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

Percentage Accurate: 79.8% → 79.8%

Time: 3.0s

Alternatives: 12

Speedup: 1.0×

• 37.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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: 79.8% 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: 79.8% 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 80.4%

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

Alternative 2: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{t\_1 + b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+16}:\\ \;\;\;\;\frac{t\_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (/ (+ t_1 b) (* z c))))
   (if (<= b -1.4e-62)
     t_2
     (if (<= b 9e+16) (/ (- t_1 (* (* (* z 4.0) t) a)) (* 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 + b) / (z * c);
	double tmp;
	if (b <= -1.4e-62) {
		tmp = t_2;
	} else if (b <= 9e+16) {
		tmp = (t_1 - (((z * 4.0) * t) * a)) / (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 + b) / (z * c)
    if (b <= (-1.4d-62)) then
        tmp = t_2
    else if (b <= 9d+16) then
        tmp = (t_1 - (((z * 4.0d0) * t) * a)) / (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 + b) / (z * c);
	double tmp;
	if (b <= -1.4e-62) {
		tmp = t_2;
	} else if (b <= 9e+16) {
		tmp = (t_1 - (((z * 4.0) * t) * a)) / (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 + b) / (z * c)
	tmp = 0
	if b <= -1.4e-62:
		tmp = t_2
	elif b <= 9e+16:
		tmp = (t_1 - (((z * 4.0) * t) * a)) / (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(Float64(t_1 + b) / Float64(z * c))
	tmp = 0.0
	if (b <= -1.4e-62)
		tmp = t_2;
	elseif (b <= 9e+16)
		tmp = Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) / 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 + b) / (z * c);
	tmp = 0.0;
	if (b <= -1.4e-62)
		tmp = t_2;
	elseif (b <= 9e+16)
		tmp = (t_1 - (((z * 4.0) * t) * a)) / (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[(N[(t$95$1 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e-62], t$95$2, If[LessEqual[b, 9e+16], N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.40000000000000001e-62 or 9e16 < b

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 37.1%

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

   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 23.2%

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

   9. Taylor expanded in x around -inf

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

   11. Applied rewrites 74.1%

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

   if -1.40000000000000001e-62 < b < 9e16

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 76.1%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x \cdot 9 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* x 9.0) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= a -1.08e+144)
     t_1
     (if (<= a 1.9e+58) (/ (+ (* (* x 9.0) y) b) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((x * 9.0) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (a <= -1.08e+144) {
		tmp = t_1;
	} else if (a <= 1.9e+58) {
		tmp = (((x * 9.0) * y) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	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 = (((x * 9.0d0) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
    if (a <= (-1.08d+144)) then
        tmp = t_1
    else if (a <= 1.9d+58) then
        tmp = (((x * 9.0d0) * y) + b) / (z * c)
    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 c) {
	double t_1 = (((x * 9.0) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (a <= -1.08e+144) {
		tmp = t_1;
	} else if (a <= 1.9e+58) {
		tmp = (((x * 9.0) * y) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (((x * 9.0) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if a <= -1.08e+144:
		tmp = t_1
	elif a <= 1.9e+58:
		tmp = (((x * 9.0) * y) + b) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(x * 9.0) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (a <= -1.08e+144)
		tmp = t_1;
	elseif (a <= 1.9e+58)
		tmp = Float64(Float64(Float64(Float64(x * 9.0) * y) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((x * 9.0) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (a <= -1.08e+144)
		tmp = t_1;
	elseif (a <= 1.9e+58)
		tmp = (((x * 9.0) * y) + b) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(x * 9.0), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.08e+144], t$95$1, If[LessEqual[a, 1.9e+58], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0800000000000001e144 or 1.8999999999999999e58 < a

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 60.3%

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

   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 51.0%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 66.2%

