sqrt C (should all be same)

Percentage Accurate: 54.4% → 99.4%

Time: 5.2s

Alternatives: 3

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: 54.4% 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: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \sqrt{2 \cdot x\_m} \cdot \sqrt{x\_m} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m) :precision binary64 (* (sqrt (* 2.0 x_m)) (sqrt x_m)))

C

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

Fortran

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

Java

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

Python

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

Julia

x_m = abs(x)
function code(x_m)
	return Float64(sqrt(Float64(2.0 * x_m)) * sqrt(x_m))
end

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(N[Sqrt[N[(2.0 * x$95$m), $MachinePrecision]], $MachinePrecision] * N[Sqrt[x$95$m], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.2%

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

   1. associate-*r* 52.2%

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

   2. sqrt-prod 46.7%

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

4. Applied egg-rr 46.7%

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

5. Final simplification 46.7%

   \[\leadsto \sqrt{2 \cdot x} \cdot \sqrt{x} \]
6. Add Preprocessing

Alternative 2: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \frac{\sqrt{2}}{\frac{1}{x\_m}} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m) :precision binary64 (/ (sqrt 2.0) (/ 1.0 x_m)))

C

x_m = fabs(x);
double code(double x_m) {
	return sqrt(2.0) / (1.0 / x_m);
}

Fortran

x_m = abs(x)
real(8) function code(x_m)
    real(8), intent (in) :: x_m
    code = sqrt(2.0d0) / (1.0d0 / x_m)
end function

Java

x_m = Math.abs(x);
public static double code(double x_m) {
	return Math.sqrt(2.0) / (1.0 / x_m);
}

Python

x_m = math.fabs(x)
def code(x_m):
	return math.sqrt(2.0) / (1.0 / x_m)

Julia

x_m = abs(x)
function code(x_m)
	return Float64(sqrt(2.0) / Float64(1.0 / x_m))
end

MATLAB

x_m = abs(x);
function tmp = code(x_m)
	tmp = sqrt(2.0) / (1.0 / x_m);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(N[Sqrt[2.0], $MachinePrecision] / N[(1.0 / x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.2%

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

   1. add-exp-log 48.8%

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

   2. *-un-lft-identity 48.8%

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

   3. exp-prod 48.6%

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

   4. exp-1-e 48.6%

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

   5. *-commutative 48.6%

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

   6. sqrt-prod 48.5%

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

   7. sqrt-prod 42.7%

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

   8. add-sqr-sqrt 42.7%

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

4. Applied egg-rr 42.7%

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

   1. e-exp-1 42.7%

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

   2. pow-exp 43.0%

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

   3. *-un-lft-identity 43.0%

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

   4. add-exp-log 47.9%

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

   5. *-commutative 47.9%

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

   6. add-sqr-sqrt 47.7%

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

   7. associate-*l* 47.8%

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

   8. pow1/2 47.8%

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

   9. sqrt-pow1 47.8%

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

   10. metadata-eval 47.8%

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

   11. pow1/2 47.8%

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

   12. sqrt-pow1 47.8%

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

   13. metadata-eval 47.8%

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

6. Applied egg-rr 47.8%

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

8. Applied egg-rr 47.9%

   \[\leadsto \color{blue}{\frac{\sqrt{2}}{\frac{1}{x}}} \]

9. Final simplification 47.9%

   \[\leadsto \frac{\sqrt{2}}{\frac{1}{x}} \]
10. Add Preprocessing

Alternative 3: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x\_m \cdot \sqrt{2} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m) :precision binary64 (* x_m (sqrt 2.0)))

C

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

Fortran

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

Java

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

Python

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

Julia

x_m = abs(x)
function code(x_m)
	return Float64(x_m * sqrt(2.0))
end

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_] := N[(x$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.2%

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

   1. sqrt-prod 51.9%

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

   2. sqrt-prod 46.4%

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

   3. add-sqr-sqrt 47.9%

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

4. Applied egg-rr 47.9%

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

5. Final simplification 47.9%

   \[\leadsto x \cdot \sqrt{2} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(FPCore (x)
  :name "sqrt C (should all be same)"
  :precision binary64
  (sqrt (* 2.0 (* x x))))