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

Percentage Accurate: 99.8% → 99.8%

Time: 5.9s

Alternatives: 2

Speedup: 1.0×

• 26.1% 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, 0.0× speedup

Math

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

FPCore

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

C

x_m = fabs(x);
double code(double x_m) {
	return x_m * sqrt((x_m * (x_m * 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 * (x_m * 9.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. associate-*r* 99.7%

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

   3. add-sqr-sqrt 48.6%

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

   4. associate-*r* 48.6%

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

   5. add-sqr-sqrt 48.5%

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

   6. associate-*l* 48.5%

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

   7. sqrt-unprod 48.7%

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

   8. sqrt-prod 43.2%

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

   9. pow3 43.2%

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

   10. sqrt-pow1 48.7%

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

   11. metadata-eval 48.7%

       \[\leadsto {x}^{\color{blue}{1.5}} \cdot \left(\sqrt{x} \cdot 3\right) \]

   12. pow1/2 48.7%

       \[\leadsto {x}^{1.5} \cdot \left(\color{blue}{{x}^{0.5}} \cdot 3\right) \]

4. Applied egg-rr 48.7%

   \[\leadsto \color{blue}{{x}^{1.5} \cdot \left({x}^{0.5} \cdot 3\right)} \]
5. Step-by-step derivation

   1. add-sqr-sqrt 48.6%

      \[\leadsto {x}^{1.5} \cdot \color{blue}{\left(\sqrt{{x}^{0.5} \cdot 3} \cdot \sqrt{{x}^{0.5} \cdot 3}\right)} \]

   2. sqrt-unprod 48.7%

      \[\leadsto {x}^{1.5} \cdot \color{blue}{\sqrt{\left({x}^{0.5} \cdot 3\right) \cdot \left({x}^{0.5} \cdot 3\right)}} \]

   3. swap-sqr 48.7%

      \[\leadsto {x}^{1.5} \cdot \sqrt{\color{blue}{\left({x}^{0.5} \cdot {x}^{0.5}\right) \cdot \left(3 \cdot 3\right)}} \]

   4. unpow1/2 48.7%

      \[\leadsto {x}^{1.5} \cdot \sqrt{\left(\color{blue}{\sqrt{x}} \cdot {x}^{0.5}\right) \cdot \left(3 \cdot 3\right)} \]

   5. unpow1/2 48.7%

      \[\leadsto {x}^{1.5} \cdot \sqrt{\left(\sqrt{x} \cdot \color{blue}{\sqrt{x}}\right) \cdot \left(3 \cdot 3\right)} \]

   6. add-sqr-sqrt 48.7%

      \[\leadsto {x}^{1.5} \cdot \sqrt{\color{blue}{x} \cdot \left(3 \cdot 3\right)} \]

   7. metadata-eval 48.7%

      \[\leadsto {x}^{1.5} \cdot \sqrt{x \cdot \color{blue}{9}} \]

6. Applied egg-rr 48.7%

   \[\leadsto {x}^{1.5} \cdot \color{blue}{\sqrt{x \cdot 9}} \]
7. Step-by-step derivation

   1. add-sqr-sqrt 48.5%

      \[\leadsto \color{blue}{\sqrt{{x}^{1.5} \cdot \sqrt{x \cdot 9}} \cdot \sqrt{{x}^{1.5} \cdot \sqrt{x \cdot 9}}} \]

   2. sqrt-unprod 39.6%

      \[\leadsto \color{blue}{\sqrt{\left({x}^{1.5} \cdot \sqrt{x \cdot 9}\right) \cdot \left({x}^{1.5} \cdot \sqrt{x \cdot 9}\right)}} \]

   3. swap-sqr 39.6%

      \[\leadsto \sqrt{\color{blue}{\left({x}^{1.5} \cdot {x}^{1.5}\right) \cdot \left(\sqrt{x \cdot 9} \cdot \sqrt{x \cdot 9}\right)}} \]

   4. pow-prod-up 39.6%

      \[\leadsto \sqrt{\color{blue}{{x}^{\left(1.5 + 1.5\right)}} \cdot \left(\sqrt{x \cdot 9} \cdot \sqrt{x \cdot 9}\right)} \]

   5. metadata-eval 39.6%

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

   6. pow3 39.6%

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

   7. add-sqr-sqrt 78.7%

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

   8. associate-*l* 78.5%

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

   9. associate-*r* 78.5%

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

   10. associate-*l* 78.6%

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

   11. sqrt-prod 99.7%

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

   12. sqrt-prod 48.6%

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

   13. add-sqr-sqrt 61.5%

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

   14. associate-*l* 61.5%

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

8. Applied egg-rr 61.5%

   \[\leadsto \color{blue}{x \cdot \sqrt{x \cdot \left(x \cdot 9\right)}} \]
9. Add Preprocessing

Alternative 2: 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 2024097 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))