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

   if -1.0800000000000001e144 < a < 1.8999999999999999e58

   1. Initial program 81.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 54.1%

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

   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 20.0%

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

   9. Taylor expanded in x around -inf

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

   11. Applied rewrites 75.5%

       \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 62.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 9 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z \cdot c}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+241}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (- (* x 9.0) (* (* (* z 4.0) t) a)) (* z c))))
   (if (<= a -3.4e+144)
     t_1
     (if (<= a 1.55e+241) (/ (+ (* (* x 9.0) y) b) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * 9.0) - (((z * 4.0) * t) * a)) / (z * c);
	double tmp;
	if (a <= -3.4e+144) {
		tmp = t_1;
	} else if (a <= 1.55e+241) {
		tmp = (((x * 9.0) * y) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	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 = ((x * 9.0d0) - (((z * 4.0d0) * t) * a)) / (z * c)
    if (a <= (-3.4d+144)) then
        tmp = t_1
    else if (a <= 1.55d+241) then
        tmp = (((x * 9.0d0) * y) + b) / (z * c)
    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 c) {
	double t_1 = ((x * 9.0) - (((z * 4.0) * t) * a)) / (z * c);
	double tmp;
	if (a <= -3.4e+144) {
		tmp = t_1;
	} else if (a <= 1.55e+241) {
		tmp = (((x * 9.0) * y) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * 9.0) - (((z * 4.0) * t) * a)) / (z * c)
	tmp = 0
	if a <= -3.4e+144:
		tmp = t_1
	elif a <= 1.55e+241:
		tmp = (((x * 9.0) * y) + b) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * 9.0) - Float64(Float64(Float64(z * 4.0) * t) * a)) / Float64(z * c))
	tmp = 0.0
	if (a <= -3.4e+144)
		tmp = t_1;
	elseif (a <= 1.55e+241)
		tmp = Float64(Float64(Float64(Float64(x * 9.0) * y) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * 9.0) - (((z * 4.0) * t) * a)) / (z * c);
	tmp = 0.0;
	if (a <= -3.4e+144)
		tmp = t_1;
	elseif (a <= 1.55e+241)
		tmp = (((x * 9.0) * y) + b) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * 9.0), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+144], t$95$1, If[LessEqual[a, 1.55e+241], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3999999999999999e144 or 1.55e241 < a

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 67.6%

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

   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 60.1%

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

   if -3.3999999999999999e144 < a < 1.55e241

   1. Initial program 80.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 54.1%

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

   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 24.8%

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

   9. Taylor expanded in x around -inf

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

   11. Applied rewrites 69.9%

       \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 60.6% accurate, 1.6× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 56.2%

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

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 30.2%

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

9. Taylor expanded in x around -inf

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

11. Applied rewrites 63.8%

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

Alternative 6: 14.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.12 \cdot 10^{+245}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -2.12e+245) (* (* x 9.0) 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 <= -2.12e+245) {
		tmp = (x * 9.0) * 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 <= (-2.12d+245)) then
        tmp = (x * 9.0d0) * 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 <= -2.12e+245) {
		tmp = (x * 9.0) * y;
	} else {
		tmp = (x * 9.0) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -2.12e+245:
		tmp = (x * 9.0) * 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 <= -2.12e+245)
		tmp = Float64(Float64(x * 9.0) * 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 <= -2.12e+245)
		tmp = (x * 9.0) * 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, -2.12e+245], N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(x * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1199999999999999e245

   1. Initial program 83.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 34.6%

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

   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 43.0%

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

   if -2.1199999999999999e245 < y

   1. Initial program 80.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 35.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 13.9%

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

Alternative 7: 35.4% 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 80.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 38.4%

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

Alternative 8: 8.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot y + b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -7.8e+75) (+ (* (* x 9.0) y) b) (* (* (* z 4.0) t) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -7.8e+75) {
		tmp = ((x * 9.0) * y) + b;
	} else {
		tmp = ((z * 4.0) * t) * a;
	}
	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 <= (-7.8d+75)) then
        tmp = ((x * 9.0d0) * y) + b
    else
        tmp = ((z * 4.0d0) * t) * 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 c) {
	double tmp;
	if (y <= -7.8e+75) {
		tmp = ((x * 9.0) * y) + b;
	} else {
		tmp = ((z * 4.0) * t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -7.8e+75:
		tmp = ((x * 9.0) * y) + b
	else:
		tmp = ((z * 4.0) * t) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -7.8e+75)
		tmp = Float64(Float64(Float64(x * 9.0) * y) + b);
	else
		tmp = Float64(Float64(Float64(z * 4.0) * t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -7.8e+75)
		tmp = ((x * 9.0) * y) + b;
	else
		tmp = ((z * 4.0) * t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -7.8e+75], N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision], N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.80000000000000075e75

   1. Initial program 71.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 16.5%

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

   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 16.7%

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

   if -7.80000000000000075e75 < y

   1. Initial program 82.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 7.9%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 7.9%

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

Alternative 9: 6.9% 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 80.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 9.5%

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

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 7.0%

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

Alternative 10: 7.3% 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 80.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 9.5%

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

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 7.0%

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

Alternative 11: 3.4% accurate, 5.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * 9.0) + 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 = (x * 9.0d0) + 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) + b;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 9.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 34.5%

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

9. Taylor expanded in x around -inf

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

11. Applied rewrites 3.4%

    \[\leadsto x \cdot 9 + b \]
12. Add Preprocessing

Alternative 12: 3.2% 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 80.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 9.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 34.5%

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

9. Taylor expanded in x around -inf

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

11. Applied rewrites 3.3%

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

Developer Target 1: 80.8% 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 2024313 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :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)))