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

Percentage Accurate: 99.8% → 99.8%

Time: 4.3s

Alternatives: 6

Speedup: 1.4×

• 25.1% 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: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 3 + \left(-12 \cdot x + 9 \cdot {x}^{2}\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 3.0 (+ (* -12.0 x) (* 9.0 (pow x 2.0)))))

C

double code(double x) {
	return 3.0 + ((-12.0 * x) + (9.0 * pow(x, 2.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 3.0d0 + (((-12.0d0) * x) + (9.0d0 * (x ** 2.0d0)))
end function

Java

public static double code(double x) {
	return 3.0 + ((-12.0 * x) + (9.0 * Math.pow(x, 2.0)));
}

Python

def code(x):
	return 3.0 + ((-12.0 * x) + (9.0 * math.pow(x, 2.0)))

Julia

function code(x)
	return Float64(3.0 + Float64(Float64(-12.0 * x) + Float64(9.0 * (x ^ 2.0))))
end

MATLAB

function tmp = code(x)
	tmp = 3.0 + ((-12.0 * x) + (9.0 * (x ^ 2.0)));
end

Wolfram

code[x_] := N[(3.0 + N[(N[(-12.0 * x), $MachinePrecision] + N[(9.0 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $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. 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. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{3 + \left(-12 \cdot x + 9 \cdot {x}^{2}\right)} \]

5. Final simplification 99.9%

   \[\leadsto 3 + \left(-12 \cdot x + 9 \cdot {x}^{2}\right) \]

Alternative 2: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(3.0 + N[(N[(-12.0 * x), $MachinePrecision] + N[(x * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $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. 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. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{3 + \left(-12 \cdot x + 9 \cdot {x}^{2}\right)} \]
5. Step-by-step derivation

   1. metadata-eval 99.9%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{\left(3 \cdot 3\right)} \cdot {x}^{2}\right) \]

   2. unpow2 99.9%

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

   3. swap-sqr 99.8%

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

   4. pow2 99.8%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{\left(3 \cdot x\right)}^{2}}\right) \]

   5. *-commutative 99.8%

      \[\leadsto 3 + \left(-12 \cdot x + {\color{blue}{\left(x \cdot 3\right)}}^{2}\right) \]

6. Applied egg-rr 99.8%

   \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{\left(x \cdot 3\right)}^{2}}\right) \]
7. Step-by-step derivation

   1. unpow-prod-down 99.9%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{x}^{2} \cdot {3}^{2}}\right) \]

   2. metadata-eval 99.9%

      \[\leadsto 3 + \left(-12 \cdot x + {x}^{2} \cdot \color{blue}{9}\right) \]

   3. *-commutative 99.9%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{9 \cdot {x}^{2}}\right) \]

   4. unpow2 99.9%

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

   5. associate-*r* 99.9%

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

8. Applied egg-rr 99.9%

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

9. Final simplification 99.9%

   \[\leadsto 3 + \left(-12 \cdot x + x \cdot \left(x \cdot 9\right)\right) \]

Alternative 3: 99.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(3.0 + N[(x * N[(-12.0 + N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $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. 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. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{3 + \left(-12 \cdot x + 9 \cdot {x}^{2}\right)} \]
5. Step-by-step derivation

   1. metadata-eval 99.9%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{\left(3 \cdot 3\right)} \cdot {x}^{2}\right) \]

   2. unpow2 99.9%

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

   3. swap-sqr 99.8%

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

   4. pow2 99.8%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{\left(3 \cdot x\right)}^{2}}\right) \]

   5. *-commutative 99.8%

      \[\leadsto 3 + \left(-12 \cdot x + {\color{blue}{\left(x \cdot 3\right)}}^{2}\right) \]

6. Applied egg-rr 99.8%

   \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{\left(x \cdot 3\right)}^{2}}\right) \]

7. Taylor expanded in x around 0 99.9%

   \[\leadsto 3 + \color{blue}{\left(-12 \cdot x + 9 \cdot {x}^{2}\right)} \]
8. Step-by-step derivation

   1. unpow2 99.9%

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

   2. associate-*l* 99.9%

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

   3. *-commutative 99.9%

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

   4. metadata-eval 99.9%

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

   5. associate-*l* 99.8%

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

   6. distribute-rgt-out 99.8%

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

   7. +-commutative 99.8%

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

   8. associate-*l* 99.9%

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

   9. metadata-eval 99.9%

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

   10. *-commutative 99.9%

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

9. Simplified 99.9%

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

10. Final simplification 99.9%

    \[\leadsto 3 + x \cdot \left(-12 + x \cdot 9\right) \]

Alternative 4: 97.5% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(3.0 + N[(x * N[(x * 9.0), $MachinePrecision]), $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. 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. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{3 + \left(-12 \cdot x + 9 \cdot {x}^{2}\right)} \]
5. Step-by-step derivation

   1. metadata-eval 99.9%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{\left(3 \cdot 3\right)} \cdot {x}^{2}\right) \]

   2. unpow2 99.9%

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

   3. swap-sqr 99.8%

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

   4. pow2 99.8%

      \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{\left(3 \cdot x\right)}^{2}}\right) \]

   5. *-commutative 99.8%

      \[\leadsto 3 + \left(-12 \cdot x + {\color{blue}{\left(x \cdot 3\right)}}^{2}\right) \]

6. Applied egg-rr 99.8%

   \[\leadsto 3 + \left(-12 \cdot x + \color{blue}{{\left(x \cdot 3\right)}^{2}}\right) \]

7. Taylor expanded in x around 0 99.9%

   \[\leadsto 3 + \color{blue}{\left(-12 \cdot x + 9 \cdot {x}^{2}\right)} \]
8. Step-by-step derivation

   1. unpow2 99.9%

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

   2. associate-*l* 99.9%

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

   3. *-commutative 99.9%

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

   4. metadata-eval 99.9%

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

   5. associate-*l* 99.8%

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

   6. distribute-rgt-out 99.8%

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

   7. +-commutative 99.8%

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

   8. associate-*l* 99.9%

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

   9. metadata-eval 99.9%

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

   10. *-commutative 99.9%

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

9. Simplified 99.9%

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

10. Taylor expanded in x around inf 98.2%

    \[\leadsto 3 + x \cdot \color{blue}{\left(9 \cdot x\right)} \]
11. Step-by-step derivation

    1. *-commutative 98.2%

       \[\leadsto 3 + x \cdot \color{blue}{\left(x \cdot 9\right)} \]

12. Simplified 98.2%

    \[\leadsto 3 + x \cdot \color{blue}{\left(x \cdot 9\right)} \]

13. Final simplification 98.2%

    \[\leadsto 3 + x \cdot \left(x \cdot 9\right) \]

Alternative 5: 51.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ 3 + -12 \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(3.0 + N[(-12.0 * x), $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. 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. Taylor expanded in x around 0 50.1%

   \[\leadsto \color{blue}{3 + -12 \cdot x} \]
5. Step-by-step derivation

   1. *-commutative 50.1%

      \[\leadsto 3 + \color{blue}{x \cdot -12} \]

6. Simplified 50.1%

   \[\leadsto \color{blue}{3 + x \cdot -12} \]

7. Final simplification 50.1%

   \[\leadsto 3 + -12 \cdot x \]

Alternative 6: 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. Taylor expanded in x around 0 49.9%

   \[\leadsto \color{blue}{3} \]

5. Final simplification 49.9%

   \[\leadsto 3 \]

Developer target: 99.8% 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 2023334 
(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)))