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

Percentage Accurate: 99.8% → 99.7%

Time: 3.8s

Alternatives: 3

Speedup: 1.0×

• 24.8% 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: 99.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x\_m \cdot \sqrt{{x\_m}^{2} \cdot 9} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m) :precision binary64 (* x_m (sqrt (* (pow x_m 2.0) 9.0))))

C

x_m = fabs(x);
double code(double x_m) {
	return x_m * sqrt((pow(x_m, 2.0) * 9.0));
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    code = x_m * sqrt(((x_m ** 2.0d0) * 9.0d0))
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	return x_m * Math.sqrt((Math.pow(x_m, 2.0) * 9.0));
}

Python

x_m = math.fabs(x)
def code(x_m):
	return x_m * math.sqrt((math.pow(x_m, 2.0) * 9.0))

Julia

x_m = abs(x)
function code(x_m)
	return Float64(x_m * sqrt(Float64((x_m ^ 2.0) * 9.0)))
end

MATLAB

x_m = abs(x);
function tmp = code(x_m)
	tmp = x_m * sqrt(((x_m ^ 2.0) * 9.0));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(x$95$m * N[Sqrt[N[(N[Power[x$95$m, 2.0], $MachinePrecision] * 9.0), $MachinePrecision]], $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. metadata-eval 99.8%

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

   4. sqrt-pow1 77.9%

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

   5. metadata-eval 77.9%

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

   6. pow2 77.9%

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

   7. *-commutative 77.9%

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

   8. *-commutative 77.9%

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

   9. associate-*r* 77.9%

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

   10. associate-*r* 77.9%

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

   11. swap-sqr 77.7%

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

   12. pow2 77.7%

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

   13. metadata-eval 77.7%

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

   14. pow-prod-down 77.7%

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

   15. pow-prod-up 77.8%

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

   16. metadata-eval 77.8%

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

   17. metadata-eval 77.8%

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

   18. metadata-eval 77.8%

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

   19. metadata-eval 77.8%

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

4. Applied egg-rr 77.8%

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

   1. pow1/2 77.8%

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

   2. metadata-eval 77.8%

      \[\leadsto {\left({x}^{\color{blue}{\left(2 \cdot 2\right)}} \cdot 9\right)}^{0.5} \]

   3. pow-sqr 77.7%

      \[\leadsto {\left(\color{blue}{\left({x}^{2} \cdot {x}^{2}\right)} \cdot 9\right)}^{0.5} \]

   4. associate-*l* 77.9%

      \[\leadsto {\color{blue}{\left({x}^{2} \cdot \left({x}^{2} \cdot 9\right)\right)}}^{0.5} \]

   5. unpow-prod-down 99.8%

      \[\leadsto \color{blue}{{\left({x}^{2}\right)}^{0.5} \cdot {\left({x}^{2} \cdot 9\right)}^{0.5}} \]

   6. pow-pow 62.1%

      \[\leadsto \color{blue}{{x}^{\left(2 \cdot 0.5\right)}} \cdot {\left({x}^{2} \cdot 9\right)}^{0.5} \]

   7. metadata-eval 62.1%

      \[\leadsto {x}^{\color{blue}{1}} \cdot {\left({x}^{2} \cdot 9\right)}^{0.5} \]

   8. pow1 62.1%

      \[\leadsto \color{blue}{x} \cdot {\left({x}^{2} \cdot 9\right)}^{0.5} \]

6. Applied egg-rr 62.1%

   \[\leadsto \color{blue}{x \cdot {\left({x}^{2} \cdot 9\right)}^{0.5}} \]
7. Step-by-step derivation

   1. unpow1/2 62.1%

      \[\leadsto x \cdot \color{blue}{\sqrt{{x}^{2} \cdot 9}} \]

8. Simplified 62.1%

   \[\leadsto \color{blue}{x \cdot \sqrt{{x}^{2} \cdot 9}} \]

9. Final simplification 62.1%

   \[\leadsto x \cdot \sqrt{{x}^{2} \cdot 9} \]
10. Add Preprocessing

Alternative 2: 99.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ {x\_m}^{2} \cdot 3 \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m) :precision binary64 (* (pow x_m 2.0) 3.0))

C

x_m = fabs(x);
double code(double x_m) {
	return pow(x_m, 2.0) * 3.0;
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    code = (x_m ** 2.0d0) * 3.0d0
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	return Math.pow(x_m, 2.0) * 3.0;
}

Python

x_m = math.fabs(x)
def code(x_m):
	return math.pow(x_m, 2.0) * 3.0

Julia

x_m = abs(x)
function code(x_m)
	return Float64((x_m ^ 2.0) * 3.0)
end

MATLAB

x_m = abs(x);
function tmp = code(x_m)
	tmp = (x_m ^ 2.0) * 3.0;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(N[Power[x$95$m, 2.0], $MachinePrecision] * 3.0), $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. Final simplification 99.8%

   \[\leadsto {x}^{2} \cdot 3 \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m) :precision binary64 (* x_m (* x_m 3.0)))

C

x_m = fabs(x);
double code(double x_m) {
	return x_m * (x_m * 3.0);
}

Fortran

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

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	return x_m * (x_m * 3.0);
}

Python

x_m = math.fabs(x)
def code(x_m):
	return x_m * (x_m * 3.0)

Julia

x_m = abs(x)
function code(x_m)
	return Float64(x_m * Float64(x_m * 3.0))
end

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(x$95$m * N[(x$95$m * 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

Reproduce

herbie shell --seed 2024027 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))