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

Percentage Accurate: 99.8% → 99.8%

Time: 3.5s

Alternatives: 2

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(x * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot x \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto x \cdot \left(x \cdot 3\right) \]
4. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(3.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow1 99.8%

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

   2. metadata-eval 99.8%

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

   3. sqrt-pow1 77.1%

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

   4. *-commutative 77.1%

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

   5. associate-*r* 77.1%

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

   6. unpow-prod-down 77.0%

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

   7. pow-prod-down 77.0%

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

   8. pow-prod-up 77.1%

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

   9. metadata-eval 77.1%

      \[\leadsto \sqrt{{x}^{\color{blue}{4}} \cdot {3}^{2}} \]

   10. metadata-eval 77.1%

       \[\leadsto \sqrt{{x}^{4} \cdot \color{blue}{9}} \]

4. Applied egg-rr 77.1%

   \[\leadsto \color{blue}{\sqrt{{x}^{4} \cdot 9}} \]
5. Step-by-step derivation

   1. sqrt-prod 77.1%

      \[\leadsto \color{blue}{\sqrt{{x}^{4}} \cdot \sqrt{9}} \]

   2. metadata-eval 77.1%

      \[\leadsto \sqrt{{x}^{4}} \cdot \color{blue}{3} \]

   3. add-cube-cbrt 76.5%

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

   4. cbrt-prod 76.7%

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

   5. add-sqr-sqrt 76.8%

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

   6. sqrt-pow1 76.8%

      \[\leadsto \left(\sqrt[3]{{x}^{4}} \cdot \sqrt[3]{\color{blue}{{x}^{\left(\frac{4}{2}\right)}}}\right) \cdot 3 \]

   7. metadata-eval 76.8%

      \[\leadsto \left(\sqrt[3]{{x}^{4}} \cdot \sqrt[3]{{x}^{\color{blue}{2}}}\right) \cdot 3 \]

   8. associate-*l* 76.7%

      \[\leadsto \color{blue}{\sqrt[3]{{x}^{4}} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right)} \]

   9. pow1/3 74.7%

      \[\leadsto \color{blue}{{\left({x}^{4}\right)}^{0.3333333333333333}} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right) \]

   10. pow-pow 41.6%

       \[\leadsto \color{blue}{{x}^{\left(4 \cdot 0.3333333333333333\right)}} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right) \]

   11. metadata-eval 41.6%

       \[\leadsto {x}^{\color{blue}{1.3333333333333333}} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right) \]

   12. metadata-eval 41.6%

       \[\leadsto {x}^{\color{blue}{\left(0.3333333333333333 \cdot 4\right)}} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right) \]

   13. pow-pow 41.6%

       \[\leadsto \color{blue}{{\left({x}^{0.3333333333333333}\right)}^{4}} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right) \]

   14. pow1/3 98.6%

       \[\leadsto {\color{blue}{\left(\sqrt[3]{x}\right)}}^{4} \cdot \left(\sqrt[3]{{x}^{2}} \cdot 3\right) \]

   15. unpow2 98.6%

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

   16. cbrt-prod 98.3%

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

   17. pow2 98.3%

       \[\leadsto {\left(\sqrt[3]{x}\right)}^{4} \cdot \left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot 3\right) \]

6. Applied egg-rr 98.3%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{4} \cdot \left({\left(\sqrt[3]{x}\right)}^{2} \cdot 3\right)} \]
7. Step-by-step derivation

   1. associate-*r* 98.4%

      \[\leadsto \color{blue}{\left({\left(\sqrt[3]{x}\right)}^{4} \cdot {\left(\sqrt[3]{x}\right)}^{2}\right) \cdot 3} \]

   2. *-commutative 98.4%

      \[\leadsto \color{blue}{3 \cdot \left({\left(\sqrt[3]{x}\right)}^{4} \cdot {\left(\sqrt[3]{x}\right)}^{2}\right)} \]

   3. unpow2 98.4%

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

   4. associate-*r* 98.4%

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

   5. pow-plus 98.3%

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

   6. metadata-eval 98.3%

      \[\leadsto 3 \cdot \left({\left(\sqrt[3]{x}\right)}^{\color{blue}{5}} \cdot \sqrt[3]{x}\right) \]

   7. pow-plus 98.4%

      \[\leadsto 3 \cdot \color{blue}{{\left(\sqrt[3]{x}\right)}^{\left(5 + 1\right)}} \]

   8. metadata-eval 98.4%

      \[\leadsto 3 \cdot {\left(\sqrt[3]{x}\right)}^{\color{blue}{6}} \]

8. Simplified 98.4%

   \[\leadsto \color{blue}{3 \cdot {\left(\sqrt[3]{x}\right)}^{6}} \]
9. Step-by-step derivation

   1. pow1/3 41.4%

      \[\leadsto 3 \cdot {\color{blue}{\left({x}^{0.3333333333333333}\right)}}^{6} \]

   2. pow-pow 99.7%

      \[\leadsto 3 \cdot \color{blue}{{x}^{\left(0.3333333333333333 \cdot 6\right)}} \]

   3. metadata-eval 99.7%

      \[\leadsto 3 \cdot {x}^{\color{blue}{2}} \]

   4. pow2 99.7%

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

10. Applied egg-rr 99.7%

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

11. Final simplification 99.7%

    \[\leadsto 3 \cdot \left(x \cdot x\right) \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))