Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 99.8% → 99.9%

Time: 6.5s

Alternatives: 5

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, -12 + x \cdot 9, 3\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (fma x (+ -12.0 (* x 9.0)) 3.0))

C

double code(double x) {
	return fma(x, (-12.0 + (x * 9.0)), 3.0);
}

Julia

function code(x)
	return fma(x, Float64(-12.0 + Float64(x * 9.0)), 3.0)
end

Wolfram

code[x_] := N[(x * N[(-12.0 + N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Step-by-step derivation

   1. distribute-rgt-in 99.8%

      \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + 1 \cdot 3} \]

   2. metadata-eval 99.8%

      \[\leadsto \left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) \cdot 3 + \color{blue}{3} \]

   3. *-commutative 99.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot 3\right)} - x \cdot 4\right) \cdot 3 + 3 \]

   4. distribute-lft-out-- 99.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3 - 4\right)\right)} \cdot 3 + 3 \]

   5. associate-*l* 99.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3 - 4\right) \cdot 3\right)} + 3 \]

   6. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(x \cdot 3 - 4\right) \cdot 3, 3\right)} \]

   7. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{3 \cdot \left(x \cdot 3 - 4\right)}, 3\right) \]

   8. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(x \cdot 3 + \left(-4\right)\right)}, 3\right) \]

   9. +-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3 \cdot \color{blue}{\left(\left(-4\right) + x \cdot 3\right)}, 3\right) \]

   10. distribute-rgt-in 99.8%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-4\right) \cdot 3 + \left(x \cdot 3\right) \cdot 3}, 3\right) \]

   11. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{-4} \cdot 3 + \left(x \cdot 3\right) \cdot 3, 3\right) \]

   12. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{-12} + \left(x \cdot 3\right) \cdot 3, 3\right) \]

   13. associate-*l* 99.8%

       \[\leadsto \mathsf{fma}\left(x, -12 + \color{blue}{x \cdot \left(3 \cdot 3\right)}, 3\right) \]

   14. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(x, -12 + x \cdot \color{blue}{9}, 3\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, -12 + x \cdot 9, 3\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot 9\right) \cdot x\\ \mathbf{if}\;x \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.66:\\ \;\;\;\;3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (* x 9.0) x))) (if (<= x -0.58) t_0 (if (<= x 1.66) 3.0 t_0))))

C

double code(double x) {
	double t_0 = (x * 9.0) * x;
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 1.66) {
		tmp = 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * 9.0d0) * x
    if (x <= (-0.58d0)) then
        tmp = t_0
    else if (x <= 1.66d0) then
        tmp = 3.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x * 9.0) * x;
	double tmp;
	if (x <= -0.58) {
		tmp = t_0;
	} else if (x <= 1.66) {
		tmp = 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x * 9.0) * x
	tmp = 0
	if x <= -0.58:
		tmp = t_0
	elif x <= 1.66:
		tmp = 3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x * 9.0) * x)
	tmp = 0.0
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 1.66)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x * 9.0) * x;
	tmp = 0.0;
	if (x <= -0.58)
		tmp = t_0;
	elseif (x <= 1.66)
		tmp = 3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * 9.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.58], t$95$0, If[LessEqual[x, 1.66], 3.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.57999999999999996 or 1.65999999999999992 < x

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto 3 \cdot \color{blue}{\left(\left(x \cdot 3\right) \cdot x - \left(x \cdot 4 - 1\right)\right)} \]

      2. associate-*l* 99.6%

         \[\leadsto 3 \cdot \left(\color{blue}{x \cdot \left(3 \cdot x\right)} - \left(x \cdot 4 - 1\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.8%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   6. Step-by-step derivation

      1. metadata-eval 97.8%

         \[\leadsto \color{blue}{\left(3 \cdot 3\right)} \cdot {x}^{2} \]

      2. unpow2 97.8%

         \[\leadsto \left(3 \cdot 3\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

      3. swap-sqr 97.5%

         \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right)} \]

      4. pow2 97.5%

         \[\leadsto \color{blue}{{\left(3 \cdot x\right)}^{2}} \]

   7. Applied egg-rr 97.5%

      \[\leadsto \color{blue}{{\left(3 \cdot x\right)}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 97.5%

         \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right)} \]

      2. swap-sqr 97.8%

         \[\leadsto \color{blue}{\left(3 \cdot 3\right) \cdot \left(x \cdot x\right)} \]

      3. metadata-eval 97.8%

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

      4. associate-*r* 97.7%

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

      5. *-commutative 97.7%

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

   9. Applied egg-rr 97.7%

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

   if -0.57999999999999996 < x < 1.65999999999999992

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto 3 \cdot \color{blue}{\left(\left(x \cdot 3\right) \cdot x - \left(x \cdot 4 - 1\right)\right)} \]

      2. associate-*l* 100.0%

         \[\leadsto 3 \cdot \left(\color{blue}{x \cdot \left(3 \cdot x\right)} - \left(x \cdot 4 - 1\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.0%

