sqrt D (should all be same)

Percentage Accurate: 55.2% → 100.0%

Time: 4.0s

Alternatives: 1

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \sqrt{2 \cdot {x}^{2}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{2 \cdot {x}^{2}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 2.0× 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 54.5%

   \[\sqrt{2 \cdot {x}^{2}} \]
2. Step-by-step derivation

   1. unpow2 54.5%

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

3. Simplified 54.5%

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

   1. add-cube-cbrt 53.5%

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

   2. pow3 53.5%

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

   3. *-commutative 53.5%

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

   4. sqrt-prod 53.5%

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

   5. sqrt-prod 49.7%

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

   6. add-sqr-sqrt 50.7%

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

5. Applied egg-rr 50.7%

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

   1. rem-cube-cbrt 51.5%

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

   2. *-commutative 51.5%

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

   3. add-sqr-sqrt 51.3%

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

   4. associate-*l* 51.4%

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

   5. pow1/2 51.4%

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

   6. sqrt-pow1 51.4%

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

   7. metadata-eval 51.4%

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

   8. pow1/2 51.4%

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

   9. sqrt-pow1 51.4%

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

   10. metadata-eval 51.4%

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

7. Applied egg-rr 51.4%

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

   1. associate-*r* 51.3%

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

   2. pow-prod-up 51.5%

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

   3. metadata-eval 51.5%

      \[\leadsto {2}^{\color{blue}{0.5}} \cdot x \]

   4. pow1/2 51.5%

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

   5. add-sqr-sqrt 50.3%

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

   6. sqrt-unprod 54.3%

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

   7. swap-sqr 54.1%

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

   8. add-sqr-sqrt 54.5%

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

9. Applied egg-rr 54.5%

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

    1. count-2 54.5%

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

    2. hypot-def 100.0%

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

11. Simplified 100.0%

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

12. Final simplification 100.0%

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

Reproduce

herbie shell --seed 2023230 
(FPCore (x)
  :name "sqrt D (should all be same)"
  :precision binary64
  (sqrt (* 2.0 (pow x 2.0))))