + b) / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = t_1 / (z * c)
	tmp = 0
	if t_1 <= -2e+40:
		tmp = t_2
	elif t_1 <= 2e-73:
		tmp = ((((z * 4.0) * t) * a) + b) / (z * c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(t_1 / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e+40)
		tmp = t_2;
	elseif (t_1 <= 2e-73)
		tmp = Float64(Float64(Float64(Float64(Float64(z * 4.0) * t) * a) + b) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = t_1 / (z * c);
	tmp = 0.0;
	if (t_1 <= -2e+40)
		tmp = t_2;
	elseif (t_1 <= 2e-73)
		tmp = ((((z * 4.0) * t) * a) + b) / (z * c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+40], t$95$2, If[LessEqual[t$95$1, 2e-73], N[(N[(N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000006e40 or 1.99999999999999999e-73 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

   5. Applied rewrites 54.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} \]

   if -2.00000000000000006e40 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999999e-73

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} + b}{z \cdot c} \]

   5. Applied rewrites 44.3%

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

Alternative 4: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\\ \mathbf{if}\;b \leq 1.1 \cdot 10^{+216}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y - t\_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (* z 4.0) t) a)))
   (if (<= b 1.1e+216)
     (/ (- (* (* x 9.0) y) t_1) (* z c))
     (/ (+ t_1 b) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * 4.0) * t) * a;
	double tmp;
	if (b <= 1.1e+216) {
		tmp = (((x * 9.0) * y) - t_1) / (z * c);
	} else {
		tmp = (t_1 + b) / (z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z * 4.0d0) * t) * a
    if (b <= 1.1d+216) then
        tmp = (((x * 9.0d0) * y) - t_1) / (z * c)
    else
        tmp = (t_1 + b) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * 4.0) * t) * a;
	double tmp;
	if (b <= 1.1e+216) {
		tmp = (((x * 9.0) * y) - t_1) / (z * c);
	} else {
		tmp = (t_1 + b) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((z * 4.0) * t) * a
	tmp = 0
	if b <= 1.1e+216:
		tmp = (((x * 9.0) * y) - t_1) / (z * c)
	else:
		tmp = (t_1 + b) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * 4.0) * t) * a)
	tmp = 0.0
	if (b <= 1.1e+216)
		tmp = Float64(Float64(Float64(Float64(x * 9.0) * y) - t_1) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + b) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * 4.0) * t) * a;
	tmp = 0.0;
	if (b <= 1.1e+216)
		tmp = (((x * 9.0) * y) - t_1) / (z * c);
	else
		tmp = (t_1 + b) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[b, 1.1e+216], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < 1.1e216

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

   5. Applied rewrites 59.7%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

   if 1.1e216 < b

   1. Initial program 70.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} + b}{z \cdot c} \]

   5. Applied rewrites 65.4%

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

Alternative 5: 15.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-303}:\\ \;\;\;\;\left(\left(x \cdot 9\right) \cdot y\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -8e-303) (* (* (* x 9.0) y) y) (/ (* x 9.0) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -8e-303) {
		tmp = ((x * 9.0) * y) * y;
	} else {
		tmp = (x * 9.0) / (z * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (y <= (-8d-303)) then
        tmp = ((x * 9.0d0) * y) * y
    else
        tmp = (x * 9.0d0) / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -8e-303) {
		tmp = ((x * 9.0) * y) * y;
	} else {
		tmp = (x * 9.0) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -8e-303:
		tmp = ((x * 9.0) * y) * y
	else:
		tmp = (x * 9.0) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -8e-303)
		tmp = Float64(Float64(Float64(x * 9.0) * y) * y);
	else
		tmp = Float64(Float64(x * 9.0) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -8e-303)
		tmp = ((x * 9.0) * y) * y;
	else
		tmp = (x * 9.0) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -8e-303], N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] * y), $MachinePrecision], N[(N[(x * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999944e-303

   1. Initial program 75.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

   5. Applied rewrites 8.9%

      \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(b + 9 \cdot \left(x \cdot y\right)\right) - \color{blue}{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} \]

   8. Applied rewrites 5.5%

      \[\leadsto \left(x \cdot 9\right) \cdot \color{blue}{y} \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(9 \cdot x\right) \cdot y \]

   11. Applied rewrites 11.8%

       \[\leadsto \left(\left(x \cdot 9\right) \cdot y\right) \cdot y \]

   if -7.99999999999999944e-303 < y

   1. Initial program 73.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

   5. Applied rewrites 35.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{9 \cdot \color{blue}{\left(x \cdot y\right)}}{z \cdot c} \]

