sqrt B (should all be same)

Percentage Accurate: 55.1% → 100.0%

Time: 2.6s

Alternatives: 1

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \sqrt{\left(2 \cdot x\right) \cdot x} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return math.sqrt(((2.0 * x) * x))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{\left(2 \cdot x\right) \cdot x} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return math.sqrt(((2.0 * x) * x))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{hypot}\left(x, x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (hypot x x))

C

double code(double x) {
	return hypot(x, x);
}

Java

public static double code(double x) {
	return Math.hypot(x, x);
}

Python

def code(x):
	return math.hypot(x, x)

Julia

function code(x)
	return hypot(x, x)
end

MATLAB

function tmp = code(x)
	tmp = hypot(x, x);
end

Wolfram

code[x_] := N[Sqrt[x ^ 2 + x ^ 2], $MachinePrecision]

Derivation

1. Initial program 52.4%

   \[\sqrt{\left(2 \cdot x\right) \cdot x} \]
2. Step-by-step derivation

   1. sqrt-prod 52.5%

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

3. Applied egg-rr 52.5%

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

4. Taylor expanded in x around 0 53.3%

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

   1. unpow1 53.3%

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

   2. exp-to-pow 48.1%

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

   3. metadata-eval 48.1%

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

   4. associate-*l* 48.1%

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

   5. *-commutative 48.1%

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

   6. associate-*r* 48.1%

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

   7. *-commutative 48.1%

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

   8. metadata-eval 48.1%

      \[\leadsto e^{\left(\log \left(\sqrt{2} \cdot x\right) \cdot \color{blue}{\left(0.3333333333333333 \cdot 6\right)}\right) \cdot 0.5} \]

   9. associate-*l* 47.7%

      \[\leadsto e^{\color{blue}{\left(\left(\log \left(\sqrt{2} \cdot x\right) \cdot 0.3333333333333333\right) \cdot 6\right)} \cdot 0.5} \]

   10. exp-prod 25.8%

       \[\leadsto \color{blue}{{\left(e^{\left(\log \left(\sqrt{2} \cdot x\right) \cdot 0.3333333333333333\right) \cdot 6}\right)}^{0.5}} \]

   11. associate-*l* 26.1%

       \[\leadsto {\left(e^{\color{blue}{\log \left(\sqrt{2} \cdot x\right) \cdot \left(0.3333333333333333 \cdot 6\right)}}\right)}^{0.5} \]

   12. metadata-eval 26.1%

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

   13. exp-to-pow 52.1%

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

   14. unpow2 52.1%

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

   15. swap-sqr 51.9%

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

   16. rem-square-sqrt 52.4%

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

   17. unpow1/2 52.4%

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

   18. count-2 52.4%

       \[\leadsto \sqrt{\color{blue}{x \cdot x + x \cdot x}} \]

   19. hypot-def 100.0%

       \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

6. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]

7. Final simplification 100.0%

   \[\leadsto \mathsf{hypot}\left(x, x\right) \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x)
  :name "sqrt B (should all be same)"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))