sqrt B (should all be same)

Percentage Accurate: 54.1% → 100.0%

Time: 5.6s

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: 54.1% 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 52.7%

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

   1. add-cube-cbrt 51.8%

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

   2. pow3 51.8%

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

   3. associate-*l* 51.7%

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

   4. sqrt-prod 51.7%

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

   5. sqrt-unprod 51.1%

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

   6. add-sqr-sqrt 52.2%

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

3. Applied egg-rr 52.2%

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

   1. rem-cube-cbrt 53.0%

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

   2. add-sqr-sqrt 52.9%

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

   3. associate-*l* 52.9%

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

   4. pow1/2 52.9%

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

   5. sqrt-pow1 52.9%

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

   6. metadata-eval 52.9%

      \[\leadsto {2}^{\color{blue}{0.25}} \cdot \left(\sqrt{\sqrt{2}} \cdot x\right) \]

   7. pow1/2 52.9%

      \[\leadsto {2}^{0.25} \cdot \left(\sqrt{\color{blue}{{2}^{0.5}}} \cdot x\right) \]

   8. sqrt-pow1 52.9%

      \[\leadsto {2}^{0.25} \cdot \left(\color{blue}{{2}^{\left(\frac{0.5}{2}\right)}} \cdot x\right) \]

   9. metadata-eval 52.9%

      \[\leadsto {2}^{0.25} \cdot \left({2}^{\color{blue}{0.25}} \cdot x\right) \]

5. Applied egg-rr 52.9%

   \[\leadsto \color{blue}{{2}^{0.25} \cdot \left({2}^{0.25} \cdot x\right)} \]
6. Step-by-step derivation

   1. associate-*r* 52.9%

      \[\leadsto \color{blue}{\left({2}^{0.25} \cdot {2}^{0.25}\right) \cdot x} \]

   2. add-sqr-sqrt 51.8%

      \[\leadsto \left({2}^{0.25} \cdot {2}^{0.25}\right) \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \]

   3. associate-*r* 51.8%

      \[\leadsto \color{blue}{\left(\left({2}^{0.25} \cdot {2}^{0.25}\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}} \]

   4. pow-prod-up 51.8%

      \[\leadsto \left(\color{blue}{{2}^{\left(0.25 + 0.25\right)}} \cdot \sqrt{x}\right) \cdot \sqrt{x} \]

   5. metadata-eval 51.8%

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

   6. pow1/2 51.8%

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

   7. sqrt-prod 52.1%

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

   8. count-2 52.1%

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

   9. pow1/2 52.1%

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

   10. metadata-eval 52.1%

       \[\leadsto {\left(x + x\right)}^{\color{blue}{\left(2 \cdot 0.25\right)}} \cdot \sqrt{x} \]

   11. pow-sqr 51.8%

       \[\leadsto \color{blue}{\left({\left(x + x\right)}^{0.25} \cdot {\left(x + x\right)}^{0.25}\right)} \cdot \sqrt{x} \]

   12. associate-*r* 51.9%

       \[\leadsto \color{blue}{{\left(x + x\right)}^{0.25} \cdot \left({\left(x + x\right)}^{0.25} \cdot \sqrt{x}\right)} \]

   13. add-sqr-sqrt 51.7%

       \[\leadsto \color{blue}{\sqrt{{\left(x + x\right)}^{0.25} \cdot \left({\left(x + x\right)}^{0.25} \cdot \sqrt{x}\right)} \cdot \sqrt{{\left(x + x\right)}^{0.25} \cdot \left({\left(x + x\right)}^{0.25} \cdot \sqrt{x}\right)}} \]

   14. sqrt-unprod 25.9%

       \[\leadsto \color{blue}{\sqrt{\left({\left(x + x\right)}^{0.25} \cdot \left({\left(x + x\right)}^{0.25} \cdot \sqrt{x}\right)\right) \cdot \left({\left(x + x\right)}^{0.25} \cdot \left({\left(x + x\right)}^{0.25} \cdot \sqrt{x}\right)\right)}} \]

7. Applied egg-rr 52.7%

   \[\leadsto \color{blue}{\sqrt{x \cdot \left(x + x\right)}} \]
8. Step-by-step derivation

   1. distribute-lft-in 52.7%

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

   2. hypot-def 100.0%

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

9. Simplified 100.0%

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

10. Final simplification 100.0%

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

Reproduce

herbie shell --seed 2023278 
(FPCore (x)
  :name "sqrt B (should all be same)"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))