   8. Applied rewrites 19.7%

      \[\leadsto \frac{x \cdot \color{blue}{9}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 36.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ (* (* x 9.0) y) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * 9.0) * y) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((x * 9.0d0) * y) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * 9.0) * y) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((x * 9.0) * y) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(x * 9.0) * y) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((x * 9.0) * y) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \frac{\color{blue}{\left(b + 9 \cdot \left(x \cdot y\right)\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

5. Applied rewrites 36.1%

   \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} \]
6. Add Preprocessing

Alternative 7: 11.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 9\right) \cdot y\right) \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (* (* (* x 9.0) y) y))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * 9.0) * y) * y;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((x * 9.0d0) * y) * y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * 9.0) * y) * y;
}

Python

def code(x, y, z, t, a, b, c):
	return ((x * 9.0) * y) * y

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(x * 9.0) * y) * y)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((x * 9.0) * y) * y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

5. Applied rewrites 9.3%

   \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(b + 9 \cdot \left(x \cdot y\right)\right) - \color{blue}{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} \]

8. Applied rewrites 5.7%

   \[\leadsto \left(x \cdot 9\right) \cdot \color{blue}{y} \]

9. Taylor expanded in x around 0

   \[\leadsto \left(9 \cdot x\right) \cdot y \]

11. Applied rewrites 10.0%

    \[\leadsto \left(\left(x \cdot 9\right) \cdot y\right) \cdot y \]
12. Add Preprocessing

Alternative 8: 7.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 9\right) \cdot y + b \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (+ (* (* x 9.0) y) b))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * 9.0) * y) + b;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((x * 9.0d0) * y) + b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * 9.0) * y) + b;
}

Python

def code(x, y, z, t, a, b, c):
	return ((x * 9.0) * y) + b

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(x * 9.0) * y) + b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((x * 9.0) * y) + b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

5. Applied rewrites 9.3%

   \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right) + b \]

8. Applied rewrites 6.1%

   \[\leadsto \left(x \cdot 9\right) \cdot y + b \]
9. Add Preprocessing

Alternative 9: 7.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 9\right) \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (* (* x 9.0) y))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * 9.0) * y;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = (x * 9.0d0) * y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * 9.0) * y;
}

Python

def code(x, y, z, t, a, b, c):
	return (x * 9.0) * y

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(x * 9.0) * y)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (x * 9.0) * y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

5. Applied rewrites 9.3%

   \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(b + 9 \cdot \left(x \cdot y\right)\right) - \color{blue}{4 \cdot \left(a \cdot \left(t \cdot z\right)\right)} \]

8. Applied rewrites 5.7%

   \[\leadsto \left(x \cdot 9\right) \cdot \color{blue}{y} \]
9. Add Preprocessing

Alternative 10: 3.0% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ z \cdot 4 + b \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (+ (* z 4.0) b))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (z * 4.0) + b;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = (z * 4.0d0) + b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (z * 4.0) + b;
}

Python

def code(x, y, z, t, a, b, c):
	return (z * 4.0) + b

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(z * 4.0) + b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (z * 4.0) + b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(z * 4.0), $MachinePrecision] + b), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

5. Applied rewrites 9.3%

   \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b} \]

6. Taylor expanded in x around 0

   \[\leadsto -4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b \]

8. Applied rewrites 31.4%

   \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} + b \]

9. Taylor expanded in x around 0

   \[\leadsto -4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b \]

11. Applied rewrites 3.1%

    \[\leadsto z \cdot 4 + b \]
12. Add Preprocessing

Alternative 11: 3.1% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 9 \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (* x 9.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x * 9.0;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = x * 9.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x * 9.0;
}

Python

def code(x, y, z, t, a, b, c):
	return x * 9.0

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x * 9.0)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x * 9.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * 9.0), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]

5. Applied rewrites 9.3%

   \[\leadsto \color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b} \]

6. Taylor expanded in x around 0

   \[\leadsto -4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b \]

8. Applied rewrites 31.4%

   \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} + b \]

9. Taylor expanded in y around -inf

   \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-9 \cdot x + -1 \cdot \frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{y}\right)\right)} \]

11. Applied rewrites 3.1%

    \[\leadsto x \cdot \color{blue}{9} \]
12. Add Preprocessing

Developer Target 1: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))