sqrt B (should all be same)

Percentage Accurate: 54.5% → 100.0%

Time: 4.8s

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: 54.5% 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 53.0%

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

   1. add-exp-log 49.3%

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

   2. associate-*l* 49.2%

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

   3. sqrt-prod 49.2%

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

   4. sqrt-unprod 41.0%

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

   5. add-sqr-sqrt 41.0%

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

3. Applied egg-rr 41.0%

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

   1. add-exp-log 45.8%

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

   2. add-sqr-sqrt 45.7%

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

   3. associate-*l* 45.8%

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

   4. pow1/2 45.8%

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

   5. sqrt-pow1 45.8%

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

   6. metadata-eval 45.8%

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

   7. pow1/2 45.8%

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

   8. sqrt-pow1 45.8%

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

   9. metadata-eval 45.8%

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

5. Applied egg-rr 45.8%

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

   1. add-sqr-sqrt 44.4%

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

   2. sqrt-unprod 52.8%

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

   3. associate-*r* 52.7%

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

   4. associate-*r* 52.7%

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

   5. swap-sqr 52.6%

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

   6. pow-prod-up 53.0%

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

   7. metadata-eval 53.0%

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

   8. pow1/2 53.0%

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

   9. pow-prod-up 52.5%

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

   10. metadata-eval 52.5%

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

   11. pow1/2 52.5%

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

   12. add-sqr-sqrt 53.0%

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

7. Applied egg-rr 53.0%

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

   1. associate-*r* 53.0%

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

   2. count-2 53.0%

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

   3. *-commutative 53.0%

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

   4. distribute-lft-in 53.0%

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

   5. 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 2023274 
(FPCore (x)
  :name "sqrt B (should all be same)"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))