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

Percentage Accurate: 99.8% → 99.8%

Time: 7.3s

Alternatives: 3

Speedup: 1.0×

• 24.9% 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. Taylor expanded in x around 0 99.8%

   \[\leadsto \color{blue}{3 \cdot {x}^{2}} \]
4. Step-by-step derivation

   1. unpow2 99.8%

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

5. Applied egg-rr 99.8%

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

Alternative 3: 4.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ x \cdot 2 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x 2.0))

C

double code(double x) {
	return x * 2.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * 2.0d0
end function

Java

public static double code(double x) {
	return x * 2.0;
}

Python

def code(x):
	return x * 2.0

Julia

function code(x)
	return Float64(x * 2.0)
end

MATLAB

function tmp = code(x)
	tmp = x * 2.0;
end

Wolfram

code[x_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. add-sqr-sqrt 99.5%

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

   2. sqrt-unprod 72.6%

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

   3. pow1/2 72.6%

      \[\leadsto \color{blue}{{\left(\left(\left(x \cdot 3\right) \cdot x\right) \cdot \left(\left(x \cdot 3\right) \cdot x\right)\right)}^{0.5}} \]

   4. pow2 72.6%

      \[\leadsto {\color{blue}{\left({\left(\left(x \cdot 3\right) \cdot x\right)}^{2}\right)}}^{0.5} \]

   5. *-commutative 72.6%

      \[\leadsto {\left({\color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)}}^{2}\right)}^{0.5} \]

   6. associate-*r* 72.6%

      \[\leadsto {\left({\color{blue}{\left(\left(x \cdot x\right) \cdot 3\right)}}^{2}\right)}^{0.5} \]

   7. unpow-prod-down 72.6%

      \[\leadsto {\color{blue}{\left({\left(x \cdot x\right)}^{2} \cdot {3}^{2}\right)}}^{0.5} \]

   8. pow-prod-down 72.6%

      \[\leadsto {\left(\color{blue}{\left({x}^{2} \cdot {x}^{2}\right)} \cdot {3}^{2}\right)}^{0.5} \]

   9. pow-prod-up 72.6%

      \[\leadsto {\left(\color{blue}{{x}^{\left(2 + 2\right)}} \cdot {3}^{2}\right)}^{0.5} \]

   10. metadata-eval 72.6%

       \[\leadsto {\left({x}^{\color{blue}{4}} \cdot {3}^{2}\right)}^{0.5} \]

   11. metadata-eval 72.6%

       \[\leadsto {\left({x}^{4} \cdot \color{blue}{9}\right)}^{0.5} \]

4. Applied egg-rr 72.6%

   \[\leadsto \color{blue}{{\left({x}^{4} \cdot 9\right)}^{0.5}} \]
5. Step-by-step derivation

   1. unpow1/2 72.6%

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

6. Simplified 72.6%

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

   1. sqrt-prod 72.6%

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

   2. metadata-eval 72.6%

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

   3. sqrt-pow1 99.8%

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

   4. metadata-eval 99.8%

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

   5. unpow2 99.8%

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

   6. associate-*l* 99.8%

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

   7. expm1-log1p-u 75.5%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot 3\right)\right)} \]

   8. log1p-define 48.3%

      \[\leadsto x \cdot \mathsf{expm1}\left(\color{blue}{\log \left(1 + x \cdot 3\right)}\right) \]

   9. expm1-define 48.3%

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

   10. add-exp-log 72.6%

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

   11. flip-- 72.6%

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

   12. metadata-eval 72.6%

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

   13. *-commutative 72.6%

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

   14. associate-*l/ 64.6%

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

   15. clear-num 64.6%

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

   16. +-commutative 64.6%

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

   17. associate-+r+ 64.6%

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

   18. metadata-eval 64.6%

       \[\leadsto \frac{1}{\frac{\color{blue}{2} + x \cdot 3}{\left(\left(1 + x \cdot 3\right) \cdot \left(1 + x \cdot 3\right) - 1\right) \cdot x}} \]

8. Applied egg-rr 71.4%

   \[\leadsto \color{blue}{\frac{1}{\frac{2 + x \cdot 3}{x \cdot \mathsf{expm1}\left(2 \cdot \mathsf{log1p}\left(x \cdot 3\right)\right)}}} \]

9. Taylor expanded in x around 0 65.7%

   \[\leadsto \frac{1}{\frac{2 + x \cdot 3}{x \cdot \color{blue}{\left(6 \cdot x\right)}}} \]
10. Step-by-step derivation

    1. *-commutative 65.7%

       \[\leadsto \frac{1}{\frac{2 + x \cdot 3}{x \cdot \color{blue}{\left(x \cdot 6\right)}}} \]

11. Simplified 65.7%

    \[\leadsto \frac{1}{\frac{2 + x \cdot 3}{x \cdot \color{blue}{\left(x \cdot 6\right)}}} \]

12. Taylor expanded in x around inf 4.7%

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

    1. *-commutative 4.7%

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

14. Simplified 4.7%

    \[\leadsto \color{blue}{x \cdot 2} \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024157 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))