sqrt A (should all be same)

Percentage Accurate: 53.5% → 100.0%

Time: 16.0s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x) :precision binary64 (sqrt (+ (* x x) (* x x))))

C

double code(double x) {
	return sqrt(((x * x) + (x * x)));
}

Fortran

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

Java

public static double code(double x) {
	return Math.sqrt(((x * x) + (x * x)));
}

Python

def code(x):
	return math.sqrt(((x * x) + (x * x)))

Julia

function code(x)
	return sqrt(Float64(Float64(x * x) + Float64(x * x)))
end

MATLAB

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

Wolfram

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

Initial Program: 53.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (sqrt (+ (* x x) (* x x))))

C

double code(double x) {
	return sqrt(((x * x) + (x * x)));
}

Fortran

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

Java

public static double code(double x) {
	return Math.sqrt(((x * x) + (x * x)));
}

Python

def code(x):
	return math.sqrt(((x * x) + (x * x)))

Julia

function code(x)
	return sqrt(Float64(Float64(x * x) + Float64(x * x)))
end

MATLAB

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

Wolfram

code[x_] := N[Sqrt[N[(N[(x * x), $MachinePrecision] + 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 51.6%

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

   1. hypot-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(x, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 11.3% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ x + x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ x x))

C

double code(double x) {
	return x + x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x + x
end function

Java

public static double code(double x) {
	return x + x;
}

Python

def code(x):
	return x + x

Julia

function code(x)
	return Float64(x + x)
end

MATLAB

function tmp = code(x)
	tmp = x + x;
end

Wolfram

code[x_] := N[(x + x), $MachinePrecision]

Derivation

1. Initial program 51.6%

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

   1. hypot-define 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 56.4%

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

7. Simplified 10.4%

   \[\leadsto \color{blue}{x \cdot -2} \]
8. Step-by-step derivation

   1. add-sqr-sqrt 9.0%

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

   2. sqrt-unprod 13.5%

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

   3. swap-sqr 13.5%

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

   4. metadata-eval 13.5%

      \[\leadsto \sqrt{\left(x \cdot x\right) \cdot \color{blue}{4}} \]

   5. metadata-eval 13.5%

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

   6. swap-sqr 13.5%

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

   7. sqrt-unprod 11.3%

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

   8. add-log-exp 3.4%

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

   9. add-sqr-sqrt 4.5%

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

   10. exp-lft-sqr 4.5%

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

   11. log-prod 4.5%

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

   12. add-log-exp 7.9%

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

   13. add-log-exp 12.3%

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

9. Applied egg-rr 12.3%

   \[\leadsto \color{blue}{x + x} \]
10. Add Preprocessing

Alternative 3: 5.3% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ 512 \end{array} \]

FPCore

(FPCore (x) :precision binary64 512.0)

C

double code(double x) {
	return 512.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 512.0d0
end function

Java

public static double code(double x) {
	return 512.0;
}

Python

def code(x):
	return 512.0

Julia

function code(x)
	return 512.0
end

MATLAB

function tmp = code(x)
	tmp = 512.0;
end

Wolfram

code[x_] := 512.0

Derivation

1. Initial program 51.6%

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

   1. hypot-define 100.0%

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

3. Simplified 100.0%

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

6. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{{\left(\frac{0}{0}\right)}^{9}} \]

8. Simplified 5.3%

   \[\leadsto \color{blue}{512} \]
9. Add Preprocessing

Alternative 4: 5.4% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ 32 \end{array} \]

FPCore

(FPCore (x) :precision binary64 32.0)

C

double code(double x) {
	return 32.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 32.0d0
end function

Java

public static double code(double x) {
	return 32.0;
}

Python

def code(x):
	return 32.0

Julia

function code(x)
	return 32.0
end

MATLAB

function tmp = code(x)
	tmp = 32.0;
end

Wolfram

code[x_] := 32.0

Derivation

1. Initial program 51.6%

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

   1. hypot-define 100.0%

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

3. Simplified 100.0%

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

6. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{{\left(\frac{0}{0}\right)}^{5}} \]

8. Simplified 5.3%

   \[\leadsto \color{blue}{32} \]
9. Add Preprocessing

Alternative 5: 3.8% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.0)

C

double code(double x) {
	return 0.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.0d0
end function

Java

public static double code(double x) {
	return 0.0;
}

Python

def code(x):
	return 0.0

Julia

function code(x)
	return 0.0
end

MATLAB

function tmp = code(x)
	tmp = 0.0;
end

Wolfram

code[x_] := 0.0

Derivation

1. Initial program 51.6%

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

   1. hypot-define 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 56.4%

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

7. Simplified 10.4%

   \[\leadsto \color{blue}{x \cdot -2} \]
8. Step-by-step derivation

   1. add-sqr-sqrt 9.0%

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

   2. sqrt-unprod 13.5%

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

   3. pow1/2 13.5%

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

9. Applied egg-rr 3.9%

   \[\leadsto \color{blue}{{\log \left({1}^{x}\right)}^{0.5}} \]
10. Step-by-step derivation

    1. pow-base-1 3.9%

       \[\leadsto {\log \color{blue}{1}}^{0.5} \]

    2. metadata-eval 3.9%

       \[\leadsto {\color{blue}{0}}^{0.5} \]

    3. metadata-eval 3.9%

       \[\leadsto \color{blue}{0} \]

11. Simplified 3.9%

    \[\leadsto \color{blue}{0} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(FPCore (x)
  :name "sqrt A (should all be same)"
  :precision binary64
  (sqrt (+ (* x x) (* x x))))