sqrt C (should all be same)

Percentage Accurate: 53.6% → 100.0%

Time: 3.2s

Alternatives: 1

Speedup: 1.0×

Specification

Math

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

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(2.0 * Float64(x * x)))
end

MATLAB

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

Wolfram

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

Initial Program: 53.6% accurate, 1.0× speedup

Math

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

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(2.0 * Float64(x * x)))
end

MATLAB

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

Wolfram

code[x_] := N[Sqrt[N[(2.0 * N[(x * x), $MachinePrecision]), $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 59.8%

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

   1. add-sqr-sqrt 59.5%

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

   2. pow2 59.5%

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

   3. *-commutative 59.5%

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

   4. sqrt-prod 59.4%

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

   5. sqrt-prod 56.7%

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

   6. add-sqr-sqrt 56.8%

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

3. Applied egg-rr 56.8%

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

   1. pow1/2 56.8%

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

   2. metadata-eval 56.8%

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

   3. metadata-eval 56.8%

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

   4. metadata-eval 56.8%

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

   5. pow-prod-up 56.5%

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

   6. pow-prod-down 59.4%

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

   7. *-commutative 59.4%

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

   8. *-commutative 59.4%

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

   9. swap-sqr 59.3%

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

   10. add-sqr-sqrt 59.5%

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

   11. metadata-eval 59.5%

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

5. Applied egg-rr 59.5%

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

6. Taylor expanded in x around 0 52.2%

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

   1. unpow2 52.2%

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

   2. *-commutative 52.2%

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

   3. exp-prod 31.1%

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

   4. *-commutative 31.1%

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

   5. exp-prod 31.1%

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

   6. pow-sqr 31.1%

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

   7. metadata-eval 31.1%

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

   8. distribute-lft-neg-in 31.1%

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

   9. distribute-rgt-neg-out 31.1%

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

   10. log-rec 31.1%

       \[\leadsto {\left(e^{\log 2 + -2 \cdot \color{blue}{\log \left(\frac{1}{x}\right)}}\right)}^{\left(2 \cdot 0.25\right)} \]

8. Simplified 100.0%

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

9. Final simplification 100.0%

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

Reproduce

herbie shell --seed 2023182 
(FPCore (x)
  :name "sqrt C (should all be same)"
  :precision binary64
  (sqrt (* 2.0 (* x x))))