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

Alternative 3: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot 9\right) \cdot x\\ \mathbf{if}\;x \leq -1.55:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;3 + -12 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (* x 9.0) x)))
   (if (<= x -1.55) t_0 (if (<= x 1.0) (+ 3.0 (* -12.0 x)) t_0))))

C

double code(double x) {
	double t_0 = (x * 9.0) * x;
	double tmp;
	if (x <= -1.55) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = 3.0 + (-12.0 * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * 9.0d0) * x
    if (x <= (-1.55d0)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = 3.0d0 + ((-12.0d0) * x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x * 9.0) * x;
	double tmp;
	if (x <= -1.55) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = 3.0 + (-12.0 * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x * 9.0) * x
	tmp = 0
	if x <= -1.55:
		tmp = t_0
	elif x <= 1.0:
		tmp = 3.0 + (-12.0 * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x * 9.0) * x)
	tmp = 0.0
	if (x <= -1.55)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(3.0 + Float64(-12.0 * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x * 9.0) * x;
	tmp = 0.0;
	if (x <= -1.55)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = 3.0 + (-12.0 * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * 9.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.55], t$95$0, If[LessEqual[x, 1.0], N[(3.0 + N[(-12.0 * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000004 or 1 < x

   1. Initial program 99.6%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto 3 \cdot \color{blue}{\left(\left(x \cdot 3\right) \cdot x - \left(x \cdot 4 - 1\right)\right)} \]

      2. associate-*l* 99.6%

         \[\leadsto 3 \cdot \left(\color{blue}{x \cdot \left(3 \cdot x\right)} - \left(x \cdot 4 - 1\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.8%

      \[\leadsto \color{blue}{9 \cdot {x}^{2}} \]
   6. Step-by-step derivation

      1. metadata-eval 97.8%

         \[\leadsto \color{blue}{\left(3 \cdot 3\right)} \cdot {x}^{2} \]

      2. unpow2 97.8%

         \[\leadsto \left(3 \cdot 3\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

      3. swap-sqr 97.5%

         \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right)} \]

      4. pow2 97.5%

         \[\leadsto \color{blue}{{\left(3 \cdot x\right)}^{2}} \]

   7. Applied egg-rr 97.5%

      \[\leadsto \color{blue}{{\left(3 \cdot x\right)}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 97.5%

         \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right)} \]

      2. swap-sqr 97.8%

         \[\leadsto \color{blue}{\left(3 \cdot 3\right) \cdot \left(x \cdot x\right)} \]

      3. metadata-eval 97.8%

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

      4. associate-*r* 97.7%

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

      5. *-commutative 97.7%

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

   9. Applied egg-rr 97.7%

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

   if -1.55000000000000004 < x < 1

   1. Initial program 100.0%

      \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto 3 \cdot \color{blue}{\left(\left(x \cdot 3\right) \cdot x - \left(x \cdot 4 - 1\right)\right)} \]

      2. associate-*l* 100.0%

         \[\leadsto 3 \cdot \left(\color{blue}{x \cdot \left(3 \cdot x\right)} - \left(x \cdot 4 - 1\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{3 + -12 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 * ((((x * 3.0d0) * x) - (x * 4.0d0)) + 1.0d0)
end function

Java

public static double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

Python

def code(x):
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0)

Julia

function code(x)
	return Float64(3.0 * Float64(Float64(Float64(Float64(x * 3.0) * x) - Float64(x * 4.0)) + 1.0))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
end

Wolfram

code[x_] := N[(3.0 * N[(N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] - N[(x * 4.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 5: 51.1% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 3.0)

C

double code(double x) {
	return 3.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0
end function

Java

public static double code(double x) {
	return 3.0;
}

Python

def code(x):
	return 3.0

Julia

function code(x)
	return 3.0
end

MATLAB

function tmp = code(x)
	tmp = 3.0;
end

Wolfram

code[x_] := 3.0

Derivation

1. Initial program 99.8%

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right) \]
2. Step-by-step derivation

   1. associate-+l- 99.8%

      \[\leadsto 3 \cdot \color{blue}{\left(\left(x \cdot 3\right) \cdot x - \left(x \cdot 4 - 1\right)\right)} \]

   2. associate-*l* 99.8%

      \[\leadsto 3 \cdot \left(\color{blue}{x \cdot \left(3 \cdot x\right)} - \left(x \cdot 4 - 1\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(3 \cdot x\right) - \left(x \cdot 4 - 1\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 50.2%

   \[\leadsto \color{blue}{3} \]
6. Add Preprocessing

Developer target: 99.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x))))

C

double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (((9.0d0 * x) * x) - (12.0d0 * x))
end function

Java

public static double code(double x) {
	return 3.0 + (((9.0 * x) * x) - (12.0 * x));
}

Python

def code(x):
	return 3.0 + (((9.0 * x) * x) - (12.0 * x))

Julia

function code(x)
	return Float64(3.0 + Float64(Float64(Float64(9.0 * x) * x) - Float64(12.0 * x)))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 + (((9.0 * x) * x) - (12.0 * x));
end

Wolfram

code[x_] := N[(3.0 + N[(N[(N[(9.0 * x), $MachinePrecision] * x), $MachinePrecision] - N[(12.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024034 -o generate:simplify
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))